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In the model of demand and supply what are the endogenous variables?
Price and quantity of the good exchanged in the market
In the model of demand an supply what are the exogenous variables?
Variables underlying the supply and the demand function in the market we study
What for a model is the model of supply and demand?
The model of supply and demand is a model of price determination in a single market.
How is a market defined?
A market is defined as the set of (potential) buyers and (potential) sellers of the good.
What is the main assumption of the model?
The main assumption of the model is perfect competition, that is we assume that all the market participants are price takers and they choose, for any given price that prevails in the market, how much to buy and how much to sell.
What does the main assumption of the model allows us to do?
The main assumption of the model (the equilibrium condition) allows us to find the price that prevails in the market and the quantity of the good that is exchanged in the market.
What is the definition of the supply curve?
The supply curve shows the quantity of the good that the producers are willing to sell at each given price, holding constant all the other factors that affect the quantity supplied, that is the supply curve is a relationship between the quantity supplied
of the good and the price of the good, that can be written as function.
What is the definition of supply function?
The market supply function is a relationship between the quantity supplied of the good and all the variables that affect the quantity that the producers are willing to sell (including the price of the good) that can be written as a function.
What is the difference between supply curve and function?
Therefore for one given supply function Qs = f(p; x1; xR), there are (possibly infinitely)
many supply curves. In other words, when we define (or draw) a supply curve,
we are fixing one particular values of the (exogenous) variables x1; xR and when we
change (even one of) the values of the (exogenous) variables x1; xR we are shifting the supply curve, that is we are drawing a new one.
What is the difference between shifts of the supply curve and movements along the supply curve?
We talk about movements along the supply curve when the exogenous variables
x1; xR do not change, but the quantity supplied changes.
We talk about a shift of the supply curve when at least one of the exogenous
variables x1; xR changes and this determines a different supply curve.
What is the law of supply? 2 assumptions are made here
A common assumption we make about the market supply function is that the partial derivative of the supply function (not curve) with respect to the the price p is larger than 0. This assumption is known as the law of supply.
Another way to state this assumption is that along each given supply curve, the quantity
supplied increases as the price increases
How is the market supply function related to the individual choices of the producers?
Assume that in a market there are 100 potential sellers of a given good (say, corn). If we know the 100 individual supply functions, then we also know the market supply function of corn. Viceversa, if we are given only the market supply function of corn, we must keep in mind that it comes from the individual choices. This is the reason why, the market supply is nothing
but the sum of the supply functions of the single sellers. Only if identical can we know the individual supply curve then.
What do you add to create the market supply curve?
You add the quantities.
Individual supply, Profit maximisation and law of supply.
A firm will choose to produce and sell the quantity of the good that maximises the profits of the firm. Pricetaker so chooses only the q. For each price p, the quantity supplied maximises the profits. This alone guarantees that the quantity supplied does not decrease as the price increases. Of course, it is possible that as the price increases the quantity supplied by all the firms in the market stays constant (especially in the short run). When this happens we have portions of the supply curve that are vertical lines and we say that the supply is infinitely inelastic (see later the discussion on elasticities).
What is the link between profit maximisation and law of supply?
Because firms are profit maximisers and that for each price price, you have a quantity that maximises the profits of the firm, you have that it is not possible that when p increases, the q decreases. This would exactly be against the law of supply and because it is not possible, the law of supply is always respected for profit maximising firms. Main assumption. However, law of supply doesn't mean that q is increasing, can stay constant, when in short run and supply inelastic.
What is the definition of the market demand curve?
The market demand curve shows the quantity of the good that the buyers
are willing to buy at each given price, holding constant all the other factors that affect the quantity demanded, that is the demand curve is a relationship between the quantity demanded of the good and the price of the good, that can be written as function.
What is the definition of the demand function?
The market demand function is a relationship between the quantity demanded of the good and all the variables that affect the quantity that the buyers are willing to buy (including the price of the good) that can be written as function. Note that y1; yT are all the (exogenous) variables that affect the quantity demanded of the good beyond the price of the good.
How many demand curves are there for 1 given demand function?
For one given demand function QD = g(p; y1; yT ), there are (possibly infinitely) many
demand curves. In other words, when we define (or draw) a demand curve, we are fixing one particular values of the (exogenous) variables y1; yT and when we change (even one of) the values of the (exogenous) variables y1; yT we are shifting the demand curve, that is we are drawing a new one.
How do you know what can be the exogenous variables that the quantity demanded of the good ?
one must understand how much of the demand is direct demand, that is demand
that comes from the consumers of the good, and how much of the demand is derived demand, that is demand that comes from firms using the good as an input of their production process.
Shifts of the demand curve vs Movements along the demand curve
We talk about movements along the demand curve when the exogenous
variables y1; yT do not change, but the quantity demanded changes after a price change. We talk about a shift of the demand curve when at least one of the exogenous variables y1; yT changes and this determines a different demand curve. In both cases Q changes but p doesn't need to change in the shifts of the demand curve. For example, when the price of a substitute changes, shift of the curve but when the
demand curve shifts, the quantity demanded could change even if the price of the good does not change.
Law of demand. We consider a demand function Qd = g(p,y1, ... , yT). What is the common assumption we make for the law of demand?
A common assumption that we make is that the partial derivative of the demand function with respect to price is strictly negative; that is the demand curve is decreasing.
Is this assumption of the law of demand reasonable?
Unlike the case of the law of supply, we
do not "prove" the law of demand, that is we do not derive the validity of the law of
demand from assumptions on the the behavior of the individual buyers. Rather, the law of demand is a very robust empirical fact, that is very important in economics.
Where does the demand function come from?
The demand function originates from individual behavior. In particular the demand function comes from the choice of the individual buyers, who must decide whether and how much to buy of the good that we are considering. Therefore also the demand function is the sum of the demand functions of the individual buyers.
In order to find the market demand curve what do you do?
You add the quantities of each individual demand curve.
What is the difference between excess supply, surplus, shortage and excess demand, market-clearing price or market equilibrium?
The quantity supplied at the given price p' is higher than the quantity demanded at
p'; that is S(p') > D(p'). We call this situation surplus (or excess supply). The quantity supplied at the given price p' is lower than the quantity demanded at p'; that is S(p') < D(p'). We call this situation shortage (or excess demand). The quantity supplied at the given price p' is equal to the quantity demanded at p'; that is S(p0) = D(p0). We call this situation market equilibrium (or market-clearing price).
What is the crucial assumption we make in the supply-demand model?
The crucial assumption in the supply-demand model is that the price of the good that we are considering is determined by market clearing condition S(p) = D(p). This market equilibrium determines both the endogenous variables in the model, that is the price at which the good is sold and the quantity of the good that is exchanged.
What does the market equilibrium determine?
This market equilibrium determines both the endogenous variables in the model, that is the price at which the good is sold and the quantity of the good that is exchanged.
What is the market clearing condition?
The market clearing condition can be interpreted as stating that in a competitive market the price will not settle if there is a surplus or a shortage.
How can we use the supply-demand model (2 ways)?
The first is to explain (maybe to predict) the behavior of the price and the quantity
sold in given markets.
The second is to study the welfare effects on the market participants of government
policies, such as price supports, production quotas, subsidies etc. (see topic 2 "Welfare
analysis and government policies in competitive markets").
What are the steps to a get a comparative statics right?
1. Identify all the changes in the relevant exogenous variables
2. Understand how the change of the exogenous variable changes the demand and the
supply curves. Which curve will shift? In which direction?
3. Identify the new equilibrium (price and quantity) and compare it with the previous
The comparative statics analysis is only qualitative if we don't make an attempt to quantify some of the determinants of the equilibria. To have quantitative predictions from the competitive markets model what do we have to do?
To have quantitative predictions from the
competitive markets model we introduce the concept of elasticity.
What is the general concept of elasticity?
If you have a function z = f(x; y), the
x-elasticity of z measures how sensitive is the variable z to a change of the variable x. So what is in the () as a function of term is the x and the z is the whole function.
What is the price elasticity of demand?
The price elasticity of demand is the percentage change in quantity demanded
resulting from a 1% increase in price (x is the price here, the variable and z is the Q, so the whole function).
What is the relationship between elasticities and slopes?
x-elasticity of z is nothing but the slope of the function f with respect to x multiplied by x/z. For example if we consider the price elasticity of demand, we understand immediately that both concepts have to do with movements along the demand curve. In particular the slope of the demand curve dQd/dp is calculated keeping constant all the exogenous variables underlying the demand curve and the same is true for the price elasticity of demand.
Why do economists prefer to use elasticities?
An important difference between elasticities and slopes is that the slope depends on the unit of measure of the quantity of good considered, while the elasticity is unit free.
How do we define the total expenditure in the market?
For a given price of the good p and quantity exchanged in the market Q, define the total expenditure in the market (or total revenues) as pQ. Usually, when the price changes the total expenditure also changes; by how much and in which direction?
What can you say about the signs of the slope of the demand function and the price elasticity of demand?
First notice that, since the price elasticity of demand, E, has the same sign of the slope
of the demand function (dQd/dP ), it is always negative, because the quantity demanded decreases when the price of the good increases (law of demand).
Price elasticity of demand and total expenditure
Then, observe that the higher is the absolute value of the price elasticity of demand (that is /E/) the more the quantity demanded decreases for a given price change. We say that the higher is /E/, the
more elastic is the demand to its own price.
What is the unitary price elasticity of demand?
Next consider that if the price elasticity of demand is equal to negative one (E = -1),
it means that when the price increase by 1%, the quantity demanded decreases by 1%.
As a result for such cases we have that the total expenditure does not change when the price changes. This case (unitary price elasticity of demand) is particular and somehow provides a border between to major cases, elastic demand and inelastic demand.
1. If /E/> 1, we say that the demand is elastic and when the price increases, the total
expenditure pQ decreases.
2. If /E/ < 1 we say that the demand is inelastic. and when the price increases, the total expenditure pQ increases.
What can we do if just have reliable estimates of the price elasticity of demand and price elasticity of supply and the equilibrium point (p
If we have reliable estimates of the price elasticity of demand and the price elasticity of supply we can obtain the linear approximation of the demand and supply curves passing through the equilibrium point (p;Q) that also we can observe. In this way we have numerical expressions for the demand and supply curves that we can use to predict the change in equilibrium price and equilibrium quantity resulting from a change in an exogenous
What does consumer theory study?
Consumer theory studies how a single economic agent (consumer) uses her limited resources (income) to choose what to consume.
What is the main assumption of consumer theory?
The main assumption of the theory is that the consumer chooses to spend her income
in the best possible way (of course from the point of view of the consumer herself).
What is a consumption basket?
The consumption basket is the object of the choice.
What does the consumption basket need to have as features?
Integer, unit of measure for each good so that xi represents the quantity of good i measured in the unit of measure we have chosen. Given this, we can now define a consumption basket as (x1, ..., xN) E Rn+
Who can we rewrite the main assumption of the theory?
The consumer chooses among the consumption basket that are affordable, the one she likes the best
How do we divide the study of consumer theory in two main components?
1. What the consumer likes, that we call the preferences of the consumer, represented
by an utility function.
2. What the consumer can afford, that we call the budget constraint of the consumer,
that represent the set of the feasible choices.
What is at the core of the concept of preferences and utility function?
The concept of preferences and utility function is a way to describe how a consumer can rank different choices.
What is at the core of the concept of budget constraint?
It is the set of feasible choices for the consumer.
What is the final step of consumer theory?
We build on the concept of preferences and utility function and on the concept of budget constraint to describe the choice problem of the consumer and will characterize the solution of this problem.
What is the goal of the concept of preferences and utility function?
It is to find a useful way to describe the consumer preferences over the set of consumption baskets. In other words, we want a way to describe how the consumer ranks the different consumption baskets.
What are the two interpretations of preferences?
Operational interpretation of preferences: We can interpret the preference relation
A>B as an operational notation. That is, if the consumer has only two baskets he
can choose from and A>B then we know that the consumer will choose A.
Welfare interpretation of preferences: We can also interpret the preference relation
A>B from the point of view of the welfare of the consumer. That is if A>B then
we know that the consumer is "happier" consuming A than consuming B.
What is the goal of the utility function?
The goal is to find a useful way to describe the ranking of the consumption baskets. We
can achieve this goal by assuming that the preferences of the consumer are represented by an utility function.
What is an utility function? What does it mean that it represent the preferences of a
An utility function u(x1; x2) represents the preferences of a consumer if
It is a function with domain the set of consumption baskets (that is R2
+) and range R. For any two consumption baskets A and B
u(A)>(B) if and only if A>B
What is the utility function representation theorem?
We want to understand what it means to assume that there exist an utility function that represents the preferences of the consumer.
What are the implicit assumptions that we make
on the preferences of the consumers if we assume that there exist an utility function that represents the preferences of the consumer?
complete preferences (always rank), transitive preferences (A,B,C) and continuous preferences
What does our explicit assumption about preferences that are represented by a utility function imply about the implicit assumptions?
If we assume that a consumer has preferences that are represented by a continuous utility function we are implicitly assuming that the preferences of the consumer are complete, transitive
What is the main result of the theorem?
These 3 assumptions are the only assumptions that we need to make, if we want to represent a consumer preferences by means of a utility function. Consider a consumer with preferences that are complete, transitive and continuous.
Then there must exist a (continuous) utility function u(x1; x2) that represents the
preferences of the consumer.
What the common mistakes about the utility function and what is important to bear in mind?
The key to understand the concept of utility function is to realize that an utility function
represents the preferences of a given consumer, so that everything we need to know about Mary's preferences, it is summarized by her utility function. One mistake is to think that the number u(A) means something in itself (A is a basket).
It does not! The only think we do with U(A) is to compare it with the number
U(B) to assess whether A is preferred to B by the consumer. Another mistake is to think that the number U(A)-U(B) means something in itself. Again it does not. The only use of that number is that if U(A)-U(B) > 0 it means A is (strictly) preferred to B for the consumer and if U(A) = U(B) then the consumer is indifferent between A and B. In fact there are infinitely many utility functions that represent the preferences of each consumer.
How many utility functions are there that represent the preferences of one given consumer?
Infinitely many for each consumer, what is important to acknowledge is that monotone transformation preserve the ranking of the baskets.
What can be summarised for the mistakes?
All these mistakes can be summarized by saying that often students do not understand that the utility is an ordinal concept, it is introduced only to represent the ordinal ranking that (we assume) consumer have over the consumption baskets.
Who is happier Mary or Mr. Fish?
The concept of happier is only for welfare analysis of preferences, not of utilities.
What is an IC?
Take a basket A = (x1'; x2'); it is important to be able to find all the consumption baskets that give the consumer the same level of utility.
What are the properties of the indifference curves?
1. The consumer is indifferent among all the consumption baskets that belong to a
given indifference curve.
2. If two baskets A and B do not belong to the same indifference curve it must be that
either u(A) > u(B) or u(B) > u(A), but not u(A) = u(B) (otherwise A and B would
belong to the same indifference curve)
What is the most important concept in consumer theory?
It is the marginal rate of substitution.
What is the dry definition of MRS?
The marginal rate of substitution of good 1 for good 2, MRS (x1;x2) is the absolute value of the slope of the indifference curve. A common notation for the marginal rate of substitution is dx2/dx1
What are the economic interpretations of MRS?
The rate of change of good 2 respect to a small change of good 1, necessary to keep
the consumer indifferent.
The maximum amount of good 2 the consumer is willing to give up in exchange for an extra unit of good 1.
The consumer's marginal value of good 1 in terms of good 2
Where does the implicit function theorem come from?
Implicit Function Theorem
What does the marginal utility to good 1 represent?
The marginal utility respect to good 1, MU1 represents the growth of rate of the
utility respect to a small change of good 1, keeping constant the quantity of good 2.
What does the marginal utility to good 2 represent?
The marginal utility respect to good 2, MU2 represents the growth of rate of the utility respect to a small change of good 2, keeping constant the quantity
of good 1.
What are additional assumptions on preferences?
Nonsatiation and convex preferences
What is a consequence of nonsatiation?
The nonsatiation (more is better) assumption is very important. A consequence of the more is better assumption is that indifference curves cannot be "thick" and in fact they slope downward (that is, if you express the indifference curves as x2 as a function of x1,
this function is decreasing).
What does it mean to have preferences that are convex?
Based on the idea that in
many cases (not all the time) consumers like diversification, or in other words that the
consumers like the average basket better than the extreme baskets. Another way to call
this assumption is to say that preferences are convex.
What is another way to denote the assumption that consumers like diversification?
Another way to call this assumption is to say that preferences are convex.
What is the definition of convex preferences?
Preferences are are said to be convex, if whenever a consumer is indifferent
between two baskets A and B, she always prefers an "average basket" C to both A and B.
What do we mean by smooth preferences?
By smooth preferences, we mean preferences for which the indifference curve is a smooth function, that is a function without kinks. A characteristic of smooth functions is that the MRSx1;x2 is well defined for each basket.
What is the very simple definition of convex preferences we have for smooth preferences (i.e. the MRSx1;x2 is well defined for each basket)?
Preferences are convex if the MRSx1;x2 is decreasing along any indifference
What is the economic interpretation of the convexity assumption?
As you know, we can interpret the marginal rate of substitution of x1 for x2 as the marginal value of the good 1 (in terms of good 2). Then, a decreasing marginal rate of substitution along an indifference curve means that the marginal value of good 1 decreases the more good 1 (and the less good 2) the consumer already consumes.
What is a budget constraint?
It is the description of all possible consumption choices that a consumer can afford.
How can we know if a consumption basket belongs to the budget constraint?
Plug in the budget constraint
What is the definition of a budget constraint?
The budget constraint is the set of all consumption baskets that a consumer can afford.
What is a synonym for budget constraint?
What do we need to define the budget constraint?
More precisely, if we are given a price pi for each good i and a level of monetary income, I, we can define the budget constraint (or budget set)
What is the budget line?
The budget line is the set of consumption baskets that the consumer can afford spending all of her resources (income)
What do we need to define the budget line?
More precisely, if we are given a price pi for each good i and a level of monetary income, I, we can define the budget line.
How can the BL be interpreted and what can we do with this interpretation?
The budget line can be interpreted as the maximum quantity of good 2 the consumer
can buy if she buys x1 units of good 1. Following this interpretation, we can express the budget line as a function; we can express x2 as a function of x1.
What is the intercept of the Budget Line function?
What is the slope of the Budget Line function?
What is the importance of the absolute value of the slope of the budget line?
p1/p2 is the opportunity cost of consuming good 1 (in terms of good 2). That is, how many units of good 2, the consumer must give up to obtain one extra unit of good 1.
What do we have to assume so that optimal basket must belong to the BL?
If we assume that the preferences satisfy nonsatiation.
What is the difference between interior or corner solution?
A basket in which all goods are consumed in strictly positive amounts (i.e. x1 > 0 and x2 > 0 is in the interior of the consumption basket set R2+), while a basket in which at least one good is not consumed at all
(that is xi = 0) is called a corner basket.
How can we state that a basket is optimal?
We already know that the optimal choice for the consumer lies on the budget line because of nonsatiation.
Then, among all the baskets that lie on the budget line, how do we find the optimal one? A is the optimal basket because all the baskets strictly preferred to A are not affordable (they lie above the budget line).
What is the economic interpretation of a corner solution?
Since at A the indifference curve lies above the budget line, it means that MRSx1;x2(0; 20)<p1/p2. The economic interpretation is that the consumer for the first unit of good 1 is willing to give up a maximum amount of good 2 not greater than p1/p2. In other words the marginal value of the first unit of good 1 is smaller than the opportunity cost of good 1.
What is the meaning of an intersection that is nonempty?
A cannot be the optimal basket because the set of baskets strictly preferred to A and the budget constraint overlap (that is they have common elements, their intersection is nonempty). This means that there are baskets strictly preferred to A that are affordable.
What does it mean that the set of baskets strictly preferred to A and the budget constraint overlap?
There are baskets strictly preferred to A that are affordable.
What is the feasibility condition?
That is, the optimal basket must be on the budget line
What is the tangency condition?
MRS = p1/p2 (derivative of IC and absolute value of derivative of BL)
What are the 2 equations we have to solve to find the optimal basket in the interior solution?
Feasibility and tangency condition
What must be true for the tangency condition to hold?
That the optimal basket is an interior solution and thus that x>0 for both goods.
What is the object of the choice of the consumer?
the consumption basket or (consumption bundle)
What is the budget constraint?
It is the set of all the consumption baskets that the consumer can afford. It is a list of quantities of different goods.
In a plan they are infinitely many baskets but how to check if the consumption baskets belong to the budget constraint?
We need to check if the consumer can afford it. If it can afford it then it belongs to the budget constraint.
On what elements does the budget constraint depend on?
price of goods and Income
What is the budget line in relation with the budget constraint?
The budget line is a subset of the budget constraint. With the BL the inequality becomes an equality.
The budget line shows:
the set of consumption baskets that a consumer can afford spending their entire income. So the BL gives us all the baskets in which the consumer spends all the income. The BL is the border of the budget constraint and the trade-off that the consumer faces.
What does the function of the BL tell us?
It tells you what is the maximum amount of good 2 (x2) that the consumer can afford if she consumes x1 unit of good 1.
Slope of BL shows us 2 things:
1) How many units of x2 the consumer must give up to obtain 1 unit of x1
2) How many units of eggs the consumer can obtain by giving up 1 unit of x1?
The absolute value of the slope of BL is the answer in both cases.
What is the economic meaning of the slope of BL?
The cost of 1 extra unit of good 1 is given by how many units of good 2 the consumer must give up (the opportunity cost of good x1 in terms of good x2).
What can preferences don't tell us?
Consumer preferences don't tell us whether a consumer likes a good better another but it tells us about how a consumer ranks any 2 baskets. We talk about baskets, so a combination of goods and not about 1 good over another.
What does a utility function do?
It assigns a number to each consumption basket.
What do the 3 implicit assumptions tell us about the existence of a utility function?
If we assume that the preferences of Mary are complete, transitive and continuous then there is always a utility function that represents Mary's preferences.
What is the consumer choice problem?
The consumer will choose among the baskets that belong to the budget constraint, the consumption basket that maximises consumer's utility.
What does the non-satiation tell us about the shape of the IC?
It tells us that the IC must go through the 2 ? quadrants but we don't exactly how.
What does the assumption the more is better tell us?
We know with this assumption for sure that the IC are decreasing.
What is the average basket?
It is always on the segment that connects 2 points.
We know that in order to describe the shape of an IC we need assumptions, which one indicate what?
The assumption the more the better meant that the IC are decreasing. The assumption of diversification (that average is better) tells us that the IC are convex and smooth, only in special cases can it have the form of a Leontief function with a kink. It also has the implication that the MRS is decreasing along each IC because as you have more of good 1 and less of good 2 you value less good 1 in terms of good 2.
The nonsatiation tell us that the optimal basket must belong to the budget line meaning p1x1 + p2x2 = I.
What does a constant MRS indicate?
It indicates a line, an IC that is linear.
Interpretations of MRS
- MRS gives how much a consumer values one extra unit of good 1 in terms of good 2
- MRS is the maximum rate at which the consumer is willing to accept as a trade to get good 1
- MRS of good 1 for good 2 is the absolute value of the slop of IC
- MRS is the maximum number of good 2 that the consumer is willing to give up for an extra unit of coffee
- MRS is the minimum number of units of x2 that the consumer is willing to accept to give up a marginal unit of good 1
What is the difference between a linear and a convex MRS?
The MRS is not constant along but also decreases.
Notice that an an IC is nothing but a ______ of the utility function u(x,y)
Why are is the definition of the MRS stating that the absolute value of the IC calculated at (x,y) is equal to the definition fo MRS as the partial derivative of the function with respect to x1 and x2 meaning the marginal utilities of good 1 and of good 2?
Implicit function theorem
What is the generic IC?
IC that passes through a given basket and that gives u bar level of utility is given by all the baskets that the utility of x,y is equal to this constant utility of x,y.
In consumer theory we have two economic interpretations for the 2 blocks, what are those (what we also call the characterisation of optimal choice)?
1) MRS: VALUE
2) Opportunity cost px/py => spending all my money on consumption and I consume 8x and 7y, now if I want to consume another unit of y, I need to give up px/py, which is the absolute value of the slope of BL.
What is the bang for the buck?
The extra utility the consumer gets spending a dollar in good x is equal to the extra utility the consumer gets spending a dollar in good y.
What are the two alternative economic interpretations at the optimal choice of the consumer for an interior solution?
The marginal value of good x is equal to the marginal cost of good x (all expressed in terms of units of good y).
The marginal utility per dollar spent on each good is the same.
What does 1/px = 0.5 indicate?
With 1 extra dollar I buy 0.5 of good x
What does MUx = 3 indicate?
If I consume an extra unit of good x, my utility goes up by 3, tells how much happier I am.
What does MUx/px = 1.5 indicate?
By how much my utility goes up if I spend an extra dollar buying good x.
What happens in the corner solution for Consumer Theory when x=0 and y>0?
For a corner solution, the TC doesn't work. We have that the MRS is either equal or smaller than the px/py, meaning that the marginal value of good x is less than its marginal cost and the marginal utility per dollar spent on good x is less than the marginal utility per dollar spent on good y, the extra utility the consumer gets spending a dollar in good x is less or at most equal to the utility the consumer gets spending a dollar in good y. That is the bang for the buck is higher for good y than for good x. It is x=0 because the very first value of good x for a consumer it is less than the very first unit cost of x, so of course not buy x.
Is a utility function unique for each consumer?
No, it is unique up to monotone transformations.
Can we use the utility functions of two individuals to say who is happier?
No, we cannot.
How many IC do I have?
I have infinitely many actually that all passes through the different baskets but I have only 1 IC that passes through the optimal basket.
What happens for Leontief functions?
The MRS is not defined at the kink but need to choose the kink because the one that maximises the utility.
What are the two cases where the TC does not have to be satisfied?
Corner solution and Leontief
What does Leontief functions represent as goods?
Does the marginal utility have any economic meaning?
No, you can have the same preferences but different Marginal Utilities, this doesn't mean anything.
Can we say if a consumer likes a good more than another based on MRS compared to other MRS?
Yes, only if compared to other consumers.
What kind of theory is General Equilibrium?
General equilibrium is a theory of determination of the prices of all goods in which all the economic agents are price-takers.
What is the crucial assumption of GE?
The crucial assumption is that the "market
prices" will adjust so that the individual plans of the economic agents are consistent with each other. This means that in every market the sum of quantities that individuals want to buy must be equal to the sum of the quantities that the individuals want to sell. In other words, prices are determined so that all the markets are in equilibrium (or that all the markets "clear"). This is the fundamental idea of "competitive equilibrium".
What is the fundamental idea of competitive equilibrium?
This means that in every market the sum of quantities that individuals want to buy must be equal to the sum of the quantities that the individuals want to sell. In other words, prices are determined so that all the markets are in equilibrium (or that all
the markets "clear").
What is the simplest GE model?
The simplest general equilibrium model is a model of "exchange economy" with two
individuals and two goods.
What is an endowment? What is the individual endowment?
In an exchange economy, each individual (consumer-buyer-seller) is endowed with a basket that contains some (non-negative) quantity of each good. We call this basket the individual endowment.
What is a feature of the exchange economy and what does it have as a consequence for the total endowment?
Since, in an exchange economy there is no production, the total endowment is the sum of the individual endowments. It means no free floating and that every quantity of the good is assigned.
What is an allocation?
An allocation is a complete description of what the individuals (here the 2 individuals) own or consume; it is simply a list of two baskets, one for each individual ((x1; y1); (x2; y2)). It is a vector.
What is the initial allocation?
For example given the above initial individual endowments w1 and w2, the initial allocation is defined as the vector
((w1; w2) = (w1x; w1y); (w2x; w2y) = (18; 7); (5; 15))
What is a feasible allocation?
An allocation ((x1; y1); (x2; y2)) is feasible if x1 + x2 = wx and y1 + y2 = wy. In other words, a feasible allocation is a division of the total endowment between all the individuals in the economy such that the sum of all the individual baskets is equal to the total endowment of the goods.
What do we need to describe an exchange economy?
To describe an exchange economy we need the preferences of the individuals 1 and 2 over their consumption goods, that is the utility functions u1(x1; y1) and u2(x2; y2).
What is given by an exchange economy?
1. A set of individuals (in our case individual 1 and individual 2)
2. A list of goods (in our case two goods x and y)
3. An initial allocation (in our case (w1x; w1y); (w2x; w2y) = (18; 7); (5; 15).
4. The preferences of the individuals (in our case (u1(x1; y1), u2(x2; y2))
How is (w1x; w1y) different from (x1; y1)?
First, both (w1x; w1y) and (x1; y1) are consumption baskets for individual 1, and therefore they represent the same concept, the quantity of good x and the quantity of good y that individual 1 consumes (or owns). I introduced the notation (w1x; w1y) (instead
of using (x1; y1)) to indicate the initial basket of individual 1, that is his endowment. He can consume this endowment, but he can also sell some of good x and buy some of good y (or vice-versa). Having this different notation helps in writing the budget constraint for individual 1 as pxx1 + pyy1 = pxw1x + pyw1y.
Does a feasible allocation tells us what the individuals can afford (like feasibility condition in consumer theory)?
No, a feasible allocation is an allocation (x1; y1); (x2; y2) such that x1 + x2 = wx and
y1 + y2 = wy; that is, two baskets, one for individual 1 and one for individual 2, that
are compatible with the total endowment of goods x and y. There is no reference to
what each consumer can afford (in fact, there is no reference neither to the prices nor to the individual endowments).
When we studied consumer theory, we call "feasibility condition", the condition that
the optimal basket must lie on the budget line. This might mislead students to believe
that a feasible allocation is an allocation that can be afforded by the individuals,
but this is wrong. Let me repeat it: the concept of feasible allocation has nothing to do with prices and with what the consumers can afford.
What is the definition of a competitive equilibrium?
Consider an exchange economy, with initial allocation (w1x; w1y); (w2x; w2y) and preferences represented by utility functions u1(x1; y1) and u2(x2; y2). A competitive equilibrium is a price vector (px; py) and a (final) allocation ((x1; y1); (x2; y2)) such that
1. Individuals choose (x1; y1) and (x2; y2) to maximize their utility given their budget
2. Markets of all goods clear, that is x1 + x2 = wx and y1 + y2 = wy
What are the elements that compose a competitive equilibrium allocation?
Note that a competitive equilibrium is composed of prices (px; py) and of an allocation (x1; y1)(x2; y2)
How can a competitive equilibrium allocation be interpreted?
A competitive equilibrium allocation (x1; y1)(x2; y2) can be interpreted as the prediction
of what is the final consumption allocation in a given exchange economy.
What is the Walras's law?
What about the market for good y? It turns out that if (px; py) is such that the quantity
consumed is equal to the total endowment of good x, the same it is true for good y. This is called Walras' law: when there are N markets and N - 1 are in equilibrium so it is the last market.
What is the only thing that matters in a competitive equilibrium when it comes to prices?
Note that in a competitive equilibrium (px; py), the only thing that matters is the relative price px/py.
What does it mean that two allocations are not pareto-ranked?
In both cases one individual prefers (strictly) an allocation and the other individual prefers strictly the other allocation. In such cases, we say that the two allocations are not Pareto-ranked. That is we cannot say anything on which allocation is better using only the Pareto criterion.
What is an inefficient allocation?
An allocation A is Pareto inefficient, if it is possible to improve the utility of one individual without decreasing the utility of any other individual. In other words, an allocation A is Pareto inefficient if there is another feasible allocation (call it B) such that an individual likes B better than A and nobody considers B worse than A.
What can we tell about each feasible allocation in an exchange economy?
As it should be clear by now, each feasible allocation in an exchange economy can be either efficient (Pareto efficient) or inefficient (Pareto inefficient).
What is a pareto efficient allocation?
An allocation A is Pareto efficient (that is Pareto optimal) if there is no other
feasible allocation that Pareto improves over A.
What does an edgeworth box represent?
An Edgeworth Box diagram illustrates all the feasible allocations in a given economy.
What are the dimensions of the box?
The dimensions of the box are the total endowments of each good for the economy. The width of the box is the total endowment of good x, wx which in our example is 20 and the height of the box is the total endowment of the y good, wy, which in this case is also 20.
What does each point in the box characterise?
Each set of coordinates represents an individual allocation of the goods. As a result, every point in the box characterizes a feasible allocation.
What does it mean that every point in the Edgeworth Box represent one feasible allocation?
Hence every point in the box is on two indifference curves, one for individual 1 and one for individual 2. Therefore, two indifference curves meet at every point in the Edgeworth Box.
How can two IC meet in an Edgeworth box?
Two curves can meet in only two ways:
What is the criteria for an efficient allocation in an Edgeworth box?
From the above argument we can conclude that those points in the Edgeworth box
where the indifference curves are tangent, represent efficient allocations. When two curves are tangent, they share a common slope. So, at an efficient allocation individual 1 and individual 2's indifference curves have the same slope. In other words, individual 1 and individual 2 have the same MRS. Allocations for which the indifference curves intersect represent inefficient allocations.
What is a contract curve?
The set of all the allocations that are Pareto efficient is called the contract curve.
What do we assume for the contract curve?
Consider an exchange economy with total endowments wx = 20 and wy = 20. Also
assume that the two individuals have convex indifference curves with the marginal rate of substitution well defined over all the baskets.
What are the 3 conditions that must be satisfied to find the contract curve?
The first condition ensures that the indifference curves of individual 1 and 2 are tangent to each other in any allocation belonging to the contract curve. The conditions 2) and 3) ensure that all the allocations are feasible.
Does this method of 3 conditions to derive the contract curve always work?
In fact, there are some exceptions: the first is that if there is some Pareto efficient allocation on the edge of the Edgeworth box, the tangency condition does not need to be satisfied. Example: consider an allocation (x1 = 20; y1 = 15); (x2 = 0; y2 = 5) withMRS1(20; 15) = 2 and MRS2(0; 5) = 1. The tangency condition is clearly not satisfied, but the allocation is Pareto efficient. Another exception is when the allocation is Pareto efficient but the MRS is not well
defined at the Pareto efficient allocation.
What does the Welfare Theorems do?
So far we defined competitive equilibrium and Pareto efficiency as two completely distinct concepts. However there are important results that clarify the relation between the set of Pareto efficient allocations and the set of competitive equilibria.
What is the first welfare theorem?
The first of these results say that any competitive equilibrium allocation is also a Pareto efficient allocation. More precisely, pick any competitive equilibrium (px; py), and ((x1; y1); (x2; y2)); then the allocation ((x1; y1); (x2; y2)) must be Pareto efficient.
The first welfare theorem tells you that if you observe an allocation that is not on the
contract curve, this cannot be the outcome of a competitive equilibrium. We found that the final allocation is a competitive equilibrium and thus it is pareto efficient. It is impossible to find something better according to pareto.
What are the implications of the first welfare theorem?
The first welfare theorem is very important also because of the common interpretation
as a modern version of the "invisible hand". If all the markets were competitive, then the resulting "competitive markets allocation" would have the socially desirable feature of being Pareto efficient. Following this interpretation, the first welfare theorem would suggest that the only policies that the government should pursue are
1. Making sure that markets become competitive
2. Policies that address issues different than efficiency. For example inequitable distribution of resources. We have seen as an allocation that leaves close to nothing to one individual can still be Pareto efficient.
What does the second welfare theorem say?
The second welfare theorem says that any Pareto efficient allocation is also a competitive equilibrium. More precisely pick a Pareto efficient allocation f(x1; y1); (x2; y2)g. Then there exist a price vector (px; py) (and an initial allocation (w1; w2)) such that (px; py) and ((x1; y1); (x2; y2)) is the resulting competitive equilibrium. Given an allocation on the contract curve, how can you find the corresponding competitive
equilibrium? In other words, what is a price vector (px; py) that "does the job"? The answer is pretty simple: since the allocation is Pareto efficient, theMRS of the two
individuals must be equal; pick any prices (px; py) such that px/py = MRS and you are done.
What are the implications of the second welfare theorem?
The second welfare theorem tells you that if you could redistribute resources between
individual you could achieve any allocation on the contract curve without having to "shut down" the competitive markets.
What are the 2 building blocks of the GE topic 2 and what is the role of the Edgeworth box?
1) Competitive Equilibrium
The Edgeworth box puts these 2 together. It is a graphical tool to analyse competitive equilibrium in an exchange economy.
What is important about pareto criterion?
It doesn't apply to a specific market but to a community.
In order to link two BL what is the merging link?
It is the price ratio, they have the same price ratio and thus same slop, so can be the same.
What happens if two IC cross?
It means that they are not pareto efficient.
Is the pareto criterion only applicable to an exchange economy?
No, it can apply to any type of model, you need at least 2 economic agents and some way to measure the welfare of each of the economic agents. We are here explaining the model through the exchange economy but it is actually a very general concept.
What is another way to describe an allocation?
You have the preferences of an individual represented by a utility function which is a function of x1 and y1 which is the basket that individual A consumes and is a function of what individual A consumes. Now if I put what A consumes to what B consumes I have an allocation and if it is feasible it means that individual A and B consume all the endowment. They consume everything in the market but not more.
What is the idea of pareto?
Came up with a way to aggregate the preferences social welfare function but does not depend on comparing the utility of A and B. We can not say by how much better and prefer one allocation to another but just that it prefers it because we are not comparing utilities. However, in consumer theory, the utility doesn't allow to compare welfare of the individuals. Pareto takes this impossibility and say that if individuals not agree then we can't say what is better.
Why do we study GE?
By studying this topic, we take the idea of perfect competition and push it to the extreme. If all the markets were perfectly competitive, what would be the features of the competitive equilibrium? We know that all markets are not perfectly competitive but we assume that they are. In other words this helps us to understand what is good about perfect competition. It clarifies the invisible hand. It is a new model because the model of demand and supply is misleading. We use here the GE model instead and specifically the most simple of the GE model namely the exchange economy model.
What is the idea of competitive equilibrium?
Market prices adjust so that market clears with prices.
Why use the simplest model of GE, namely the exchange economy model?
We use it to understand how to distribute the different goods among all the economic agents. We need to decide who consumes how much of each of the different goods. We define a concept of efficiency and discuss the pros and cons. We have to show that competitive markets achieve outcomes that are efficient.
In an exchange economy who is the individual?
The individual can be buyer, seller, consumer that inherits some amounts of quantity (non-negative) of goods. This is his initial endowment.
What do we assume in a competitive equilibrium?
It is the equilibrium found in the whole economy and we assume that both individuals are price takers and utility maximisers.
What is the aggregate demand?
It is the demand of individual A and of Individual B. We find it as we put Xa + Xb = wa, which is not the same as the BL condition and feasibile condition where we use prices.
In order to use the Pareto criterion, is it necessary that the allocations are feasible. True or False?
True of course, otherwise no sense.
Does the pareto criterion use the notion of indifference?
No, it uses the notion of impossibility to rank, which doesn't mean that the allocations are equivalent.
Why did Gerratana mention the idea of wishful thinking?
Because if W is inefficient, why want from a normative point of view and policy point of view leave the economy stuck in in W if you know that there is something feasible that exists and improves the welfare of somebody without someone else suffering.
When it comes to prices what is the main difference between consumer theory and GE?
The prices of the goods that the consumer could purchase are given, they are exogenous. We don't use the model of consumer theory to explain how the prices come about. We use to explain what the consumer will consume and choose to buy given his preferences and price and income. In GE, we want to explain the prices of all the goods. We already used a model where prices come about: demand and supply model, it was also a price determination theory.
The model of demand and supply and the GE model are both price determination models: what is their main differences?
The main difference is that the model of demand and supply looks at 1 good and 1 market at a time. In the GE we look at the price determination of all goods. However, in both cases, we have price takers, we can however make predictions about the prices. Economic actors consider them as given.
When it comes to income what is the main difference between consumer theory and GE?
In the Theory of consumer we had income. Here in GE we assign to individual A an initial endowment.
When it comes to feasibility what is the main difference between consumer theory and GE?
For GE we just say if there is enough good x and just enough good y in the economy for the basket of individual A and of individual B to be consumed and that there is no waste. It is if xa+xb=wx but nothing to do with budget constraint. In the theory of consumer because of non-satiation we said that consumers always consume basket on BL, meaning must be affordable.
What is necessary in order to calculate the MRS?
We need a consumption set that contains an infinite (if finite not use MRS) amount of baskets, a utility function that represents the preferences and the main assumptions we had in Consumer Theory. This means that I can have an IC for each basket and then can calculate the slope of the IC, which is the MRS. In Pareto, more general, we only compare 2 allocations, so 4 baskets, can't calculate MRS with this. We don't have to overestimate the MRS, it is just useful when infinite many baskets and live in a world of differential calculus. In the street, not possible to do all this.
Who is Basu?
The idea of pareto efficiency doesn't need to be applied to an exchange economy. If applies to an exchange economy, we can calculate MRS then. But Basu applies it to a more abstract way and not to baskets of goods necessary but also to choices in general. If have only 2 allocations can't tell much but in an Edgeworth box, have many allocations and so can apply pareto, very powerful then as tells you which are efficient and which are not. Basu says that pareto is very helpful but it contains also allocations that are not that good for society.
What is the advantage of applying the Pareto criterion to an Edgeworth box?
If have only 2 allocations can't tell much with pareto but in an Edgeworth box, have infinite many allocations and so can apply pareto, very powerful then as tells you a set of efficient allocations, which are still infinitely many but eliminated a lot which are inefficient. It is as if you have a bunch of feasible allocations in the box and then you apply the pareto criterion and some survive and some not, the one that survive are the efficient ones and are on the curve. If you have only 2 and both are efficient, then both survived but not very useful.
Can two allocations that are efficient be pareto-ranked?
No, they cannot. Once you are in the realm of only efficient allocations, you can't distinguish between them. You can't tell if you should do a policy or not, or help this person or not. You can't separate them in terms of efficiency.
How can you check if one allocation is efficient or not in a Edgeworth box, where you have to compare against a myriad of other allocations?
You either need to know how each allocation is ranked with the one you have or you check MRS1=MRS2 and if tangent: pareto efficient and if not then inefficient. Thanks to this it becomes also easy to find a competitive equilibrium, which would be hard to find if not the welfare theorem linked pareto efficiency and competitive equilibrium. In an exchange economy with a lot of structure and known preferences and goods, it is easy to find the pareto efficient allocation, this is not true for the competitive equilibrium.
What does the first theorem allow you to do?
It allows you to say that in reality there are many pareto efficient allocations and if I let the markets operate and perfect competition you will end up in a competitive equilibrium that is pareto efficient. Don't know anything else but at least I know it will be pareto efficient. I know I can get there and know the direction but don't know how exactly.
Does the assumption MPL > 0 and MPK > 0 signify we have a convex Isoquant?
No, MPL>0 and MPK>0 only say that thin and decreasing but not convex. Convex has to do with decreasing MRTS, which we like to do by saying that labour and capital are productive.
For each initial endowment can you have multiple BL?
Yes, for each a different price ratio.
For each initial endowment can you have multiple competitive equilibrium ?
Yes, but in this class only one.
How do you find the contract curve?
The contract curve is the set of all efficient allocations of an exchange economy.
IC must be Tangent:
1)MRSa = MRSb
2) xa + ya = wa
3)xb + yb = wb
we have to find a ya as a function of xa. So that we are going to have a value of for each xa a value of ya which gives you 1 efficient allocation, infinitely many on the curve, always 0 /< xa /< wa.
What are the conditions that have to be met so that you can use the rule of MRSa=MRSb to check if pareto optimal?
The IC must be smooth with decreasing MRS, so convex and the allocation is in the interior of the Edgeworth box.
What does the producer theory addresses as an economic problem?
The topic of producer theory (or the theory of the firm) addresses the economic problem of the firm.
What is the economic problem of the firm in a competitive market?
How much to produce and how to produce it, given the conditions the firm faces, such as the technology available and the price of the inputs.
What are the two main assumptions we make?
We make two main assumptions: firms are profit maximizing and the firm is operating
in a competitive market.
What is another assumption we do?
We also add another simplifying assumption: we assume that the firm produces only one output Q.
What are the two steps in analysing the economic problem of the firm in a competitive market?
There are two steps in analyzing the economic problem of the firm in a competitive market.
1. Obtain the cost function of the firm from a given technology and given prices of the inputs.
2. Obtain the supply function from a given cost function of the firm.
What is the final result?
So the final result from this analysis will be the supply function of the individual firm, that for a given technology (or production function) can be written like
Qs = S( p; w1; ... ; wn), where Qs is the quantity supplied by the firm; p is the price of the good and w1 ; ... ; wn are the prices of the inputs that the firm uses to produce the output.
What is the process that leads to the cost function of the firm?
It is important to understand that he cost function is the final result of an interesting economic problem of the firm, called the cost minimization problem of the firm.
What is the cost minimisation problem of the firm?
Problem of choosing the inputs
that minimize the cost of producing Q
What are the exogenous variables in the cost minimisation problem of the firm?
A given production technology, Given prices of inputs
What are the endogenous variables that we obtain by solving the cost minimization problem?
By solving the cost minimization problem we obtain (these are the endogenous variables),
1. For each Q the combination of inputs that the firm chooses to produce Q. This is
called the conditional demand of inputs, L(Q) and K(Q)
2. For each Q what is the minimum cost of producing Q. This is the cost function, C(Q).
How do we describe the technology available to the firm?
We describe the technology available to the firm by means of the production function.
What is the definition of the production function?
A production function shows the highest amount of output that the firm can
produce given the quantities of inputs it employs.
What is the simplifying assumption we make about the inputs of the firm?
If we assume (again for simplicity) that the firm only uses two inputs, the production
function can be written as Q = F(x1; x2)
What is the production function and what assumption do we make about it?
A production function is a complete description of a given technology. It is important to note that we are assuming that the production is efficient, that is the firm produces the highest level of output given the inputs.
What do we assume about the way we produce and the use of inputs?
We assume that there is more than one way to produce a given amount of output Q. This brings us to the definition of an isoquant.
What is the definition of an isoquant?
An isoquant is the set of all the combinations of the inputs that produce a
given level of output (Q).
What is the role of the isoquants?
The role of the isoquants is to illustrate the firm's choice among different combination
What is the marginal product of labor?
We define the marginal product of labor as the partial derivative of the production function with respect to labor.
What is the interpretation of MPL and MPK?
Interpretation of MPL is: increase in output, when labor is increased by one unit (keeping capital constant). Similarly for MPK, increase in output, when capital is increased by one unit (keeping labor constant).
What is the MRTS L,K?
The marginal rate of technical substitution of labor for capital MRTSL;K, is the absolute value of the slope of the isoquant. The interpretation of the marginal rate of technical substitution is the rate of change
of the capital per unit of labor that keeps the quantity of output constant.
What does it mean if the MRTS is equal to 2?
An additional unit of labor and two less units of capital keep the output constant.
One less unit of labor and two more units of capital keep the output constant.
What are the assumptions we make about technology?
1. Marginal product of labor is positive MPL > 0
2. Marginal product of capital is positive MPK > 0
3. Marginal rate of technical substitution of labor for capital is decreasing along each
isoquant (increasing L and decreasing K)
What is the maintained assumption we make throughout about technology?
A maintained assumption is that the output
increases when we increase the inputs, that is MPL > 0 and MPK > 0.
What does the concept of returns to scale have to do?
The concept of returns to scale has to do with how much the output increases when the firm increases all the inputs (in the same proportion).
What is the main difference between marginal returns and returns to scale?
A confusing concept for many students is the relation between Marginal Returns and
Returns to Scale. When we talk about returns to scale, all the inputs are increasing. When we talk about marginal returns, only one input is increasing.
How do you express the cost function of a firm?
C = p1x1 + p2x2
How do we express the cost minimisation problem of the firm ?
Given the prices of the inputs and a given level of output, we assume that the firm chooses the combination of inputs so to minimize the costs. More formally we assume that the firm chooses (x1; x2) to
minimize p1x1 + p2x2 subject to Q = F(x1; x2)
What is an isocost line?
An isocost line is the set of all the baskets of inputs (x1; x2) such that the
total cost is constant. More formally,
Isocost(TC) = ((x1; x2)jp1x1 + p2x2 = TC)
What is the slope of an isocost line?
What is the opportunity costs of labor in terms of capital?
What does MPL/w = MPK/r mean?
This last expression says that at the combination of inputs at which the firm minimizes the costs, one extra dollar spent on the input labor generates the same amount of output of one extra dollar spent to buy the input capital. In other words, if a firm is minimizing costs, it is equalizing the "bang for the buck".
What happens in the corner solution for the producer theory?
The tangency condition doesn't apply, that is either K = 0 or L = 0.
What is the cost function?
The cost function gives the minimum amount of money that the firm must spend to produce each amount of output Q.
How are the returns to scale closely related to the shape of the cost function?
If the production function has increasing returns to scale, then the average cost function is decreasing (we say that there are economies of scale).
If the production function has decreasing returns to scale, then the average cost function is increasing (we say that there are diseconomies of scale).
If the production function has constant returns to scale, then the average cost function is constant (there are neither economies nor diseconomies of scale)
On which exogenous variables is the conditional demand on L and K depend?
L(q;w; r) K(q;w; r)
What is given in the profit maximisation problem of the firm?
We assume that the firm has already solved the problem of cost minimization and therefore we take the cost function as a "given" of this model (i.e. an exogenous variable).
In what type of market are we in the profit maximisation problem?
perfectly competitive market
What does the firm do when it comes to prices in a competitive market?
It is important to stress one more time that a firm in a competitive market does not choose the price, but for each given price, the firm chooses the quantity of output Q that maximizes the profits.
What is the marginal profits?
The marginal profits indicate how much the profit changes if we increase the level of output by one unit. More precisely, the marginal profit function is the derivative of the profit function with respect to the output Q.
What are marginal costs?
The marginal costs, MC(Q), indicate how much the cost changes if we increase the level of output by one unit. More precisely, the marginal cost function is the derivative of the cost function with respect to the output Q.
What are marginal revenues?
The marginal revenues, MR(Q), indicate how much the revenue changes if we increase the level of output by one unit. More precisely, the marginal revenue function is the derivative of the revenue function with respect to the output Q.
What is a necessary condition for a Q > 0 to maximize
MC (q) = P
What is the reaction between marginal cost and average cost?
Whenever the marginal costs are higher than the average costs, the average cost
function is increasing
Whenever the marginal costs are lower than the average costs, the average cost function is decreasing
When the marginal cost is equal to the average cost, the average cost function is
reaching its minimum.
What does the MC = p tell you?
For each price p it is given by the level of output q that maximizes the firm's profit.
What are non-sunk FC?
If the fixed costs are avoidable, we call them non sunk. If the fixed costs are nonsunk, (and therefore avoidable) then C(Q = 0) = 0. In particular, if the fixed costs
are sunk, then C(Q = 0) = FC
Profits (q = 0) = p(0) - C(q = 0) = - C(q = 0)
What happens in the long run for the supply curve?
The long-run shut down price is equal to the minimum level of the ATC(Q), that we
indicate with ATC. Meaning that the only reasonable long run fee entry supply curve must have infinity elasticity at p = ATC min.
What is the implication of increasing K if I have MPK>0 and MPL>0 ?
It means that if I want to stay on the same is-quant, meaning I want to produce the same level of output, I have to decrease L by a certain amount.
What are the implication of MPK>0 and MPL>0?
Thin and decreasing so the derivative is smaller than 0 but convexity is another assumption.
What does the assumption convex imply for isoquants?
I means that we have decreasing MRTS and thus that the more you have of one factor of production, the more it gets crowded and less efficient. Diversifications of inputs is better, negative slope of MRTS. The MRTS has to do with convexity but not MPL>0 and MPK>0.
What is important to know about MPL >0?
It means that output increases when I add 1 unit of labour but it doesn't tell me by how much it increases. It could be by less than the unit or more than the unit or the same. That is the question marginal returns asks. It is the rate of change of increase of output per unit of labor.
What are the 2 conditions that have to be fulfilled in the producer theory?
Feasibility condition and tangency condition
What happens if I am given q = 400 and I produce more or less?
It means that if I produce less, I am waisting resources, because if use more technology I could produce more. If I am however producing more, then also waisting cause could produce same amount with less inputs.
What is the conditional demand on labor?
What is the economic interpretation of the MRTS=3?
An extra unit of labor is as productive as 3 extra unit of capital. It means that the contribution of 1 extra units of labour is as productive as 3 extra unit of K. So if I have 6 units of labor and 18 units of K, the 6 units of labor are as efficient as the 18 units of KhaW, the ratio is of 18/6=3.
What does it mean that any isoquant I(A) is a level curve of the production function f (L,K)?
The defintion of the isoquant passing through basket A is given by the set of all combinations of inputs L+K such that the value of the production function A such that these combinations of inputs is exactly equal to the value of f (A).
What are the 2 constraints that the firm faces?
Technological constraint (the firm must use an existing body of scientific and technological knowledge) and market constraints (firm must buy and rent the inputs it uses).
What is the production function?
It represents the technological constraints through the concept of production function. It is a mathematical description of how the firm can transform inputs into outputs. It gives you the highest amount of output that the firm can produce given the quantities of inputs it employs.
What is the result of the cost minimisation problem?
the conditional demand of labor and capital.
What does the isocost tell you?
Isocost tells me what is the relation between L and L such that the cost of baskets of inputs don't change.
What does it mean if you have decreasing Marginal products but MPL>0?
Each additional unit of input will contribute to production in a positive way (the MP1 is positive) but the increase in production will be smaller and smaller the greater amount of the input.
Where do the VC come from?
From the cost minimisation problem of the firm.
What are the necessary exogenous variables that need to be defined in the problem of consumer's choice?
1. The prices of the N goods (p1; p2; pN)
2. The income of the consumer, I
What is constant in the individual demand function?
What is the inverse demand stating?
The inverse demand function represents the willingness to pay by the consumer for
(a marginal unit of) the good. So if x = 20 and p = F-1(20) = 5, we know that if the
consumer is buying 20 units of the good, her willingness to pay for a (marginal) unit
of the good is equal to 5 dollars.
What is MRS?
We also learnt the meaning of MRS(x;y)(x; y), that is how many units of good y the consumer is willing to give up to obtain a marginal unit of good 1: that is how much money she is willing to give up to get a marginal unit of good x, that is the
willingness to pay for a marginal unit of good x. But then, this means that if we take a certain amount of x (say x = 20) that the consumer buys, and we look at the corresponding price p on the demand function (say p = 5 dollars), we are in fact measuring the willingness to pay for a (marginal) unit of the good when the consumer is already consuming
x = 20 units of good x.
What is the Engel Curve?
The Engel curve describes the relation between the income of consumers
and the quantity demanded of a good, keeping constant all other variables (e.g. the
What is a normal and inferior good? What is the link with the Engel curve?
A good is normal if the consumers want to buy more of it, when their income increases. A good is inferior if the consumers want to buy less of it, when their income increases.
For a given consumer, a good is normal if her Engel curve is increasing, and it is inferior
if it is decreasing (at least for some range of income)
How can we measure the change in welfare of the individual resulting from the change in
the price (that is, how much better off is the consumer after a policy that is implemented to change the price)?
1. The change in consumer surplus
2. The compensating variation
3. The equivalent variation
What is the compensating variation?
Assume that the policy results in a price decrease of a good from p to p'. The compensating variation is defined as the amount of money we can take away from the consumer after the price reduction to make her as happy as she was before the reduction of the price.
What does EV and CV try to measure?
Both the definitions try to give a "monetary measure" to the change in welfare resulting
from the policy. By doing so, we are trying to give an objective measure of the change
of welfare resulting from a policy and also a measure that we can compare with the costs
of the policy.
What is EV?
Keep assuming that the policy results in a price reduction of a good from p to p0. The
equivalent variation is defined as the amount of money we can give to the consumer
before (or rather instead of) the price reduction to make her as happy as she would be after the reduction of the price.
When is EV and CV the same?
In fact, if the utility of the individual is quasi-linear, these two definitions give the same result. Moreover, even if the utility of the consumer is not quasi-linear, we often ignore the difference and pick one of the two.
What is the advantage of CS?
In most cases, we do not know the preferences of the individual. In these cases, how can we measure the change of welfare of the individual resulting from a change in the price? With the change in consumer's surplus that requires only to know (or estimate) the demand function for the good.
What is the link between CS, EV and CV?
In fact, if the utility function is quasi-linear, then the consumer's surplus is equal to the compensating variation (and equivalent variation).
When is CV and EV the same?
The reason for which, in this example, the compensating variation and the equivalent
variation give exactly the same monetary measure (same number) is because the preferences in the example are quasi-linear and therefore the amount consumed of good x does not change with the income (that is there are no income effects for good x).
What do we assume when we calculate the SE and IE and what is the implication of that?
Because we assume that the preferences of the individual are convex, we know that basket B is to the left of the initial basket A along the same indifference curve, that is B contains less x1 and more x2. In other words the substitution effect is always negative for the same good x1 and (conversely it is positive for the other good).
If a good has no income effect what does it mean?
It is normal because SE always goes in the direction of the law of demand.
To what is due the fact that the SE always meets the law of demand?
It is due to the convex IC, meaning that if the price of x increases, and py, stays the same, I have a relative price that is higher for px/py and thus my MRS changes, because px/py = MRS anymore but now MRS < px/py and we have that consume less x and more y so move up the IC, the steeper part of the IC.
In welfare topic 1, what is endogenous and what is exogenous?
P1, P2, and I are exogenous, while x and y, the demand function are endogenous.
What is the CS?
It is the difference between her willingness to pay for a good x and the amount she actually must pay to purchase the good. We actually pay less for each unit of x than what I am willing to pay.
What is the explanation and pendant to what we have with what happens if P for producers increase for CS?
So when p goes down, we have in CS first for the same Q as before just a drop in price gratis a bit and so the consumer saves even more money just by consuming the same. Then she saves an extra bunch by consuming a bit more because she values these units bit higher, her marginal benefit is higher than the actual price.
What is the difference between cost expression and cost function?
Cost expression is just C=wl+rk
Cost function is C(q,p1,p2) = wL() + rK()
What is the important thing to remember when it comes to cost welfare analysis part 2?
It is important to stress one more time that a firm in a competitive market does not choose the price, but for each given price, the firm chooses the quantity of output Q that maximizes the profits. So for each p what is my willingness to sell, produce etc? Like for demand function, where you were asked what is your willingness to buy for each p?
What is the difference between MC and Supply function when it comes to independent and dependent variable?
The supply function considers the price as the independent variable and the q as dependent, while the MC says that q is the independent variable and I am just asking myself to which price am I selling this q produced? I fix the price.
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