Managerial Economics Unit 1

STUDY
PLAY
The X-Corporation produces a good (called X) that is a normal good. Its competitor, Y-Corp., makes a substitute good that it markets under the name "Y." Good Y is an inferior good.

a. How will the demand for good X change if consumer incomes decrease?

b. How will the demand for good Y change if consumer incomes increase?

c. How will the demand for good X change if the price of good Y increases?

d. Is good Y a lower-quality product than good X?
a. If consumer income decreases, the demand for good X will fall/decrease as it is a normal good.

b. If consumer income increases, the demand for good Y will fall/decrease as it is an inferior good.

c. Y is a substitute good for X. Hence if price of Y increases, then it will lead to the demand for good X to increase.

d. Yes. Y is a lower-quality product than X.
The demand for good X is given by

QXd = 6,000 - (0.5)PX - PY + 9PZ + (0.10)M

Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $70,000.

a. Indicate whether goods Y and Z are substitutes or complements for good X.

b. Is X an inferior or a normal good?

c. How many units of good X will be purchased when Px = $5,230?

d. Determine the demand function and inverse demand function for good X. Graph the demand curve for good X.
a) Good Y is a complement(because the price co-officient of good Y is negative) and good Z is a substitute. ( because the price co-officient of good Z is positive).

b) Good X is a normal good.

c) When Px = $5,230
Qxd = 6,000 - (1/2)Px - Py + 9Pz + (1/10)M
= 6,000 - 0.5Px - Py + 9Pz +0.1M
Qxd = 6,000 - 0.5 5,230 - 6,500 + 9 100 + 0.1 * 70,000
= 6,000 - 2,615 - 6,500 + 900 + 7,000
Qxd = 4785 units

d) Demand function: Qxd = - Px
Inverse demand function: Px = - Qxd
Consider a market where supply and demand are given by QXS = -10 + PX and QXd = 68 - 2PX. Suppose the government imposes a price floor of $30, and agrees to purchase any and all units consumers do not buy at the floor price of $30 per unit. Assume that the government simply removes product from the market through its purchase.

a. Determine the cost to the government of buying firms' unsold units.

b. Compute the lost social welfare (deadweight loss) that stems from the $30 price floor.
After determining that P=30, substitute 30 for P for...
a. Quantity that sellers would be selling at P=30 is 68 - 2(30) = 8 as less would be demanded at higher price.
sellers would be instead manufacturing (-10 + 30) = 20 units. So they need to be compensated for 12 units of unsold goods. Thus cost to the government of buying unsold goods = 12 * 30 = $360

b. Deadweight loss are the two triangles that are lost from consumer surplus and producer surplus.
1/2(48 + 88) = $48
In a recent speech, the governor of your state announced: "One of the biggest causes of juvenile delinquency in this state is the high rate of unemployment among 16 to 19 year olds. The low wages offered by employers in the state have given fewer teenagers the incentive to find summer employment. Instead of working all summer, the way we used to, today's teenagers slack off and cause trouble. To address this problem, I propose to raise the state's minimum wage by $1.50 per hour. This will give teens the proper incentive to go out and find meaningful employment when they are not in school." Highlight a possible flaw in the governor's reasoning:
A higher minimum wage will serve as a higher price floor, reducing quantity demand for labor by firms.
The demand curve for product X is given by QXd = 520 - 4PX.

a. Find the inverse demand curve.

b. How much consumer surplus do consumers receive when Px = $50?

c. How much consumer surplus do consumers receive when Px = $30?

d. In general, what happens to the level of consumer surplus as the price of a good falls?
A) *QXd=520-4Px

*4Px=520-QXd

*Px=520-QXd
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4

*Px=130-QXd or Px = 130 - 1/4 QXd
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4

B) QXD = 520 - 4PX
QXD = 520 - 4(50) = 320
1/2 x 320 x (130-50) = 160 x 80 = 12,800


C) QXD = 520 - 4PX
QXD = 520 - 4(30) = 400
QXD = 1/2 x 400 x (130-30) = 200 x 100 = 20,000


D) As the prices of goods fall the consumer surplus will increase.
You are the manager of a midsized company that assembles personal computers. You purchase most components - such as random access memory (RAM) - in a competitive market. Based on your marketing research, consumers earning over $80,000 purchase 1.5 times more RAM than consumers with lower incomes. One morning, you pick up a copy of The Wall Street Journal and read an article indicating that input components for RAM are expected to rise in price, forcing manufacturers to produce RAM at a higher unit cost.
...
Suppose demand and supply are given by Qd = 60 - P and Qs = 1.0P - 10.

a. What are the equilibrium quantity and price in this market?

b. Determine the quantity demanded, the quantity supplied, and the magnitude of the surplus if a price floor of $48 is imposed in this market.

c. Determine the quantity demanded, the quantity supplied, and the magnitude of the shortage if a price ceiling of $25 is imposed in the market. Also, determine the full economic price paid by consumers.
A: 1. Solve for P 60-P = P-10
60+10 = P+P
2P = 70
P = 35

2. Solve for Quantity Qd = 60-P
Qd = 60-35 = 25
Qs = P-10 or 35-10 = 25
Quantity = 25

B: 1. Quantity demanded at 48
60-P = 60-48 = 12
2. Quantity supplied at 48
P-10 = 48-10 = 38
3. Surplus = supply - demand = 38-12 = 26

C: 1. Quantity demanded at 25
60-P = 60-25 = 35
2. Quantity supplied at 25
P - 10 = 25-10 = 15
3. Shortage = Quantity demanded - supply
35-15 = 20
4. Full economic price = 60 - 15 = 45
The demand curve for a product is given by QXd = 1,200 - 3PX - 0.1PZ where Pz = $300.

a. What is the own price elasticity of demand when Px = $140? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price below $140?

b. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm's revenue if it decided to charge a price above $240?

c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z substitutes or complements?
a. 1. Demand Equation : QXd = 1200 - 3Px - 0.1Pz
Pz = $300
Putting value of Pz in the Demand equation
QXd = 1200 - 3Px - 0.1 * 300
= 1200 - 3Px - 30
Now, QXd = 1170 - 3Px
Differentiating the above equation with respect to Px
dQXd / dPx = -3
Now the value of QXd when Px = $140
QXd = 1170 - 3 * 140
= 750
So when price Px is $140 Quanitity QXd is 750.
Own Price Elasticity = (dQXd / dPx) * (Px / QXd)
= - 3 * 140/750
= - 0.56
2. Demand at -0.56 is inelastic
3. If the firm prices below $140, revenue will decrease

b. 1. Demand Equation : QXd = 1200 - 3Px - 0.1Pz
Pz = $300
Putting value of Pz in the Demand equation
QXd = 1200 - 3Px - 0.1 * 300
= 1200 - 3Px - 30
Now, QXd = 1170 - 3Px
Differentiating the above equation with respect to Px
dQXd / dPx = -3
Now the value of QXd when Px = $240
QXd = 1170 - 3 * 240
= 450
So when price Px is $240 Quanitity QXd is 930.
Own Price Elasticity = (dQXd / dPx) * (Px / QXd)
= - 3 * 240/450
= - 1.6 Since absolute value is >1, demand is elastic. Finally, raising price above 240 will decrease revenue.

c. 1.
Suppose the own price elasticity of demand for good X is -3, its income elasticity is 1, its advertising elasticity is 2, and the cross-price elasticity of demand between it and good Y is -4. Determine how much the consumption of this good will change if:

a. The price of good X decreases by 5 percent.

b. The price of good Y increases by 10 percent.

c. Advertising decreases by 3 percent.

d. Income increases by 4 percent.
Own price elasticity of demand is given as -3, so 1 unit increase in price reduce the quantity demanded by 3 units
When price of X decreases by 5%, quantity will increase by 5*3 = 15%

Cross price elasticity of demand beetween X and Y is given as -4, so 1 unit increase in price of Y reduce the quantity demanded by 4 units for X
When price of Y increases by 10%, quantity of X will decrease by 4*10 = 40%
Since it is a decrease aanswer is -40

Advertising elasticity of demand is given as 2, so 1 unit increase in advertising increase the quantity demanded by 2 units
When advertising decreases by 3%, quantity will decrease by 3*2 = 6%
Since it is a decrease aanswer is -6

Income elasticity of demand is given as 1, so 1 unit increase in income increase the quantity demanded by 1 units
When income increases by 4%, quantity will increase by 1*4 = 4%
Suppose the cross-price elasticity of demand between goods X and Y is 5. How much would the price of good Y have to change in order to change the consumption of good X by 40 percent?
40/5=8
For the first time in two years, Big G (the cereal division of General Mills) raised cereal prices by 6 percent. If, as a result of this price increase, the volume of all cereal sold by Big G changed by -4 percent, what can you infer about the own price elasticity of demand for Big G cereal?
-4/6= -0.67. Since -0.67<1, this is inelastic, which means you cannot tell if revenue levels changed.
If Starbucks's marketing department estimates the income elasticity of demand for its coffee to be 1.45, how will the prospect of an economic bust (expected to decrease consumers' incomes by 6 percent over the next year) impact the quantity of coffee Starbucks expects to sell?
Answer) Use the income elasticity formula to write %ΔQ d / -6 = 1.45. Solving, we see that coffee purchases are expected to change by - 8.7 percent. Multiply both sides by -6 to get 1.45*-6 = -8.7
Revenue at a major cellular telephone manufacturer was $2.2 billion for the nine months ending March 2, up 90 percent over revenues for the same period last year. Management attributes the increase in revenues to a 119 percent increase in shipments, despite a 32 percent drop in the average blended selling price of its line of phones.

Given this information, is it surprising that the company's revenue increased when it decreased the average selling price of its phones?
119/-32 = -3.72

No. Own price elasticity is -3.72, which means demand is elastic and a decrease in price will raise revenues. Demand is elastic as -3.72>1
Revenue at a major cellular telephone manufacturer was $2.3 billion for the nine months ending March 2, up 85 percent over revenues for the same period last year. Management attributes the increase in revenues to a 108 percent increase in shipments, despite a 21 percent drop in the average blended selling price of its line of phones.

Given this information, is it surprising that the company's revenue increased when it decreased the average selling price of its phones?
108/-21 = -5.14

No. Own price elasticity is -5.14, which means demand is elastic and a decrease in price will raise revenues.
A firm's current profits are $900,000. These profits are expected to grow indefinitely at a constant annual rate of 4 percent. If the firm's opportunity cost of funds is 6 percent, determine the value of the firm:

a. The instant before it pays out current profits as dividends.

b. The value of the firm immediately after paying the dividend is:
a. PVfirm = $900,000((1 + 0.06) / (0.06 - 0.04)
= $47.70 million

b. PVEx-Dividend firm= $900,000((1 + 0.04) / (0.06 - 0.04)
= $46.80 million
Jaynet spends $35,000 per year on painting supplies and storage space. She recently received two job offers from a famous marketing firm - one offer was for $120,000 per year, and the other was for $105,000. However, she turned both jobs down to continue a painting career. If Jaynet sells 20 paintings per year at a price of $9,000 each:

a. What are her accounting profits?

b. What are her economic profits?
a. Her accounting profits are $145,000. These are computed as the difference between revenues ($180,000) and explicit costs ($35,000).

b. By working as a painter, Jaynet gives up the $120,000 she could have earned under her next best alternative. This implicit cost of $120,000 is in addition to the $35,000 in explicit costs. Since her economic costs are $155,000, her economic profits are $180,000 - $155,000 = $25,000.
Suppose the total benefit derived from a given decision, Q, is B(Q) = 20Q - 2Q2 and the corresponding total cost is C(Q) = 4 + 2Q2, so that MB(Q) = 20 - 4Q and MC(Q) = 4Q.

a. What is total benefit when Q = 2? Q = 10?

b. What is marginal benefit when Q = 2? Q = 10?

c. What level of Q maximizes total benefit?

d. What is total cost when Q = 2? Q = 10?

e. What is marginal cost when Q = 2? Q = 10?

f. What level of Q minimizes total cost?

g. What level of Q maximizes net benefits?
a. Total benefit when Q = 2 is B(2) = 20(2) - 222 = 32. When Q = 10, B(10) = 20(10) - 2102 = 0.

b. Marginal benefit when Q = 2 is MB(2) = 20 - 4(2) = 12.When Q = 10, it is MB(10) = 20 - 4(10) = -20.

c. The level of Q that maximizes total benefits satisfies MB(Q) = 20 - 4Q = 0, so Q = 5.

d. Total cost when Q = 2 is C(2) = 4 + 222 = 12. When Q = 10 C(Q) = 4 + 2102 = 204.

e. Marginal cost when Q = 2 is MC(Q) = 4(2) = 8. When Q = 10 MC(Q) = 4(10) = 40.

f. The level of Q that minimizes total cost is MC(Q) = 4Q = 0, or Q = 0.

g. Net benefits are maximized when MNB(Q) = MB(Q) - MC(Q) = 0, or 20 - 4Q - 4Q = 0. Some algebra leads to Q = 20/8 = 2.5 as the level of output that maximizes net benefits.
What is the value of a preferred stock that pays a perpetual dividend of $185 at the end of each year when the interest rate is 4 percent?
The present value of the perpetual stream of cash flows. This is given by PVPerpetuity = CF / i = $185 / 0.04 = $4,625.
The head of the accounting department at a major software manufacturer has asked you to put together a pro forma statement of the company's value under several possible growth scenarios and the assumption that the company's many divisions will remain a single entity forever. The manager is concerned that, despite the fact that the firm's competitors are comparatively small, collectively their annual revenue growth has exceeded 50 percent over each of the last five years. She has requested that the value projections be based on the firm's current profits of $3.5 billion (which have yet to be paid out to stockholders) and the average interest rate over the past 20 years (9 percent) in each of the following profit growth scenarios:

a. Profits grow at an annual rate of 11 percent. (This one is tricky.)

b. Profits grow at an annual rate of 5 percent.

c. Profits grow at an annual rate of 0 percent.

d. Profits decline at an annual rate of 3 percent.
a. Since the profits grow faster than the interest rate, the value of the firm would be infinite (which is the answer). This illustrates a limitation of using these simple formulas to estimate the value of a firm when the assumed growth rate is greater than the interest rate.

b. PVfirm = π((1 + i) / (i - g)) = $3.5(1.09 / 0.04) = $95.38 billion

c. PVfirm = π((1 + i) / (i - g)) = $3.5(1.09 / 0.09) = $42.39 billion

d. PVfirm = π((1 + i) / (i - g)) = $3.5(1.09 / 0.12) = $31.79 billion
An owner can lease her building for $120,000 per year for three years. The explicit cost of maintaining the building is $40,000, and the implicit cost is $55,000. All revenues are received, and costs borne, at the end of each year. If the interest rate is 5 percent, determine the present value of the stream of:

a. Accounting profits.

b. Economic profits.
a. The present value of the stream of accounting profits is:

PV= (120,000-40,000)/(1.05)+(120,000-40,000)/(1.05)^2+(120,000-40,000)/(1.05)^3= 217,859.84

b. The present value of the stream of economic profits is:

PV= (120,000-40,000-55,000)/(1.05)+(120,000-40,000-55,000)/(1.05)^2+(120,000-40,000-55,000)/(1.05)^3= 68,081.20
A consumer must spend all of her income on two goods (X and Y). In each of the following scenarios, indicate whether the equilibrium consumption of goods X and Y will increase or decrease. Assume good X is a normal good and good Y is an inferior good.

a. Income doubles.

b. Income quadruples and all prices double.

c. Income and all prices quadruple.

d. Income is halved and all prices double.
a. Consumption of good X will increase and consumption of good Y will decrease.

b. Consumption of good X will increase and consumption of good Y will decrease.

c. Nothing will happen to the consumption of either good.

d. Consumption of good X will decrease and consumption of good Y will increase.
A consumer's budget set for two goods (X and Y) is 400 ≥ 4X + 5Y.

a. The budget set is illustrated below. What are the values of A and B?

b. Does the budget set change if the prices of both goods double and the consumer's income also doubles?

c. Given the equation for the budget set, what are the prices of the two goods?

What is the consumer's income?
a. The initial budget set intercepts the Y-axis at 80 and intercepts the X-axis at 100.

b. Doubling all income and price leaves the budget set unchanged. The increase in income is sufficient to offset the price increases. The market rate of substitution is unchanged.

c. The consumer's income is $400, the price of X is $4 per unit and the price of Y is $5 per unit.
A worker views leisure and income as "goods" and has an opportunity to work at an hourly wage of $18 per hour.

a. The worker's opportunity set in a given 24-hour period is illustrated below. What are the values of A and B?

b. Suppose the worker is always willing to give up $12 dollars of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution?

How many hours per day will she choose to work?
a. The worker's opportunity set in a given 24-hour period is E = 432 - 18L.

b. Since the worker is always willing to trade $12 dollars of income for one hour of leisure, the worker's indifference curve does not exhibit diminishing marginal rate of substitution; the worker always trades between the two goods at the same rate. Since $12 is less than $18, the worker will choose to work 24 hours.
A consumer must divide $600 between the consumption of product X and product Y. The relevant market prices are Px = $10 and Py = $40.

a. Write the equation for the consumer's budget line.

b. In the graph below, illustrate the consumer's opportunity set.

c. In the same graph, Illustrate the consumer's opportunity set when the price of good X increases to $20.

How does this change alter the market rate of substitution between goods X and Y?
a. The consumer's budget line is $600 = $10X + $40Y. Rearranging terms and solving for Y results in Y = 15 - 0.25X.

b. For the original budget line, it intercepts the Y-axis at $600 / $40 = 15, and it intercepts the X-axis at $600 / $10 = 60.

c. When the price of X increases to $20, the budget line intercepts the Y-axis at $600 / $40 = 15 and it intercepts the X-axis at $600 / $20 = 30. The market rate of substitution changes from -PX / PY = -10 / 40 = -0.25 to -PXnew / PY = -20 / 40 = -0.5.
An internal study at Mimeo Corporation—a manufacturer of low-end photocopiers—revealed that each of its workers assembles three photocopiers per hour and is paid $3 for each assembled copier. Although the company does not have the resources needed to supervise the workers, a full-time inspector verifies the quality of each unit produced before a worker is paid for his or her output. You have been asked by your superior to evaluate a new proposal designed to cut costs. Under the plan, workers would be paid a fixed wage of $8 per hour.

Should you expect this plan to cut costs?
No - the fixed wage gives workers no incentive to work hard.

Under the existing plan, a worker that does not "goof off" produces 3 copiers per hour and thus is paid $9 each hour. Under the new plan, each worker would be paid a flat wage of $8 per hour. While it might appear on the surface that the company would save $1 per hour in labor costs by switching plans, the flat wage would be a lousy idea. Under the current plan, workers get paid the $9 only if they work hard during the hour and produce 3 machines that pass inspection. Under the new plan, workers would get paid $8 an hour regardless of how many units they produce. Since your firm has no supervisors to monitor the workers, you should not favor the plan.