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Chapter 8
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Gravity
Terms in this set (40)
Why does growth matter?
anything that affects the long run rate of economic grow
-even by a tiny amount- will have a huge effect on living standards in the long run
what does growth help us understand?
- why poor countries are poor
- design policies that can help them grow
- learn how our own growth rate is affected by shocks and government policies
What does the Solow Model do?
looks at the determinants of economic growth and the standard living in the long run
How is the Solow model different from chapter 3 model?
1. K is no longer fixed
- investment causes it to grow
- depreciation causes it to shrink
2. L is no longer fixed
- population growth causes it to grow
3. consumption function is simpler
4. No G or T
5. Cosmetic difference
The production function in aggregate terms
Y= F(K,L)
What is output per worker
y= Y/L
what is capital per worker
k= K/L
What is the national income identity? per worker terms?
Y=C+I
- y=c+i
where c=C/L and i=I/L
What is s?
s= the savings rate → the fraction of income that is saved
→ s is exogenous parameter
what is the consumption function?
c=(1-s)y
what is savings per worker?
savings (per worker)= y-c
=y-(1-s)y
=sy
What is the national income identity?
y=c+i
i=y-c
=sy
i=sy=sf(k)
What is δ?
δ= the rate of depreciation
= the fraction of the capital stock that wears out each period
What is capital accumulation?
basic idea: investment increases the capital stock; depreciation reduces capital stock
What is the equation of capital stock?
∆k= i -δk
change in capital stock = investment - depreciation
What is the equation of motion for k
∆K= sf(k)-δk
What is income per person? What is consumption per person?
income→ y=f(k)
consumption→ c=(1-2)f(k)
what is the steady state of capital stock
∆k=0 ; capital per worker will remain constant which is denoted k*
Summary of steady state capital stock
As long as k<k*, investment will exceed depreciation, and k will continue to grow toward k*
Different values of s lead to different steady state, but which is "best"?
the best steady state has the highest possible consumption per person
c*=(1-s)f(k*)
what will an increase in s do in golden rule?
increase in s will lead to a higher k* and y* which raises c*
reduces consumption's share of income (1-s) which lowers c*
What is the steady state value of k that maximizes consumption
k*gold= the golden rule level of capital
How to express c* in terms of k*
c*=y* -i*
= f(k*) - i*
=f(k*) -δk*
where is c* the biggest?
c* is the biggest where the slope of the production function equals the slope of the depreciation line
MPK=δ
The transition to the golden rule steady state
- economy does NOT have a tendency to move toward the golden rule steady state
-achieving the golden rule requires that policymakers adjust s
- adjustment leads to a new steady state with higher consumption
Starting with too much capital in the transition to the golden rule steady state
k*>k*gold
-increasing c* requires a fall in s
- consumption is higher at all points in time
Starting with too little capital in the transition to the golden rule steady state
k*gold >k*
- increasing c* requires an increase in s
- future generations enjoy higher consumption, but the current one experiences an initial drop in consumption
What is break even investment?
(δ +n)k= break-even investment
=the amount of investment necessary ti keep k constant
what is included in break-even investment?
δk to replace capital as it wears out
nk to equip new workers with capital
- otherwise k would fall as the existing capital stock is spread more thinly over a larger population of workers
What is the equation of motion for k?
∆k = sf(k)⁻(δ+n)k
sf(k)→ actual investment
(δ+n)k→ break-even investment
What is the impact of population growth
An increase in n causes an increase in break-even investment leading to a lower steady-state of k
What is the Golden Rule with population growth
to find the golden rule of capital, express c* in terms of k*
c*=y*-i*
When is c* maximized?
c* is maximized when
MPK=δ+n ↔
MPK⁻δ=n
What is the Malthusian model?
predicts population growth will outstrip the Earth's ability to produce food leading to the impoverishment of humanity
What is the facts that don't support Malthusian model?
Since Malthus, world population has increased sixfold, yet living standards are higher than ever
- Malthus neglected the effects of technological progress
What is the Kremerian model?
population growth contributes to economic growth because more people= more geniuses, scientists & engineers → faster technological progress
What is the evidence that supports the Kremerian model?
-as world population growth rate increases, so did the living standards
-regions with larger populations have enjoyed faster growth
How does a country's standard of living depend on savings rate and population rate?
positively on savings rate
negatively on population growth rate
What will an increase in the savings rate lead to?
- higher output in the long run
- faster growth temporarily
- not faster than steady-state growth
If the economy has ____ capital than the Golden Rule level, _____ savings will increase consumption for ________
More, reduce, at all points in time
less, increasing, increase for future generations but reduced for present
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