LT Class 1 notes

Christina Ammon
 Each class we cover the quiz and the essay
 Sometimes will not have enough time for both – priority given
to essay
 Will collect all essays each week, but mark one or two each
 Can give detailed feedback/ can come to office hours to
 Today: a lot to do, focus mostly on Essay + Question 3 of Quiz
Growth – Why do we care?
 One of the earliest big questions in economics: why are some
countries richer than others?
 Singapore vs. Haiti:
• Nominal: 55182 vs 820 => 67 x higher
• PPP adjusted: 78763 vs. 1703 => 46 x higher
 What makes Singapore so much richer than Haiti?
The Solow model
 In agricultural world: main input to production: land & labor
 If Land is good quality – higher income, if not - lower income
 No economic growth possible!
 Solow model: in industrial world main input capital and labor
 Now if people save: can build new capital
 => capital can be accumulated through savings
 i.e. what people save now, will be turned into capital next period
 => can let the economy grow
 BUT: in classic solow model only to a point. Why?
 Decreasing returns to capital
 At some point capital not productive enough anymore to cover
Essay Question a
Consider an economy with a government, consumers, and firms,
but no foreign sector (no exports and no imports).
Write down an expression for GDP in terms of expenditures.
 Accounting identity: Income=Expenditure=Production
 Can either express income in terms of production or
 Call Y whatever is being produced i.e. GDP
 => GDP in terms of expenditure is:
 Note: in terms of production express income as: Y=F(K,L)
Essay Question b
Use the expression in (a) to derive an expression for investment.
 Can simply rearrange
 I=Y-C-G
Essay Question c
Suppose that consumption is a fraction (1-s) of GDP while the
government spends a fraction t of GDP on government purchases.
Rewrite the expression for investment in terms of s and t.
Have from before: I= Y-C-G
Now replace
 C=(1-s)Y
 G=tY
Essay Question d
Assume s>t and no population growth.
What is the law of motion of capital per worker?
 What is a law of motion?
 What determines how capital evolves?
• New investments increase capital
• Depreciation decreases capital
 ∆K=investment-depreciation
Essay Question d
 Here have no population growth, so not necessary
 BUT: in general, turn in per capita terms (small letters)
 Divide Y=F(K,L) by L: Y/L=F(K/L, 1) => y=f(k)
 Investment per capita=I/l=(s-t)Y/L=(s-t)*f(k)
 Depreciation=δk
Question 2
In the Solow growth model, increases in capital ______ output
and ______ the amount of output used to replace depreciating
 A. increase; increase
 B. increase; decrease
 C. decrease; increase
 D. decrease; decrease
Essay Question e
Draw a diagram that illustrates the law of motion in (d) and use
the diagram to describe briefly the growth process.
How do we find the steady state?
 To solve Solow model – need to find the steady state
 Analogue to our idea of Equilibrium: “the situation in which
nothing changes”
 => variable of interest (capital per capita) does not change
 i.e. ∆k=0
 ∆k =(s-t)f(k*)-δk*=0
Essay Question f
Suppose that the economy is in steady state, and the government
reduces t to t’<t, what happens to the growth rate in the sort-run
and in the long-run?
 Short run growth:
• Look at if steady state changes
• See if we are currently below or above steady state
What happens to k*=(s-t)f(k*)/δ if t is reduced?
Is our current k below or above the new k*?
 Long run growth?
Essay Question g
Explain the economic intuition for the result in (f).
Essay Question h
Consider two economies outside the steady state. The two
economies have the same capital per worker, which is less than
either country’s steady state. Country 1 has a higher t: t1>t2.
Which economy do you expect to see growing faster?
 If t1>t2 => who has the higher steady state?
 Who is further away from their steady state?
 Do we grow faster closer to or further away from the steady
 What about long run growth?
Question 3
Suppose that the labour force grows at rate n. The low of motion
for capital per worker is:
• ∆K = (s+n)Y –dK
• ∆K = (s)Y –dK/n
• ∆K = sY –(d+n)K
• ∆K = sY –dK
Question 3
 ∆K =K’-K= sY –dK
 By definition k=K/L where L is total population. Also,
 L grows at rate n. L’=L(1+n)
 K’/L’-K/L’= K’/L’ – K/L(1+n) = sf(K)/L(1+n) – dK/L(1+n)
 (1+n)k’-k=sf(k)-dk
 Rearranging: ∆k=sf(k)-dk-nk
Question 3
Economic intuition
 Important: not important what is the size of population, but
what matters is the growth rate
 i.e. that in the next period there are more people than in the
previous one
 i.e. there are less people in one period saving, than there are
people using the capital in the next period
 E.g. period 1: have 2 people saving a constant fraction of their
income, let’s say 10 pound each
 If population growth is zero: next period have each 10 pounds
worth of new capital (minus depreciation)
 If population doubles: each only have 5 pounds worth of new
Question 4
Assume that a war reduces a country's labor force but does not
directly affect its capital stock. Then the immediate impact will
be that:
 A. total output will fall, but output per worker will rise.
 B. total output will rise, but output per worker will fall.
 C. both total output and output per worker will fall.
 D. both total output and output per worker will rise.
Question 5
If two economies are identical (including having the same saving
rates, population growth rates, and efficiency of labor), but one
economy has a smaller capital stock, then the steady-state level of
income per worker in the economy with the smaller capital stock:
 A. will be at a lower level than in the steady state of the high
capital economy.
 B. will be at a higher level than in the steady state of the high
capital economy.
 C. will be at the same level as in the steady state of the high
capital economy.
 D. will be proportional to the ratio of the capital stocks in the
two economies.
Question 1
 There is a positive correlation between
• GDP and health
• GDP per capita and health
• GDP and pollution
• GDP per capita and pollution

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