Download Problem Set 1

Intermediate Macro 302, Spring 2009
Prof. Nilsen
1
Problem Set 3
(chapters 6 - 9)
Chapter 6
1. From 2004 to 2005 a country’s output rose from 3000 to 3500, its capital stock rose from 5,000 to 6,000,
and its labor force increased from 2000 to 2500. Suppose aK = 0.3 and aN = 0.7.
(a) How much did capital contribute to economic growth over the year?
(b) How much did labor contribute to economic growth over the year?
(c) How much did productivity contribute to economic growth over the year?
Answers:
(a) 5%
(b) 17.5%
(c) – 5 5/6 %
2. A country has the per-worker production function yt = 6k2/3 where yt is output per worker and kt is the
capital-labor ratio. The depreciation rate is 0.1 and the population growth rate is 0.1. The saving function
is S = 0.1Yt, where S is total national saving and Yt is total output.
(a) What is the steady-state value of capital-labor ratio?
(b) What is the steady-state value of output per worker?
(c) What is the steady-state value of consumption per worker?
Answers:
(a) sf(k) = (n + d)k, so 0.1 = 6k 2/3 = 0.2k; or k 1/3 = 3, so k = 27.
(b) y = 6k2/3 = 54.
(c) c = (1 – s)y = 0.9y = 48.6.
3. Country A has a capital-labor ratio that is initially twice as big as that of country B, but neither is yet in
a steady state. Both countries have the same production function, f(k) = 6k1/2 Country A has a 10%
saving rate, 10% population growth rate, and 5% depreciation rate, while country B has a 20% saving
rate, 10% population growth rate, and 20% depreciation rate.
(a) Calculate the steady-state capital-labor ratio for each country. Does the initial capital-labor ratio affect
your results?
(b) Calculate output per worker and consumption per worker for each country. Which country has the
highest output per worker? The highest consumption per worker?
(c) In general, do all the fundamental characteristics of different countries need to be identical for
convergence of output per worker?
Answers:
(a) Using the formula sf(k) = (n+
d)k, country A: 0.1 x 6k1/2 = 0.15k, or k1/2 = 4, so k =
x
1/2
1/2
6k =
k, or k
= 4, so k =
also. The initial capital-labor ratios have no effect on the steady-state
capital-labor ratios.
(b) y = 6k1/2 = 24 for both countries. c = (1 – s)y, so country A has c = 0.9y = 21.6, while country B has c = 0.8y = 19.2. The
two countries have the same capital-labor ratio and output per worker, but different consumption per
worker.
(c) Convergence can arise even if the fundamental characteristics of different countries are different.
4. What happens in the steady state to the capital-labor ratio, output per worker, and consumption per
worker when each of the following events occur? You should assume that the steady-state capital labor
ratio is below the Golden Rule level.
(a) Productivity falls.
(b) Population growth falls.
–1–
Intermediate Macro 302, Spring 2009
Prof. Nilsen
2
Answers
(a) k, y, and c all fall.
(b) k, y, and c all rise.
Chapter 7
5. Suppose the money demand function is MD/P = 1000 + 0.2Y – 1000 (r + πe).
(a) Calculate velocity if Y = 2000, r = .06, and πe = .04.
(b) If the money supply (MS) is 2600, what is the price level?
(c) Now suppose the real interest rate rises to 0.11, but Y and Ms are unchanged. What happens to
velocity and the price level? So if the nominal interest rate were to rise from 0.10 to 0.15 over the course
of a year, with Y remaining at 2000, what would the inflation rate be?
Answers:
(a) V = PY/M = Y/(M/P). From the money demand function, M/P = 1300. So V = 2000/1300 =1.54.
(b) P = Ms/(Md/P) = 2600/1300 = 2.
(c) Now Md/P =1250. So V = 2000/1250 = 1.6. P = Ms/(Md/P) = 2600/1250 = 2.08. The inflation rate would be 4%.
6. What happens to M1 and M2 due to each of the following changes?
(a) You take $500 out of your checking account and put it into a passbook savings account.
(b) You take $1000 out of your checking account and buy traveler’s checks.
(c) You take $1500 out of your money-market mutual fund and deposit into your checking account.
(d) You cash in $2000 in savings bonds and invest the money in a certificate of deposit.
Answers:
(a) M1 falls $500, M2 is unchanged (remember that M1 is part of M2).
(b) M1 and M2 are both unchanged.
(c) M1 rises $1500, M2 is unchanged.
(d) M1 is unchanged, M2 rises $2000.
Chapter 8
7. What are some of the problems with using the leading indicators to forecast recessions? If you were a
policymaker, would you rely on them?
Answer: Although the leading indicators seems to be useful for forecasting the future state of the
economy, there are a number of problems in using them. First, the data are usually revised, sometimes
substantially, so a signal from the leading indicators may be reversed later. Second, they sometimes give
incorrect signals. Third, they don’t provide much information on the severity or exact timing of the
coming recession. Finally, structural changes in the economy mean the set of indicators must be revised
periodically. Policymakers should use the leading indicators as additional information, but should not
rely on them alone.
Chapter 9
8. For each of the following changes, which equilibrium curve (IS, LM, or FE) is shifted? Draw the change
in the underlying demand or supply curves (for example, money demand and supply for the LM curve)
and show how the equilibrium curve changes.
(a) Expected inflation decreases.
(b) The future marginal productivity of capital increases.
(c) Labor supply increases.
(d) Future income declines.
(e) There’s a temporary detrimental supply shock.
–2–
Intermediate Macro 302, Spring 2009
Prof. Nilsen
Answers
(a) Money demand increases; require higher r for money market eqbm; LM shifts inward
(b) Investment increases; require higher r at given Y, so IS shifts out
(c) Full-employment labor increases; FE shifts outward
(d) Public saves more, require lower r for goods market eqbm; IS shifts inward
(e) FE shifts to the left.
9. Desired consumption is Cd = 2000 - 0.9Y – 2,000r, and desired investment is Id = 1000 – 4,000r. Real
money demand is Md/P = 300 – 2000i. Other variables are G = 0, πe = 0, P = 1, and M = 100.
(a) Find the equilibrium values of the real interest rate, consumption, investment, and GDP.
(b) Suppose money supply is raised to 200. What happens to the variables listed in part (a)?
(c) Is money neutral?
Answers
(a) Money market determines r: 300 – 2000 r = 100 => r = 10%. In goods market, Y = 2000 + 0.9Y –
2000r + 1000 – 4000 r. Rearranging, find .1 Y = 3000 – 6000 r and now inserting r = 10%, find Y =
24,000. C = 23,400 and I = 600.
(b) If M = 200, 300 – 2000 r = 200 which implies that r = 5%. Using Y = 3000 – 6000r, find Y = 27000
and C = 26200 and I = 800.
(c) Money is not neutral and, somewhat strangely, it has a greater effect on consumption than
investment.
–3–
3