1) Which of the three markets that constitute a macroeconomy is irrelevant for long run growth analysis? Explain very briefly.
2) A country has the per-worker production function yt = 2kt0.5, where yt is output per worker and kt is the capital per worker. The depreciation rate is d = 0.1 and the population growth rate is n = 0.1.
a) Define the Golden Rule capital-labor ratio (per worker capital).
b) Now suppose the economy's current saving rate is 0.45. Find capital per worker and consumption per worker. Will increasing the saving rate by 0.03 increase consumption per worker?
c) Now, suppose the economy's current saving rate is 0.55. Find capital per worker and consumption per worker. Will increasing the saving rate by 0.03 increase consumption per worker?
3) A country has the per-worker production function yt = kt0.5, where yt is output per worker and kt is the capital per worker. Its saving rate is s, depreciation rate is d, and population growth rate is n. And the country is at a steady state.
a) Using a graph show what happens to steady state values of output per worker, capital per worker, and consumption per worker if the population growth rate increases to n-
b. Using a graph show what happens to steady state values of output per worker, capital per worker, and consumption per worker if the saving rate increases to s-
4) Consider the following economy:
Desired consumption Cd = 2,000 + 0.9Y - 100,000r - T
Desired investment Id = 1,000 - 45,000r
Real money demand L = Y - 6,000i
Expected inflation πe = 0.03
Full-employment output YFE = 1,000
Nominal money supply M = 2,100
Government purchases G = 500
Taxes T = 500
a) For any level of output, Y, find an equation that gives the real interest rate, r, that clears the goods market; this equation describes the IS curve.
b) For any level of output, Y, find an equation that gives the real interest rate, r, that clears the asset market; this equation describes the LM curve. Note that you will have price level, P, as an unknown in this equation.
c) Find the equilibrium values of the real interest rate, consumption, investment, and the price level.
5) For each of the following changes, what are the short-run and long-run effects on the real interest rate, output and price level? Show using IS-LM-FE diagram.
a) An increase in consumer optimism that increases desired consumption at each level of income and the real interest rate.
b) An increase in government purchases.