1. Suppose that output is produced according to the production function Y = K [(1 - u)L]
, where K is capital, L is the labor force, and u is the natural rate of
rate is s, the labor force grows at rate n, and capital
a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of unemployment (u).
b. Write an equation that describes the steady state of this economy. Find the steady state capital per worker and steady state output per worker.
c. Does this production function have constant returns to scale? Explain.
2. 2. A small open economy is described by the following equations: C = 60 +.75(Y - T)
I = 150 - 20r
NX = 150 – 50e
M/P = Y - 40r G = 1500
M = 2000 P=2
R* = 5
Assume a balanced budget.
a. Derive and graph the IS* and LM* curves.
b. Calculate the equilibrium exchange rate, level of income, and net exports.
c. Assume a floating exchange rate. Calculate what happens to the exchange rate, the level of income, and net exports if the government increases its spending by 50. Use a graph to explain What you find.
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