problem: A country has the per-worker production function y_{t} = 6 k_{t}^{0.5}, where y_{t} is output per worker and k_{t} is the capital-labor ratio. The depreciation rate is 0.1 and the population growth rate is 0.1. The saving function is:
S_{t} = 0.1 Y_{t},
Where S_{t} is total national saving and Y_{t} is total output.
a) Determine the steady-state value of capital-labor ratio?
b) Determine the steady-state value of output per worker?
c) Determine the steady-state value of consumption per worker?
problem: According to the Solow model, how would each of the given affect consumption per worker in the long run (that is, in the steady state)? Draw a figure and elucidate.
a) The destruction of a part of the nation’s capital stock in a war.
b) A permanent raise in the rate of immigration (that raises the overall population growth rate).
problem: Money demand in an economy in which no interest is paid on money is:
M_{d}/P = 500 + 0.2Y - 1000i
a) Assume that P = 100, Y = 1000, and i = 0.10. Find out real money demand, nominal money demand and velocity.
b) Supposing that the money demand function as written holds, show how velocity is influenced by a raise in real income, by an increase in the nominal interest rate, and by an increase in the price level.
problem: The income elasticity of money demand is 2/3. Real income is expected to grow by 4.5% over the next year, and the real interest rate is expected to remain constant over the next year. The rate of inflation has been zero for several years.
When the central bank wants zero inflation over the next year, what growth rate of the nominal money supply would it prefer?
problem: Suppose that prices and wages adjust rapidly and hence the markets for labor, goods, and assets are always in equilibrium. What are the effects of each of the given on real money demand and the current price level? Describe in words.
a) The temporary increase in government purchases.
b) The reduction in expected inflation.