17 Jul WHAT IS THE PER-WORKER PRODUCTION FUNCTION Y = F(K)?
Assume that a country’s production function is Y = K1/3L2/3.
a.
What is the per-worker production function y = f(k)?
b.
Assume that the country possesses 27,000 units of capital and 8,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function?
c.
Assume that 8 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital–labor ratio the steady-state capital–labor ratio?
d.
If the saving rate equals the steady-state level, what is consumption per worker?
Consider a production function per worker is y =k1/2, and the marginal product of capital for this production function is 0.5k(-1/2) . Assume that in this economy, capital depreciates at a rate of 10%, people consume 70% of each additional dollar of income, saving the rest. And the technological progress at a rate of 5% and population grows at a rate of 2%.
a.
If the economy is in a steady state, calculate the steady state value of y.
b.
If the economy decides to achieve the Golden Rule level of capital and actually reaches it, what will be the marginal product of capital?
Assume that the long-run aggregate supply curve is vertical at Y = 4,000 while the short-run aggregate supply curve is horizontal at P = 2.0. The aggregate demand curve is Y = 5(M/P) and M = 800.
a.
If the economy is initially in long-run equilibrium, what are the values of Pand Y?
b.
Now suppose a supply shock moves the short-run aggregate supply curve to P = 2.0. What are the new short-run P and Y?
c.
What is the velocity of money in part (b)?
d.
Suppose that after the supply shock the Fed wanted to hold output at its long-run level. What level of M would be required? If this level of M were maintained, what would be long-run equilibrium P and Y?
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