Question

In: Economics

Suppose that an economy's production function is given as Y=A·K2-L1/2, and the price of output, nominal...

Suppose that an economy's production function is given as Y=A·K2-L1/2, and the price of output, nominal wage rate, and the rental price of capital are given as P, W, and R, respectively.

i) Derive the demand for labor (Lº) as a function of real wage (W/P), using a representative firm's profit maximization. That is, solve the problem of Max [P·Y– (W-L + R:K)] for L.

(ii) If the capital stock doubles (from 'K' to '2K'), how much is the demand for labor affected?

(iii) If the productivity (or technology) parameter doubles (from 'A' to '2A'), how much is the demand for labor affected?

Solutions

Expert Solution

Solution:

(i) Labor Demand function

L° = (1/4)* [(W/P)^(2/3)] * [ R^2/(AW^2)]^ (2/3)

(ii) New labor demand is 0.3968 times of L°

(iii) New labor demand is 0.6299 times of L°

Rahul Sunny answered 1 year ago
Next > < Previous

Related Solutions

Suppose that output (Y ) in an economy is given by the following aggregate production function:...
Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate δ and that savings is a constant proportion s of income. You may assume that δ > s. 1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. 2. Now suppose that the population grows at rate...
Suppose that output (Y ) in an economy is given by the following aggregate production function:...
Suppose that output (Y ) in an economy is given by the following aggregate production function: Yt = Kt + Nt where Kt is capital and Nt is the population. Furthermore, assume that capital depreciates at rate δ and that savings is a constant proportion s of income. You may assume that δ > s. 1. Suppose that the population remains constant. Solve for the steady-state level of capital per worker. 2. Now suppose that the population grows at rate...
Suppose a country has the production function Y = 2 √?, where Y = output and...
Suppose a country has the production function Y = 2 √?, where Y = output and K = physical capital. People devote 30% of output to producing new capital goods ( = 0.30). Further assume that capital depreciates at the rate of 3 percent per period (δ = 0.03). a. Suppose that the country invested in 6 units of new capital in the current period. By how many units will output change in the next period? b. What are the...
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL= K1/2 / 2L1/2 & MPK = L1/2 / 2K 1/2 a) If the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output Q...
3. A Firm has the following production function: y = L1/3K1/2 
 (a) Does this production function...
3. A Firm has the following production function: y = L1/3K1/2 
 (a) Does this production function exhibit increasing, decreasing, or constant returns to scale? Prove. 
 (b) Suppose in the short run, capital is fixed at K = 100. Assuming that the output and factor prices are p, w, and r respectively, Find firms factor demand for labor. What will the effects be when W, R, and p increase? Explain your results intuitively. 
 (c) Now, suppose the government decides to impose...
A production function is given by q = L1/3K1/3 and a total cost function is given...
A production function is given by q = L1/3K1/3 and a total cost function is given by TC = q2/3. Under what conditions could these belong to the same firm?
A production function is given by q = L1/5K1/5 and a total cost function is given...
A production function is given by q = L1/5K1/5 and a total cost function is given by TC = q2/5. Under what conditions could these belong to the same firm?
2. Suppose that the production function is Y=20K0.3N0.7. With the production function, the marginal product of...
2. Suppose that the production function is Y=20K0.3N0.7. With the production function, the marginal product of labor is MPN=14K0.3N-0.3. The capital stock is K=214. The labor supply curve is NS=100[(1-t)w]2, where w is the real wage rate, t is the tax rate on labor income, and hence (1-t)w is the after-tax real wage rate. a)Assume that the tax rate on labor income, t, equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real...
Suppose that the production function for your firm is given by: F(L,K)=L1/2K1/2 w=$1 and r=$1. In...
Suppose that the production function for your firm is given by: F(L,K)=L1/2K1/2 w=$1 and r=$1. In the long-run, how many workers and capital should you hire in order to produce Q units of output? Select one: a. L=2Q; K=Q b. L=Q; K=Q2 c. L=0.5Q; K=0.5Q d. L=Q; K=Q e. None of the above
Suppose that the production function for output in an economy is given by Yt=Kt0.25N0.75 The number...
Suppose that the production function for output in an economy is given by Yt=Kt0.25N0.75 The number of workers, N, is constant. The saving rate is s, and the depreciation rate of physical capital is δ. a) Write down the equation showing the evolution of physical capital stock over time. Explain in words. b)    Derive the steady state levels of capital per worker and output per worker in terms of the saving rate (s) and the depreciation rate (δ).
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT