Suppose the production function in Europe is Y = K1/3L2/3, where K is the amount of...
Suppose the production function in Europe is Y = K1/3L2/3, where K is the amount of land and L is the amount of labor. The economy begins with 8,000 units of land and 1,000,000 units of labor. Use a calculator and equations in the chapter to find a numerical answer to each of the following questions.
a How much output does the economy produce?
b What are the wage and the rental price of land?
c What amount of output is due to labor?
d If a plague kills half the population, what is the new level of output?
e What is the new wage and rental price of land?
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Suppose the production function in Europe is Y =
K1/3L2/3, where K
is the amount of...
Suppose the firm's production function is Q = K1/3L2/3. a. If the rental rate of capital...
Suppose the firm's production function is Q = K1/3L2/3. a. If the rental rate of capital R = $30 and the wage rate W = $40, what is the cost-minimizing capital-to-labor ratio? b. If the rental rate of capital R is $35 and the wage rate W is $70, and assuming the same production function, how many units of labor and capital should the firm use to produce 12 units of output? c. What is the total cost of producing...
Work It Out. Consider an economy with the following Cobb-Douglas production function: Y= 5K/3L2/3 where L...
Work It Out. Consider an economy with the following Cobb-Douglas production function: Y= 5K/3L2/3 where L the wag the sect are will a. If w wh a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.) b. The economy has 27,000 units of capital and a labor force of 1,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage,...
3. A closed economy has a production function: Y-K1 3L2/3, where K denotes machines and L...
3. A closed economy has a production function: Y-K1 3L2/3, where K denotes machines and L denotes workers. The population grows at a rate 2% per year and there is no technological progress. The depreciation rate is 3%. The saving rate, s, depends on the level of capital per worker, k, as follows: 5% if k < 5 (7k-30)% if 5 < k < 10 40% if k > 10 8 There are three steady states with k > 0:...
You are given the following production function Q = K1/3L2/3, where Q is output, L is...
You are given the following production function Q = K1/3L2/3, where Q is output, L is labor, and K is capital. First, calculate the marginal product of capital and the marginal product of labor. Next, calculate the marginal rate of technical substitution of labor for capital, MRTSL,K. What does this tell you about the production function?
1. Consider the following production functions. In each case determine if: • the function is Cobb...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
1. Suppose the production function in an economy is Y- of capital and L is the...
1. Suppose the production function in an economy is Y- of capital and L is the amount of labor. The economy begins with 8I units of capital and 16 units of labor. a. Suppose also, that one more unit of labor is added to the production process every year for the next four years. What is the marginal product of labor for each year? b. Now, suppose the wage paid per hour is $1.13, the rental price of capital is...
Is my answer correct? Suppose that a firm's short-run production function is F(K,L) = L+VKL, where...
Is my answer correct?
Suppose that a firm's short-run production function is F(K,L) = L+VKL, where capital is fixed at K = 4. The rental rate of capital is $24 and the wage rate is $2. The variable cost of production of 48 units of output is (Hint: The amount of labor required to produce 48 units of output is an integer.) 0 $24 0 0 0
5. Suppose a firm has the production function Q = K1/2 L1/4 M1/4 The wage rate...
5. Suppose a firm has the production function Q = K1/2 L1/4 M1/4 The wage rate w = 16 , rental rate r = 2 , and the price of the materials m = 1. 1) Suppose in the short run, K is fixed at K *. What’s the solution to the firm’s short run cost-minimization problem? 2) What is the solution to the firm’s long run cost minimization problem given that the firm wants to produce Q units of...
4. Suppose that the production is described by Y = F(KL) = AK0.40.6 where A is...
4. Suppose that the production is described by Y = F(KL) = AK0.40.6 where A is a constant greater than zero that measures the productivity of the available technology. K denotes the capital stock, while L is the total amount of labor. a. Suppose that A = 1, K = 10, and L = 20. What are the real wage and the real rental price of capital in this economy? b. Suppose that a hurricane destroys the capital stock by...
5. Suppose a firm has the production function Q=K1/2 [4M1/4 The wage rate w=16, rental rate...
5. Suppose a firm has the production function Q=K1/2 [4M1/4 The wage rate w=16, rental rate r=2, and the price of the materials m=1. 1) Suppose in the short run, K is fixed at K*. What's the solution to the firm's short run cost-minimization problem? 2) What is the solution to the firm's long run cost minimization problem given that the firm wants to produce Q units of output? 3) Suppose that Q = 10,K* = 20. Compare the long...
Work It Out. Consider an economy with the following Cobb-Douglas production function: Y= 5K/3L2/3 where L the wag the sect are will a. If w wh a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.) b. The economy has 27,000 units of capital and a labor force of 1,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage,...
3. A closed economy has a production function: Y-K1 3L2/3, where K denotes machines and L denotes workers. The population grows at a rate 2% per year and there is no technological progress. The depreciation rate is 3%. The saving rate, s, depends on the level of capital per worker, k, as follows: 5% if k < 5 (7k-30)% if 5 < k < 10 40% if k > 10 8 There are three steady states with k > 0:...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
1. Suppose the production function in an economy is Y- of capital and L is the amount of labor. The economy begins with 8I units of capital and 16 units of labor. a. Suppose also, that one more unit of labor is added to the production process every year for the next four years. What is the marginal product of labor for each year? b. Now, suppose the wage paid per hour is $1.13, the rental price of capital is...
Is my answer correct?
Suppose that a firm's short-run production function is F(K,L) = L+VKL, where capital is fixed at K = 4. The rental rate of capital is $24 and the wage rate is $2. The variable cost of production of 48 units of output is (Hint: The amount of labor required to produce 48 units of output is an integer.) 0 $24 0 0 0
4. Suppose that the production is described by Y = F(KL) = AK0.40.6 where A is a constant greater than zero that measures the productivity of the available technology. K denotes the capital stock, while L is the total amount of labor. a. Suppose that A = 1, K = 10, and L = 20. What are the real wage and the real rental price of capital in this economy? b. Suppose that a hurricane destroys the capital stock by...
5. Suppose a firm has the production function Q=K1/2 [4M1/4 The wage rate w=16, rental rate r=2, and the price of the materials m=1. 1) Suppose in the short run, K is fixed at K*. What's the solution to the firm's short run cost-minimization problem? 2) What is the solution to the firm's long run cost minimization problem given that the firm wants to produce Q units of output? 3) Suppose that Q = 10,K* = 20. Compare the long...
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