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6. Suppose the wage is $8, the rental rate of capital is...
6. Suppose the wage is $8, the rental rate of capital is $128, and the firm's...
6. Suppose the wage is $8, the rental rate of capital is $128, and the firm's CRS Cobb-Douglas production function is q = 3L1/3K2/3 a. What is the cost-minimizing bundle of labor and capital for producing output of q = 600 units? b. What is total cost at this bundle?
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...
consider an industry that uses capital, K and labor, L to produce output, X, according to...
consider an industry that uses capital, K and labor, L to produce output, X, according to a Cobb-Douglas production function: x=K L where 0 <X<1 is the share parameter for capital and 0<B,1 is the share parameter for labor. Denote the rental price of capital by r and the wage by w. Determine the capital to labor ratio (K/L) wh9ich minimizes the cost of producing a fixed amount of output, X. Under what conditions does optimal ratio of capital to...
1. There is a furniture manufacturer using labor (L) and capital (K) to produce tables. Its production function is given by q= 10L^.75 K^.40. It pays a wage of $5 per hour and rents capital at a rate...
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
A firm production is represented by the following Cobb-Douglas function: Q=K1/4L3/4 The rental rate, r, of...
A firm production is represented by the following Cobb-Douglas function: Q=K1/4L3/4 The rental rate, r, of capital is given by $100 and the price of labor w is $200. a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs? b. How much capital and labor should be used to produce 300 units? c. What is the minimum cost of producing 300 units? d. What is the additional cost of...
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production...
A firm has a Cobb-Douglas production function of Q = K^(0.25) L^(0.75) (a) Does this production technology exhibit increasing, constant, or decreasing returns to scale? (b) Suppose that the rental rate of capital is r = 1, the wage rate is w = 1, and the ?rm wants to produce Q = 3. In the long-run, what combination of L and K should they use? (It would be good to practice doing this with the Lagrangian, even if you can...
Question 2. In this problem, we will consider how the rental price of capital Rt and...
Question 2. In this problem, we will consider how the rental price of capital Rt and the wage rate we are determined under the assumptions of the Solow growth model. Suppose there exists a representative firm in this economy with Cobb-Douglas production function given by Y = K L-, and that the price of its output P has been normalized to 1. a) Write out the firm's profit function. (Hint: think about what total revenues and total costs are if...
TRUE OR FALSE: As a result of the increase in wage, the firms supply curve will...
TRUE OR FALSE: As a result of the increase in wage, the firms
supply curve will only change if its subsituties towards capital at
each level of output.
6. Substitution effect due to a relative change in input price Аа аа Suppose a firm is initially producing 100 units of output at point B, where the purple line (diamond symbols) labeled Isocosti lies tangent to isoquant IQ (Q = 100). Suppose that initially the wage is $10 and the rental...
Suppose that a firm had a production function given by q-21 K The rental rate for...
Suppose that a firm had a production function given by q-21 K The rental rate for the fim is $10 and the wage is s5 Solve the optimization condition for K and then fill in the value that appears in front of L K- Round to the nearest 2 decimal places if necessary.) Suppose that a firm had a production function given by q-L025k075. The wage rate (w) is $10 and the rental rate () is $10 Calculate the amount...
Please help! Please show all work! 2. (21 points. Suppose a firm's production function is given...
Please help! Please show all work!
2. (21 points. Suppose a firm's production function is given by Q = L 1/2*K12. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = 72 L 1/2K1/2and MPK = 12L12K-1/2 a) Suppose the price of labor is w=18, and the price of capital is r=2. Derive the firm's total cost function. b) What is the firm's marginal cost? c) For this problem, you will sketch the graph...
6. Suppose the wage is $8, the rental rate of capital is $128, and the firm's CRS Cobb-Douglas production function is q = 3L1/3K2/3 a. What is the cost-minimizing bundle of labor and capital for producing output of q = 600 units? b. What is total cost at this bundle?
1. There is a furniture manufacturer using labor (L) and capital
(K) to produce tables. Its production function is given by q=
10L^.75 K^.40. It pays a
wage of $5 per hour and rents capital at a rate of $15. The firm
wants to find the cost-minimizing bundle of inputs to produce
10,000 tables. Assume K is on the y-axis in what
follows.
Write out the firm’s cost function.
Calculate the firm’s isocost equation.
What is the slope of the...
Question 2. In this problem, we will consider how the rental price of capital Rt and the wage rate we are determined under the assumptions of the Solow growth model. Suppose there exists a representative firm in this economy with Cobb-Douglas production function given by Y = K L-, and that the price of its output P has been normalized to 1. a) Write out the firm's profit function. (Hint: think about what total revenues and total costs are if...
TRUE OR FALSE: As a result of the increase in wage, the firms
supply curve will only change if its subsituties towards capital at
each level of output.
6. Substitution effect due to a relative change in input price Аа аа Suppose a firm is initially producing 100 units of output at point B, where the purple line (diamond symbols) labeled Isocosti lies tangent to isoquant IQ (Q = 100). Suppose that initially the wage is $10 and the rental...
Suppose that a firm had a production function given by q-21 K The rental rate for the fim is $10 and the wage is s5 Solve the optimization condition for K and then fill in the value that appears in front of L K- Round to the nearest 2 decimal places if necessary.) Suppose that a firm had a production function given by q-L025k075. The wage rate (w) is $10 and the rental rate () is $10 Calculate the amount...
Please help! Please show all work!
2. (21 points. Suppose a firm's production function is given by Q = L 1/2*K12. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = 72 L 1/2K1/2and MPK = 12L12K-1/2 a) Suppose the price of labor is w=18, and the price of capital is r=2. Derive the firm's total cost function. b) What is the firm's marginal cost? c) For this problem, you will sketch the graph...
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