A firm is employing 100 hours of labor and 50 tons of cement to produce 500...
- A firm is employing 100 hours of labor and 50 tons of cement to produce 500 blocks. Labor costs $4 per hour and cement costs $12 per ton. For the quantities employed, MPL = 3 and MPC = 2. Show this situation in an isoquant-isocost diagram. Is the firm producing at minimum cost? If not, explain and show in the diagram, how the firm can produce the same output at a lower total cost.
Homework Answers
The firm is employing 100 hours of labor and 50 tons of cement to produce 500 blocks. This is shown below in the diagram. Wage rental ratio is w/r = 4/12 = 1/3. At the same time MRTS = MPL/MPK = 3/2. Note that at the current combination of (L = 100, K = 50), MRTS > w/r. When this happens it implies that labor is more productive. This also implies that the firm is not producing at minimum cost. To reduce the cost, firm should increase the use of labor and reduce capital usages so that MRTS declines and reaches the price ratio of 1/3/ This is shown below cost minimizing bundle is (L*, K*).
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A firm is employing 100 hours of labor and 50 tons of cement to
produce 500...
Question 7 rding to the production function: uses labor and machines to produce output according to...
Question 7 rding to the production function: uses labor and machines to produce output according to the where Lis ALK) = 41/212, ere is the number of units of labor used and K is the amount of capita or is $40 per unit and the cost of employing capital is $10 per unit. mount of capital employed. The cost (0): On the graph below, draw an isocost line for this firm that includes combin capital and labor that cost $400...
2. Assume that a firm needs to produce 500 units of output and it has ability...
2. Assume that a firm needs to produce 500 units of output and it has ability to choose how much capital and labor to use as inputs. Firm's production function and marginal products of factors are 2VL, and MPK 100L ых 100K . Use this information to answer the following questions. In your computations keep at least three decimal places. (a) If initial wage w is $12.50 and rental rate of capital, r, is $17.50, find the cost-minimizing labor- capital...
A firm uses capital and labor to produce output according to the production q = 4VLK...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
A firm uses 100 hours of labor and 20 units of capital to produce 5,000 bicycles...
A firm uses 100 hours of labor and 20 units of capital to produce 5,000 bicycles a day. Labor’s marginal product is 4 bicycles per day and the marginal product of capital is 10 bicycles per day. Each unit of labor costs $20 and each unit of capital costs $40 per hour. If the firm wants to continue producing 5,000 bicycles per day at the lowest possible cost, it should A. Continue using 100 hours of labor and 20 units...
9. A firm uses capital and labor to produce a single output good. The production function...
9. A firm uses capital and labor to produce a single output good. The production function is given by F(K,L)=K^0.5L, where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, respectively r=$5 and w=$6. Based on this information, characterize the optimal (output maximizing) allocation of inputs given that the firm decided to limit its total cost to $12,000. Illustrate your solution graphically:...
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...
15 09. 00 points) Suppose that a firm's cost per unit of labor (w) is $30 per day and its cost per a. Draw the isocost line for a total cost per day of s15,000. (Base case) and Draw the What...
15 09. 00 points) Suppose that a firm's cost per unit of labor (w) is $30 per day and its cost per a. Draw the isocost line for a total cost per day of s15,000. (Base case) and Draw the What are the maximum amount of K and L possibly used to produce 100 units? unit of capital (r) is $50 per day isoquant curve when this firm is producing efficiently, assuming output is 100 units b. If the price...
5. The marginal product of labor in the production of computer chips is 50 chips per...
5. The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/2. What is the marginal product of capital? 6. Suppose that a firm's production function is q = 10LT/2K1/2. The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a. The firm is currently producing 100 units of...
The following graph illustrates various cost lines (aka isocost lines), where units of labor are measured...
The following graph illustrates various cost lines (aka isocost lines), where units of labor are measured along the horizontal axis, units of capital are measured along the vertical axis. Assume the wage rate is $20 per unit of labor and the rental rate is $100 per unit of capital. - Isocost Lines (ICL) Units of Capital ICL3 ICL ICL 500 1 000 1 500 Units of Labor 2 000 2 500 3 000 Figure Description: Units of labor are measured...
Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and u...
Equation Description: A firm is attempting to minimize total
cost subject to sufficiently employing units of labor and units of
capital to produce an output level at least as large as a specified
output quota. Total cost equals the cost to employing units of
labor plus the cost to employing units of capital. A firm's
production function is the product of two terms: the
first term is units of capital raised to the .25 power; and, the
second term is units...
Question 7 rding to the production function: uses labor and machines to produce output according to the where Lis ALK) = 41/212, ere is the number of units of labor used and K is the amount of capita or is $40 per unit and the cost of employing capital is $10 per unit. mount of capital employed. The cost (0): On the graph below, draw an isocost line for this firm that includes combin capital and labor that cost $400...
2. Assume that a firm needs to produce 500 units of output and it has ability to choose how much capital and labor to use as inputs. Firm's production function and marginal products of factors are 2VL, and MPK 100L ых 100K . Use this information to answer the following questions. In your computations keep at least three decimal places. (a) If initial wage w is $12.50 and rental rate of capital, r, is $17.50, find the cost-minimizing labor- capital...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
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...
15 09. 00 points) Suppose that a firm's cost per unit of labor (w) is $30 per day and its cost per a. Draw the isocost line for a total cost per day of s15,000. (Base case) and Draw the What are the maximum amount of K and L possibly used to produce 100 units? unit of capital (r) is $50 per day isoquant curve when this firm is producing efficiently, assuming output is 100 units b. If the price...
5. The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/2. What is the marginal product of capital? 6. Suppose that a firm's production function is q = 10LT/2K1/2. The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a. The firm is currently producing 100 units of...
The following graph illustrates various cost lines (aka isocost lines), where units of labor are measured along the horizontal axis, units of capital are measured along the vertical axis. Assume the wage rate is $20 per unit of labor and the rental rate is $100 per unit of capital. - Isocost Lines (ICL) Units of Capital ICL3 ICL ICL 500 1 000 1 500 Units of Labor 2 000 2 500 3 000 Figure Description: Units of labor are measured...
Equation Description: A firm is attempting to minimize total
cost subject to sufficiently employing units of labor and units of
capital to produce an output level at least as large as a specified
output quota. Total cost equals the cost to employing units of
labor plus the cost to employing units of capital. A firm's
production function is the product of two terms: the
first term is units of capital raised to the .25 power; and, the
second term is units...
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