Suppose that widgets can be produced using two different production techniques, A and B. The followingtable provides the total input requirements for each of five different total output levels.Q = 1Tech. K LA4 1B1 3TotalCostQ = 2KL622 5Q=1$ 6LKQ = 3K L944 8Assuming that the price of labor (PL) is $1 and the price of capital (PK) is $3, calculate the total cost ofproduction for each of the five levels of output using the optimal (least-cost) technology at each level.Q=2$ 11To do this, complete the table below by calculating the total cost of production, filling in the missingvalues using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.)Q = 5K L8127 115 12 7 15Q = 4KQ = 3$ 20LQ=4$ 27Q=5$36How many labor hours (units of labor) would be employed at each level of output? How many machinehours (units of capital)?To answer this, complete the table below for the units of labor and units of capital that would be used toproduce each level of output. (Enter your responses as whole numbers.)Q=1 Q=2 Q = 3Q=4 Q = 5

There are two production techniques, A and B Input requirement for each level of output is given…

Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q = 1 Q=2 Tech. K LK A B Q=3 L K L 4 Q=4 K L 12 7 11 8 8 5 12 7 15 4 1 6 2 9 1 3 2 5 4 Q=5 KL Assuming that the price of labor (PL) is $1 and the price of capital (PK) is $3, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level.

Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q = 1 Q=2 Tech. K LK A B Q=3 L K L 4 Q=4 K L 12 7 11 8 8 5 12 7 15 4 1 6 2 9 1 3 2 5 4 Q=5 KL Assuming that the price of labor (PL) is $1 and the price of capital (PK) is $3, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.4P

See similar textbooks

Similar questions

What is the difference between a fixed input and a variable input?
Digging calms by hand in Sunset Bay requires only labor input. The total number of calms obtained per hour (q) is given by :Q = 100√LWhere L is labor input per hour. A. Graph the relationship between q an LB. What the average productivity of labor in Sunset Bay? Graph this relationship and show that output per unit of labor input diminishes for increase in labor input. C. It can be shown that the marginal productivity of labor in Sunset By is given by:MPL =50√LGraph this relationship and show that labor’s marginal productivity is less than average productivity for all values of L . Explain why this is do.D. Explain the concept of diminishing returns to labor and how this concept related to increasing marginal costs.
The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1
A firm currently uses 40 units of labor (L) and 20 units of capital (K) to produce 400 units ofoutput. Input prices equal $30 for labor and $60 for capital, while the marginal products are 6 for labor and 3 forcapital. To minimize the cost of producing its current level of output, should the firm use more L and less K,more K and less L, or leave its input combination unchanged? Explain your answer.
Q)solve it correctly The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimized
1. Given the following production function Q = 20L2K and the unit prices of labor and capital to be Birr 48 and 12 respectively, then a. What combination of labor and capital maximizes output with a cost of Birr 720? b. What is the maximum output? c. Show the output maximizing condition graphically.
The production function for good X in the table below exhibits increasing marginal returns to capital over what outout range? Production Function for Good X Choose Multiple Choice: Between o and 1,524 Between 2,391 and 3,048 Between o and 2,991 Between 3,016 and 2,945 L* K MPx=(AQ/AK) AP=(Q/K) Marginal Product of Capital Average Product of Capital Labor Capital Output 10 57 5.7 5.70 20 324 26.7 16. 20 30 657 33.3 40 1,072 41.5 26.80 se 1,524 45.2 30.48 60 1,976 45.2 32.93 70 2,391 41.5 34.16 se 2,724 33.3 34.05 9e 2,991 A 33.23 1ee 3,848 5.7 30.48 9. 11e 3,016 -3.2 27.42 120 2,945 -7.1 24.54
6. The Miller Company is trying to determine the combination of inputs to produce a specific volume of bar stools ordered. The production function for the firm is given: Q = 14LK? The wage of a worker is $80/day and the price of a machine is $240/day. If they need to produce 4,536 bar stools per day: a. What is the optimal combination of Labor and Capital, i.e. find the cost-minimizing combination of inputs to produce 4,536 bar stools? b. What is the total cost of using the inputs found in part a?
If capital and labour are perfect complements then the marginal products of capital and labour are undefined A True Faise Question 16 A firm uses 10 units of labour and 20 units of capital to produce 10 units of output. The marginal product of labour is 0.5. If there are constant returns to scale the marginal product of labour must be 0.25 True B False Question 17 Afirm uses 10 units of labour and 30 units of capital to produce 10 units of output. The marginal product of labour is 05. If there are constant returns to scale the marginal product of labout must be 0.25 A True False
Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correct
A firm can manufacture a product according to the production function Q = 2(K)1/4 (L)3/4 where K represents capital equipment and L is labor. The company has already spent $10,000 on the 4 units capital. a. Please show the expression for the average product of labor, APL and the marginal product of labor, MPL. If workers at the firm are paid a competitive wage of $100 and the product is sold for $200 each, what is optimal level of labor usage and what is the maximum profit?
For a firm to maximize profit, it must minimize the cost of producing whatever quantity it produces. Use the isocost and isoquant tools to present a firm that is choosing the optimal levels of labor and capital (i.e., tools) to produce a certain quantity and a certain cost. Then, show in your diagram how this firm would respond if it were to expand and spend more on its inputs, assuming it is best for the firm to become more “capital intensive” as it grows. Comment on WHY a firm might best become more capital intensive as it expands, even when the relative prices of labor and capital remain unchanged.