A cost-minimising firm produces output (q) using capital (K) and labour (L) with the production technology q = F(K, L). At the current level of output, the marginal product of labour is 4 and the marginal product of capital is 5. The firm pays $10 per unit of labour and $8 per unit of capital. In order to minimise the cost of producing the current output level, the firm should (select all that apply): a) not change its input mix because the current input mix already minimises costs. b) increase K and reduce L. c) increase L and reduce K. d) reduce both K and L. e) increase both K and L. f) none of the above.

A cost-minimising firm produces output (q) using capital (K) and labour (L) with the production technology q = F(K, L). At the current level of output, the marginal product of labour is 4 and the marginal product of capital is 5. The firm pays $10 per unit of labour and $8 per unit of capital. In order to minimise the cost of producing the current output level, the firm should (select all that apply): a) not change its input mix because the current input mix already minimises costs. b) increase K and reduce L. c) increase L and reduce K. d) reduce both K and L. e) increase both K and L. f) none of the above.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Suppose the production of Scooby Snacks at x units of labor and y units of capital is given by the Cobb-Douglas production function P(x, y) = kx"y" where m, n, k are known positive constants and m+ n = 1. The company can spend only p dollars for the production of Scooby Snacks. The cost of one unit of labor is b dollars, while the cost of one unit of capital is c dollars. Using Lagrange multipliers, find an expression for x and y where maximum production will occur?
Maximizing profit with isoprofit curvesSuppose that you are starting up a lawn-raking business. All of your workers are required to supply their own rakes, so the only cost to you is hiring labor at an hourly rate. Suppose that the market price of raking someone's yard is $24 per lawn and the hourly wage is $18 per hour. The following graph shows the production function (PF) for your business.
Production Functions and Cost Functions in the short run and in the long run Consider the production function Q=KL. The firm needs to produce 64 units of output. The price of capital is R=$16 and the price of labor is W=$4 a. In the short run, the firm's capital is fixed at K=16. How much labor will it use? What is its short run total cost? Hint: Solve it for a generic Q and plug Q=64 only at the very end b. Find the firm's short run total cost, average total cost, and marginal cost curves. Hint: If you are trying to find cost curves, Q is unknown. c. Set up a Lagrangian to find the firm's optimal inputs in.
A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. The production function is given by: Q=60L-2L^2+180K-3K^2, where Q is total output. Determine the firm's optimal combination of capital (K) and labor (L)?
Suppose w= 1 and r= 3. Solve the cost minimization problem to find L*(q) and K*(q). Then find the cost function C(q).
Question 5: Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 500 bottles per day (i. e. MPK = 500). An additional man-hour of labor would increase output by 1000 bottles per day (i. e. MPL = 1000). The price of a man- hour of labor is $50 per hour. The price of a machine-hour of fermentation capacity is $5 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally chossing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $25 per hour. How does this change the answer from part 1?
Please type the answer, and answer both questions.
Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K¹/2 [1/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.
Hi, please help with the question
Consider the following production function: f (A, B) = gamma multiply A^alpha multiply B^Beta. where A and B are the inputs and alpha, Beta, gamma are in the set (0,1). Let wA and wB the price of the two inputs. Assume wA, wB > 0. Is the production function separable?Does the production function exhibit constant returns of scale?Compute the cost function and the conditional input demand function.How do these three functions react to a change in wA? Suppose the price of both inputs double, what happens to the conditional input demand function? And to the cost function? Suppose the desired level of output double, what happens to the conditional input demand function? And to the cost function?…
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 Tech. K L A 4 1 B 1 3 Total Cost Q = 2 K L 2 5 6 2 Q=1 $6 L K Q = 3 Assuming that the price of labor (PL) is $2 and the price of capital (PK) is $1, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level. K 9 4 Q = 4 L K L 4 12 7 11 8 8 5 12 7 15 To do this, complete the table below by calculating the total cost of production, filling in the missing values using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.) Q = 5 $27 Q=2 $ 10 Q = 5 K L Q = 3 $ 17 Q = 4 $ 26 How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? To answer this, complete the table below for the units of labor and units of capital that…
Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm has the production function Q(K, L)=KxL, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output at the lowest possible cost.a) Find the marginal product of each input.b) Determine whether the production function exhibits diminishing marginal product to each input.c) Find the marginal rate of technical substitution(MRTSLK)d) How does MRTSLK change as more L, is used holding output constant.e) Find the least costly combination of labor and capital to produce 3000 units