LABOR ECONOMICS
8th Edition
ISBN: 9781260004724
Author: BORJAS
Publisher: RENT MCG
expand_more
expand_more
format_list_bulleted
Question
Chapter 3, Problem 4P
(a)
To determine
Explain the effect of substitution effect in firm’s employment and capital change.
(b)
To determine
Explain the direction in which the scale effect changes the firm’s employment and capital stock.
(c)
To determine
Explain that preference of firm in the selection of labor and capital.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Juan Valdez owns a coffee farm in Colombia. His production function is:
f(x1,x2)=(x1−1)^0.25 x2^0.5
Assume the price of input 1 is r and the price of input 2 is w.
(a) Write down an expression for the technical rate of substitution.
(b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce.
(c) Find Juan's cost function.
(d) What is the supply function of Juan's firm?
A firm has two variable factors and a productionfunction f(x1, x2) = 6x1/21X21/3. The price of its output is 3, the price of factor 1 is 3, and the priceof factor 2 is 2.– What is the optimal production output level?– What is the maximum profit-level?
1. Juan Valdez owns a coffee farm in Colombia. His production function is:
f (x1, x2) = (x1 – 1)0.25 x9-5.
Assume the price of input 1 is r and the price of input 2 is w..
(a) Write down an expression for the technical rate of substitution.
(b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan
wants to produce.
(c) Find Juan's cost function.
(d) What is the supply function of Juan's firm?
2. Show that the profit function is convex in (p, w).
3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x"
with A > 0, a1, ¤2 > 0 and a1 + a2 0, B > 0, 0 < a < 1, and 0 + p< 1.
6. Find the profit function for the CES production function.
7. Verify Hotelling's Lemma for the CES production function with B < 1.
Knowledge Booster
Similar questions
- Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?arrow_forwardInput either "increase" or "decrease" where relevant: An increase in the prices of inputs will cause the equilibrium price to ....... and the equilibrium quantity to .....arrow_forwardConsider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.arrow_forward
- 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 minimizedarrow_forwardLet the production function be given by q=2(square root of L)(square root of K)} and Price of K be 5 and the Price of L be 2. Then, the slope of the isocost line is: Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a: -.4 b: -2.5 c: -5/2 d: 2/5 e: none of the abovearrow_forwardSuppose a firm is planning to replace a labor intensive production process with an automated robot production line. Calculate the marginal rate of technical substitution (MRTS) using the following information. Labor Intensive Production: 24 workers / 3 machines Automated Robot Production: 10 workers / 30 machines Assume both production process can produce the same level of output.arrow_forward
- 2 The prices of inputs x1; x2; x3; x4 are p1 = 2; p2 = 2; p3 = 5; and p4 = 2. If the production function is given by f(x1, x2, x3, x4) = min{x1, x2} + min{x3, x4}, what is the minimum cost of producing one unit of output?.arrow_forwardThe production function is f(L,K)= L2/3K 1/3 , where L is the amount of labor and K is the amount of capital. (a. Find the marginal products of labor and capital. Is the marginal product of labor diminishing, increasing or constant in labor? (b. Sketch several isoquants in the K-L space. (c. Find the Technical Rate of Substitution between capital and labor. (d. What are the returns to scale of this production function? Please explain it with detailsarrow_forwardThe production function is f(L,K)= L2/3K 1/3 , where L is the amount of labor and K is the amount of capital. (a. Find the marginal products of labor and capital. Is the marginal product of labor diminishing, increasing or constant in labor? (b. Sketch several isoquants in the K-L space. (c. Find the Technical Rate of Substitution between capital and labor. (d. What are the returns to scale of this production function?arrow_forward
- What is the elasticity of substitution for the production function f(K, L) = K¹/4 [³/4? (a) o = 1 (b) o = -1 (c) o = 1 (d) σ = 3 2arrow_forwardDoes the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?arrow_forwardSuppose that a firm's estimated production is: Q = K³/411/4 What is the marginal rate of technical substitution (MRTS) equal to?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning
Economics (MindTap Course List)
Economics
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Cengage Learning