Suppose the firm's production function is Q = K¹/3L2/3, where the MPK = [2/3 and MPL 3K-2/3 13 2K-¹/3 31¹/3 If the rental rate of capital R is $35 and the wage rate Wis $70, how many units of labor and capital should the firm use to produce 12 units of output? L = 18; K = 9 L = 12; K = 12 L = 9; K= 18 L = 24; K = 24 =

Suppose the firm's production function is Q = K¹/3L2/3, where the MPK = [2/3 and MPL 3K-2/3 13 2K-¹/3 31¹/3 If the rental rate of capital R is $35 and the wage rate Wis $70, how many units of labor and capital should the firm use to produce 12 units of output? L = 18; K = 9 L = 12; K = 12 L = 9; K= 18 L = 24; K = 24 =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the production function from earlier: Quantity of Haircuts 20 15 10 0+0 0 N 2 8 14 O Increasing marginal productivity O Constant marginal productivity O Decreasing marginal productivity 3 19 23 Labor (hours) 27 26 Total Product Curve From 1 labor hour up to 7 labor hours, what sort of marginal productivity does this production function have?
Consider 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.
Suppose that a firm has production function F(L, K) = L^2/3 K^1/3 for producing widgets, thewage rate for labor is w = $400, and the rental rate of capital is r = $25.a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s costminimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.d) Determine this firm’s minimum cost of producing 120 units.e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s costfunction C(Q). Show your work.
5. Selpats produces pens with the production function f(k, l) = 200vkl. The price of capital is wk = 40 and the price of labor is wL = 10. (i) Determine the optimal input bundle for producing y pens in the long run and find the long-run cost function. (ii) Determine the optimal input bundle for producing y = 10,000 pens in the long run. (iii) Now suppose that capital is fixed at k = 25 in the short run. Find the short-run total cost function and the short-run marginal cost function. Explain the relationship between the short-run and long-run marginal costs when y = 10,000. (iv) Suppose that the price of output is p. Which value of y maximizes short-run profit? р.
1/2 Consider a firm with the production function ƒ(x₁, x₂) = x¹/²x₂. The price of the two inputs is ₁ = 2 and w₂ = 1. If x₁ = x₂ = 16, the marginal product of input 1 is When ₁ is increasing and 2 stays the same, the marginal product of input 1 is Constant Decreasing Increasing This production function has Constant returns to scale Decreasing returns to scale O Increasing returns to scale None of the other answers is correct Does the production function have a diminishing technical rate of substitution? No Yes
Suppose a firm's production function is Q=200L +5L2-0.08L³. Which of the following is the Average Production of Labor (APL)? Oa. 200+10L-0.24L² Ob. 10L-0.24L² Oc. 5L-0.08L² Od. 200+5L-0.08L²
dien There are two factors in a production function y = x 113 x₂¹1³. The market price of each unit ofy is p=3, and the factor prices are w₁=1 and W₂=2 for x₁ and X₂ respectively. variable (a). Calculate your cost function as a function of y if X, and x₂ are both barible factors. (b). Now derive the functions of average and marginal cost and plot them against quantity (C). Solve for your optional output of y. Calculate the ratio of two factors (X₁/X₂) (d). In the short run the fixed factor is set at X₂=1. What is the new optimal output level now?
Consider the following table illustrating the production function of gadgets. Furthermore, suppose the firm has fixed costs of $2,000/day and the wage rate is $250/day. What is the firm's variable cost of producing 2,600 gadgets? a $1,000 b $1,750 c $2,000 d none of the above
Please help solve for (b) what is long run cost in a?