Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Question
Chapter 7, Problem 6E
a)
To determine
To find:The value of marginal revenue product.
b)
To determine
To find:The value of marginal factor cost production.
c)
To determine
To find:The value of L that maximize profit.
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2 Short-Run Cost Consider a firm with the Cobb-Douglas production function F (K, L) = K 1/3 L1/2 Suppose the firm currently has 64 units of capital. The wage rate is 32 per unit and the rental rate of capital is 8 per unit. (a) Determine the short-run cost function C(Q). (b) Determine the marginal cost function and average total cost function. (c) Determine the quantity at which average total cost is minimized. (d) Sketch a graph of the MC and ATC functions, indicating the efficient scale on the graph.
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Consider Delta, a price-taking single-output, single input firm with the following production function:f (z) = z4/5a) Define non decreasing returns to scale and non-increasing returns to scale in terms of the production function and give conditions under which f(z) satisfies these properties.
b) Suppose that the price of the input z is ѿ =1. Set up the cost minimization problem and solve for the conditional factor demand correspondence and the cost function.
c) Set up Delta's profit maximization problem using the cost function you derived in (b) above and solve for the supply correspondence and the profit function.
Consider the following short-run production function (where L = variable input, Q = output):Q = 10L - 0.5L2Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit.a. Determine the marginal revenue product function.b. Determine the marginal factor cost function.c. Determine the optimal value of L, given that the objective is to maximize profits.
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Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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- Consider a price-taking firm whose production function is given by q = 3 L1/5 K1/9 where L and K denote respectively the amount of labour and capital the firm uses to produce q units of output. Suppose the price of labour is w = 16, the price of capital is 24 and the price of the firm's output is p=225 . Find the firm's cost function. Then enter below the value of the firm's average cost at the point where q = 100.arrow_forwardConsider a price-taking firm whose production function is given by q = 3 (L-9)1/5 (K-5)1/9 where L and K denote respectively the amount of labour and capital the firm uses to produce q units of output. Suppose the price of labour is w = 16, the price of capital is 24 and the price of the firm's output is p=225 . Enter below the value of the firm's fixed cost.arrow_forwardGiven the Cobb Douglas Production Function of F(K,L) = AKtalphaLt(1-alpha) and assume that A = 3, t = 1, w = 1, r = 1, alpha = .5 Find the short run minimum cost function when K is fixed Find the total cost Compare the short run cost function and long run function when q = 50arrow_forward
- Consider an individual firm competing in a market with many other producers and producing an undifferentiated product (i.e., consumers consider the product from one firm to be exactly as good as the product from any other firm). Assume this firm faces a conventional production technology. The short-run production function has a small range of increasing marginal product (increasing marginal returns) and then is subject to the Law of Diminishing Marginal Product (diminishing marginal returns). Putting quantity q on the horizontal axis and dollars $ on the vertical axis, depict four important curves: Average Fixed Cost (AFC), Average Variable Cost (AVC), Average Total Cost (ATC), and Marginal Cost (MC). Label each of these curves with the subscript 0 to indicate that these are the original (or current) curves. For this question, assume the individual producers in this industry have no control over prices; they must accept the exogenously given price, P0. On a graph containing the four…arrow_forwardSuppose the long-run production function for a competitive firm is f(x1,x2)= min {3x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. A: Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. B: Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? C: Write down the formulas and draw the graphs of the average cost and marginal cost functions, as functions of y.arrow_forwardSuppose a short-run production function is described as Q=30L-0.05L^2 where L is the number of Labors used each hour. If each unit of output (Q) has a marginal revenue (price) of $5 and the marginal cost of labor is $40 per labor unit (L), how many units of labor (L) should be hired to maximize profit?arrow_forward
- Suppose the short-run production function is q = 11L². Suppose that the wage rate is $112 per unit of labor. What is the marginal cost at q = 255?arrow_forwardSuppose a company's revenue function is given by R(q)=−q3+400q2R(q)=-q3+400q2 and its cost function is given by C(q)=550+12qC(q)=550+12q, where qq is hundreds of units sold/produced, while R(q)R(q) and C(q)C(q) are in total dollars of revenue and cost, respectively.A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q)=MP(q)= B) How many items (in hundreds) need to be sold to maximize profits? Answer: hundred units must be sold. (Round to two decimal places.)arrow_forwardConsider a price-taking firm whose production function is given by q = 3 L1/5 K1/9 where L and K denote respectively the amount of labour and capital the firm uses to produce q units of output. Suppose the price of labour is w = 16, the price of capital is 24 and the price of the firm's output is p=225 . Find the firm's cost function. Then enter below the value of the firm's marginal cost at the point where q = 100.arrow_forward
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