Answered: c) Compute average cost (AC) at each…

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:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

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Question

Suppose a firm uses capital (K) and labor (L) to produce widgets according to the production function Q =

K^(1/4)L^(1/4)

(KL)^(1/4),

where Q is output. The goal in this problem is to find the firm's total and marginal cost functions. In order to derive the cost function, the first step is to find the location of the cost-minimizing bundle on any given isoquant. To get a numerical answer, recall that the slope of an isoquant is

-MPL/MPK

(K is on the vertical axis). Using calculus, it can be shown that this slope formula reduces to -K/L. For example, consider the input bundle with K = 8, L = 2 on the isoquant with Q = 2 (note that 2 =

161/4

). The formula indicates that the slope at this point is -4 = -8/2. In fact, the formula tells us that regardless of which isoquant an input bundle is on, the slope will be -4 as long as the ratio of K to L is 4:1. Similarly, the isoquant slope will be -1 whenever the ratio of K to L is 1:1.

In answering the following questions, use integer values only (don't enter unneeded decimal points).

c) Compute average cost (AC) at each level of output by dividing C(Q) by Q, indicating your results below:
AC
d) The next step is to find the firm's marginal cost function. MC is defined in the usual way: it's the cost of an extra unit of output given a particular starting level of Q. For example, marginal cost at Q 1, or MC(1), equals C(2)
marginal cost for all the different output levels, showing the results below:
C(1). MC(2) C(3) - C(2), and so on. Using the results of part (b). compute
QMC
1
2
e) On a piece of paper, graph both the MC and AC functions. They are
O A.
convex, upward sloping curves
O B.
upward-sloping straight lines
O horizontal lines

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