Economics (MindTap Course List)
13th Edition
ISBN: 9781337617383
Author: Roger A. Arnold
Publisher: Cengage Learning
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Chapter 21.3, Problem 3ST
To determine
Explain the relationship between marginal cost and marginal physical product (MPP).
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A company produces commercials. A 2-minute commercial, for example, needs exactly 5 minutes of filming and 8 minutes of editing. Let x1 denote the minutes of filming and x2 denote the minutes of editing.
a) Write down the production function and state whether it has increasing, constant, or decreasing returns to scale
b) Suppose that filming costs $45 per minute and editing costs $10 per minute. To produce a 5-minute commercial, how many minutes of filming and how many minutes of editing is needed to minimize cost?
c) Suppose that filming costs w1 per minute and editing costs w2 per minute. Let y denote the length (in minutes) of commericals produced. derive the conditional factor demand functions x1(w1,w2,y) and x2(w1,w2,y) and its cost function c(w1,w2,y)
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function.
S = 20L
0.30c0.70
In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100.
(a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost.
Min
50L + 100C
s.t.
,0.300.70
20L
= 55,000
L, C 2 0
(b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L > 0 and C > 0. Round your answers to the nearest integer.)
at (L, C) =
( 2467, 2880
2$
Chapter 21 Solutions
Economics (MindTap Course List)
Ch. 21.2 - Prob. 1STCh. 21.2 - Prob. 2STCh. 21.2 - Prob. 3STCh. 21.2 - Prob. 4STCh. 21.3 - Prob. 1STCh. 21.3 - Prob. 2STCh. 21.3 - Prob. 3STCh. 21.4 - Prob. 1STCh. 21.4 - Prob. 2STCh. 21.4 - Prob. 3ST
Ch. 21.4 - Prob. 4STCh. 21.5 - Prob. 1STCh. 21.5 - Prob. 2STCh. 21.5 - Prob. 3STCh. 21 - Prob. 1QPCh. 21 - Prob. 2QPCh. 21 - Prob. 3QPCh. 21 - Prob. 4QPCh. 21 - Prob. 5QPCh. 21 - Prob. 6QPCh. 21 - Prob. 7QPCh. 21 - Prob. 8QPCh. 21 - Prob. 9QPCh. 21 - Prob. 10QPCh. 21 - Prob. 11QPCh. 21 - Prob. 12QPCh. 21 - Prob. 13QPCh. 21 - Prob. 14QPCh. 21 - Prob. 15QPCh. 21 - Prob. 16QPCh. 21 - Prob. 17QPCh. 21 - Prob. 18QPCh. 21 - Prob. 19QPCh. 21 - Prob. 1WNGCh. 21 - Prob. 2WNGCh. 21 - Prob. 3WNGCh. 21 - Prob. 4WNGCh. 21 - Prob. 5WNGCh. 21 - Prob. 6WNGCh. 21 - Prob. 7WNGCh. 21 - Prob. 8WNGCh. 21 - Prob. 9WNG
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