Microeconomics
13th Edition
ISBN: 9781337617406
Author: Roger A. Arnold
Publisher: Cengage Learning
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Chapter 8.3, 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 $100.
(a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost.
Min
50L + 100C
s.t.
,0.300.70
20L
= 55,000
L, C 2 0
(b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L > 0 and C > 0. Round your answers to the nearest integer.)
at (L, C) =
( 2467, 2880
2$
What is meant by an expansion path? Illustrate expansion paths for a normal input and an inferior input.
Chapter 8 Solutions
Microeconomics
Ch. 8.2 - Prob. 1STCh. 8.2 - Prob. 2STCh. 8.2 - Prob. 3STCh. 8.2 - Prob. 4STCh. 8.3 - Prob. 1STCh. 8.3 - Prob. 2STCh. 8.3 - Prob. 3STCh. 8.4 - Prob. 1STCh. 8.4 - Prob. 2STCh. 8.4 - Prob. 3ST
Ch. 8.4 - Prob. 4STCh. 8.5 - Prob. 1STCh. 8.5 - Prob. 2STCh. 8.5 - Prob. 3STCh. 8 - Prob. 1QPCh. 8 - Prob. 2QPCh. 8 - Prob. 3QPCh. 8 - Prob. 4QPCh. 8 - Prob. 5QPCh. 8 - Prob. 6QPCh. 8 - Prob. 7QPCh. 8 - Prob. 8QPCh. 8 - Prob. 9QPCh. 8 - Prob. 10QPCh. 8 - Prob. 11QPCh. 8 - Prob. 12QPCh. 8 - Prob. 13QPCh. 8 - Prob. 14QPCh. 8 - Prob. 15QPCh. 8 - Prob. 16QPCh. 8 - Prob. 17QPCh. 8 - Prob. 18QPCh. 8 - Prob. 19QPCh. 8 - Prob. 1WNGCh. 8 - Prob. 2WNGCh. 8 - Prob. 3WNGCh. 8 - Prob. 4WNGCh. 8 - Prob. 5WNGCh. 8 - Prob. 6WNGCh. 8 - Prob. 7WNGCh. 8 - Prob. 8WNGCh. 8 - Prob. 9WNG
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- You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled 1.Find the ranges of the three stages of production. 2.Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above 3.At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? 4.Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…arrow_forwardYou have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L^2 – 0.5L^3 where L is variable input labor, Q is output of Cars assembled a. Find the ranges of the three stages of production. b. Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above. c. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L^.30K^.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant.…arrow_forwardYou have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Find the ranges of the three stages of production. Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. 4. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? 5. Assume Kia Head Office is considering hiring more laborers either at their Gwadar plant or…arrow_forward
- Demonstrate the law of diminishing yields on a graph by drawing the relationships on TP, AP and MP curves and describe it with a sentence.arrow_forwardQ1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.arrow_forwardQ1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.arrow_forward
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