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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- 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_forwardSuppose the relationship between your study time and your grade on a History midterm is given by the following table: If you study for Your grade will be 4 hours 80 5 hours 90 6 hours 93 a) What is the "marginal grade improvement (MGI)" of the 5th hour of studying? b) What is the "marginal grade improvement (MGI)" of the 6th hour of studying? c) Why might the MGI be diminishing?arrow_forwardA firm has the production function f(X, Y) = x²/2 y1/2, where X is the amount of factor x used and Y is the amount of factor y used. On a diagram we put X on the horizontal axis and Y on the vertical axis. We draw some isoquants. Now we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew Select one: O a. is vertical. b. is horizontal. c. is a ray through the origin with slope 3. d. is a ray through the origin with slope 4. O e. has a negative slope.arrow_forward
- Suppose the relationship between your study time and your grade on a History midterm is given by the following table:If you study for Your grade will be4 hours 805 hours 906 hours 93What is the "marginal grade improvement (MGI)" of the 5th hour of studying? What is the "marginal grade improvement (MGI)" of the 6th hour of studying? Why might the MGI be diminishing?arrow_forwardGiven the production function Y=3x+2x2-0.1x3 Compute The APP and MPParrow_forward4. What if the production function for education (E) is: E=T06 B08, where T is teachers and B is buildings and materials. The cost of each teacher is $54, the material cost $144 per unit and the school has a budget of $5,000 (numbers are in ,000, but this can be ignored) a. Construct the isocost equation. b. With a MPT = 0.6T04B0.8 and MPB = 0.8T06B-02, determine the appropriate input mix to get the greatest output. Also, compute output. c. Explain what would happen in the short-run (keeping capital fixed) to the appropriate input mix if the budget where changed to $4,250. Would the input combination be different in the long-run? If so, how would it change? Explain.arrow_forward
- Find the marginal & the average functions for each of the following total function, evaluate them at Q= 3 & Q=5? 1. T = Q - 13 Q +78 2. TR =12Q-Qarrow_forwardDefine a production function F:R X X 12 F(x, x2 ) = { x₁ + x2 1 2 + if x +x >0 1 2 0 if x +x¸ = 0 1 2 > R by → + where x and x, are the amounts of two 1 2 inputs used to produce a single out - put. Given input prices w ω, > 0, > 0 and W 2 consider the problem of finding the cost minimizing input combination of producing at least an output level of one unit: mina x 1 1 (xx) ≥0 1 2 + 2x2 subject to F(x,,x) ≥ 1 and 2 Find the cost - minimizing input demand. Use second order condition and Hessian Matrixarrow_forwardwhat are the two distinct input bundles (P, W) in the diagram which give q = 48?arrow_forward
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