EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
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Chapter 13, Problem 3RQ
To determine
To find:Reason for difference in
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Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. 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. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces.
.c. 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?
.d. Write down the formula and draw the graph of the average cost function, as a function of y.
.e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
Suppose the long-run production function for a competitive firm is f(L,K)= L 1/3 K 1/4 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. Fixed costs are zero.
.a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y.
.b. Draw the conditional input demand functions for labor and capital in the L-y and K-y spaces.
.c. 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?
.d. Write down the formula and draw the graph of the average cost and marginal cost functions, as functions of y.
Consider a firm that produces widgets according to the following Cobb-Douglas production function:
Q = A * L^α * K^β
where: Q is the quantity of output, L is the quantity of labor, K is the quantity of capital, A is a scale parameter (total factor productivity), α and β are the output elasticities of labor and capital respectively.
Given that A = 1, α = 0.6, β = 0.4, L = 16 and K = 9,
a) Calculate the quantity of output Q.
b) If the firm increases the quantity of labor (L) to 20 while keeping the quantity of capital (K) constant, what will be the new quantity of output?
Chapter 13 Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
Ch. 13.1 - Prob. 1MQCh. 13.1 - Prob. 2MQCh. 13.2 - Prob. 1TTACh. 13.2 - Prob. 2TTACh. 13.3 - Prob. 1MQCh. 13.3 - Prob. 2MQCh. 13.5 - Prob. 1MQCh. 13.6 - Prob. 1MQCh. 13.6 - Prob. 1TTACh. 13.6 - Prob. 2TTA
Ch. 13.6 - Prob. 1.1TTACh. 13.6 - Prob. 2.1TTACh. 13 - Prob. 1RQCh. 13 - Prob. 2RQCh. 13 - Prob. 3RQCh. 13 - Prob. 4RQCh. 13 - Prob. 5RQCh. 13 - Prob. 6RQCh. 13 - Prob. 7RQCh. 13 - Prob. 8RQCh. 13 - Prob. 9RQCh. 13 - Prob. 10RQCh. 13 - Prob. 13.1PCh. 13 - Prob. 13.2PCh. 13 - Prob. 13.3PCh. 13 - Prob. 13.4PCh. 13 - Prob. 13.5PCh. 13 - Prob. 13.6PCh. 13 - Prob. 13.7PCh. 13 - Prob. 13.8PCh. 13 - Prob. 13.9PCh. 13 - Prob. 13.10P
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