 Economics
ECON 3501 Temple University Different Production Functions Questions

ECON 3501

Temple University

ECON

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Assignment 3: Production Econ3501, Spring 2020 Moritz Ritter Temple University Question 1. Consider 2 firms with the following 2 different production functions (i.) y(L, K) = aL + bK (ii.) y(L, K) = L0.5 K 0.5 where y denotes the quantity produced and L and K are the amount of labor and capital, respectively. a. Assume K is fixed at 100. Do these production functions exhibit decreasing marginal products of labor? b. Assume K can be freely chosen. Do these production functions exhibit constant returns to scale? c. For each of the production functions, draw the isoquant associated with the output level y = 100. Assume that the rental rate for capital if 2 and the wage rate w. d. For both of the production functions, find the optimal amount of labor and capital needed to produce quantity y = 100, as a function of the wage rate. 1 . Question 2. Consider a firm with 2 different production plants that have the following production functions y1 (K) y2 (L) √ 2 K √ = 2 L = The rental rate of capital is equal to two (r = 2) and the wage rate is equal to ten (w = 10). Hence, the firm should only use plant 1 since it is cheaper to rent capital then to hire labor. True or False? Explain. 1 The MRTS for the second production function is given by: M RT S = M PL M PK = α K β L ...
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Production
Econ3501, Spring 2020
Moritz Ritter
Temple University
Date

PRODUCTION

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Question 1.
Consider 2 firms with the following 2 different production functions
(i.) y(L, K) = aL + bK
(ii.) y(L, K) = L0.5K0.5
where y denotes the quantity produced and L and K are the amount of labor and capital, respectively.
a. Assume K is fixed at 100. Do these production functions exhibit decreasing marginal products of labor?
Solution:
K is fixed at 100,
Y(L,K) = aL+ bK
Y(L,100) = aL + b(100)
Y= aL+100b
MPL= Y(l,100)/aL=1
Y(L,K)= L0.5K0.5
Y= L0.5(10)
Y = 10 L0.5
MPL= y(L,100)/ 10 L0.5

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