The production function of a firm is x= A* l^a* k^(1-a-b)*e^b. l is labor, k is capital, e is energy, x is output (sold at price p) a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale} Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Setup the profit maximization problem for the firm. d) Find the optimality conditions for all the inputs in the production function. e)Find the input demand functions for labor, capital, and energy f) Find the optimal supply function for x.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter7: Production Economics
Section: Chapter Questions
Problem 10E
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The production function of a firm is x= A* l^a* k^(1-a-b)*e^b. l is labor, k is capital, e is energy, x is output (sold at price p)

a) What is the interpretation of A?

b) Under what condition(s) does the production function exhibit constant returns to scale} Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing?

c) Setup the profit maximization problem for the firm.

d) Find the optimality conditions for all the inputs in the production function.

e)Find the input demand functions for labor, capital, and energy

f) Find the optimal supply function for x.

g) Setup the cost minimization problem Show the relevant Technical Rates of substitution.

 

(I mainly have concerns for d), e), f) questions)

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