Suppose the production function is Cobb-Douglas and f(x1,x2)) = x11/2x3/22 1. Write an expression for the marginal product of x1. 2. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain 3. Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain

Suppose the production function is Cobb-Douglas and f(x1,x2)) = x11/2x3/22 1. Write an expression for the marginal product of x1. 2. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain 3. Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.5P

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Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an expression for the marginal product of x1. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain What is the the technical rate of substitution between x2 and x1? What is the type of returns to scale of this production function? (Increasing, decreasing, constant)
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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 Find the ranges of the three stages of production. Demonstrate the relationship between Total Production, Marginal Product and Average Product 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. 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? Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively…