Only number 4b.Characterize the return of scale of production function c Question 1: Features of Production FunctionsFor each of the following production functions,1. Find the marginal product of input x1. Is the marginal product always positive? Is themarginal product increasing, constant or diminishing?Determine whether the function is separable between two groups of variables (e.g. startwith asking whether consider input 1 and 2 are separable separated from input 3 and soforth. Before you do all possible groups, do you need to? If not, why not?):3. Characterize whether or not the production function is homogenous (if it is homogenous,characterize the degree of homogeneity)2.4. Characterize the returns to scale of the production function (a) (doing the same forproduction function (b) is far more difficult, and optional)Production Functions:a) y = xf xx%b) y = In(1+ x1X2 + X1X3 + X2X3)

Solution for 4b: Production function: y = ln (1 + x1x2 + x1x3 + x2x3 )

4. Characterize the returns to scale of the production function (a) (doing the same for production function (b) is far more difficult, and optional) Production Functions: a) y = xf xx% b) y = In(1+ xX1X2 + X1X3 + X2X3)

4. Characterize the returns to scale of the production function (a) (doing the same for production function (b) is far more difficult, and optional) Production Functions: a) y = xf xx% b) y = In(1+ xX1X2 + X1X3 + X2X3)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.11P

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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 1.Find the ranges of the three stages of production. 2.Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above 3.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? 4.Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…
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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 a. Find the ranges of the three stages of production. b. 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 L you observed in (a) above c. At the end of the year it is expected that output will double with purchase of new 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? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadar plant or alternatively at the Karachi plant. What will be…
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