*4. Consider the production function: Y = AK0.310.7 a) Show the production function has the property of constant returns to scale. [Hint: Double both K and L, and check if Y doubles] b) Obtain the per capita production function [Hint: Divide the above production function by L, and express all variables in per capita terms; e.g. y = Y/L, k = K/L using lowercase letters to denote per capita variables]. c) Draw the per capita production function with k on the horizontal axis and y on the vertical axis. Does the function show diminishing marginal productivity in k?

*4. Consider the production function: Y = AK0.310.7 a) Show the production function has the property of constant returns to scale. [Hint: Double both K and L, and check if Y doubles] b) Obtain the per capita production function [Hint: Divide the above production function by L, and express all variables in per capita terms; e.g. y = Y/L, k = K/L using lowercase letters to denote per capita variables]. c) Draw the per capita production function with k on the horizontal axis and y on the vertical axis. Does the function show diminishing marginal productivity in k?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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*4. Consider the production function: Y = AK0.310.7
a) Show the production function has the property of constant returns to scale. [Hint: Double both K and L, and check if Y
doubles]
b) Obtain the per capita production function [Hint: Divide the above production function by L, and express all variables in
per capita terms; e.g. y = Y/L, k = K/L using lowercase letters to denote per capita variables].
c) Draw the per capita production function with k the horizontal axis and y on the vertical axis. Does the function show
diminishing marginal productivity in k?
d) Assume that the value of A jumps from 1 to 2. Draw the production function before and after the change in the value of
A.

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