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Category > Economics Posted 22 Jun 2017 My Price 7.00

A production function

A production function is a mathematical relation between a firm or country's inputs
{capital and labor) and outputs- We will use the Cobb-Douglas Production Function
Y = KaLI—sr
Where Y is output (GDP or national income): If is capital, and L is labor (number of
workers).
a. Show the production function can be written as 1111:?) = ix ln{K) + {1 — a}h1(L)_
[Use properties of logs discussed in Lecture 1]
h. Use your answer for part a and the relationship between logs and growth rates
discussed in Lecture 1 to show that find the growth rate of? ifn: = 0.3, K grows
at 2%, and L grows at 1%.
c. Find the marginal product of capital and labor by taking the derivative of Y with
respect to K and L.
d. Checkthat? = MPH»c K + t'd'lflac L- Thiswillbehandehenwetallc about
firm optimization behavior.

Answers

SuperTutor
(15)
Status NEW Posted 22 Jun 2017 02:06 AM My Price 7.00

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