Microeconomics Handout 7
Microeconomics, Fall 2007, Dr. Laury
A Mathematical Treatment of Production and Cost Theory
•
Let
L
=labor and
K
=capital.
•
Your production function is a CobbDouglas one of the form
q
=
K
0.5
L
0.5
.
•
You are told that the wage rate is $5 and the rental rate of capital is $20.
•
You would like to produce an output of 100 sweets.
Notice that here we are fixing output and letting cost vary.
(Note in theory of consumer choice, we did
not fix utility.
Rather, we had a given income and allowed utility to vary.)
Because of duality, however,
we can really do either.
How much capital and labor should you choose?
(Hint: find the MRTS and set this equal to w/r; next,
solve for the optimal ratio of labor to capital, then for q = 100, determine how much L and K you need)
L
K
MP
MRTS
MP
=
Recall that you find the MP by taking the derivative of the production function with respect to the
variable you’re interested in.
For example, the marginal product of labor is the derivative of the
production function with respect to L.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 Laury
 Economics, Microeconomics, Equals sign, Mathematics in medieval Islam, MRTS

Click to edit the document details