The Cobb-Douglas production model states that the yearly total dollar value of the production output P in an economy is a function of labor x (the total number of hours worked in a year)
and capital y (the total dollar value of all of the stuff purchased in order to make things).
Specifically, P = axby
1−b
. By fixing P, we create what’s known as an ‘isoquant’ and we can
then solve for y as a function of x. Let’s assume that the Cobb-Douglas production model
for the country of Sasquatchia is P = 1.23x
0.4y
0.6
.
(a) Let P = 300 and solve for y in terms of x. If x = 100, what is y?
(b) Graph the isoquant 300 = 1.23x
0.4y
0.6
. What information does an ordered pair (x, y)
which makes P = 300 give you? With the help of your classmates, find several different
combinations of labor and capital all of which yield P = 300. Discuss any patterns you
may see.