Solving
p 3
(x*1
)
2/
3
x~12/
3
w1
for
x1
gives
(x*1) 2/3
3w1 px~12/ 3
.
That is,
( x*1 ) 2/ 3
px~12/ 3 3w1
so
x*1
px~12/ 3 3w1
3/ 2
p 3w1
3/ 2
x~12/ 2 .
Short-Run Profit-Maximization; A Cobb-Douglas Example
Economic Profit
A firm uses inputs j = 1…,m to make products i = 1,…n. Output levels are y1,…,yn. Input levels are x1,…,xm. Product prices are p1,…,pn. Input prices are w1,…,wm.
level of $ .
The equation of a $ iso-profit line is
py w1x1 w2x~2.
I.e.
y
w1 p
x1
w 2x~ 2 p
.
Short-Run Iso-Profit Lines短期等利润线
y
w1 p
x1
w 2x~ 2 p
has a slope of
(x*1)1/3 x~12/3
p 3w1
1/
2
x~12/
2
.
Comparative Statics of Short-Run Profit-Maximization