This gives us: pMP1=w1
Important: We have assumed that MP1 is decreasing in x1
编辑ppt
10
Comparative Statics of Short-Run Profit-Maximization
What happens to the short-run profit-maximizing production plan as the output price p changes?
编辑ppt
11
Comparative Statics of Short-Run Profit-Maximization
The equation of a short-run iso-profit line
is
yw p 1x1p w 2x ~2
so an increase in p causes a reduction in the slope of the family of iso-profit lines
Profit-Maximization
编辑ppt
1
What Do We Do in this Chapter?
After working our “producer’s budget sets” (production sets), We are working on “producer’s choices” Please pay attention to the similarity and differences between “producer’s choices” and “consumer’s choices”
The equation of an iso-profit line is
p y w 1 x 1 w 2 x ~ 2 . I.e. yw p 1x1p w 2x ~2.
编辑ppt
5
Short-Run Iso-Profit Lines
y
Slopesw1 p
x1
编辑ppt
6
Short-Run Profit-Maximization
y
y*
y f(x 1 ,x ~ 2 )
Slopesw1 p
x
* 1
编辑ppt
x1
14
A Useful Math: The Envelope
Theorem
Suppose x* maximizes g (x; t), where t is a parameter;
function and the maximal iso-profit line are
equal.
y*
M P1
w1 p
Slopesw1 p
a
t
(
x
* 1
,
x~
2
,
y*
)
Hale Waihona Puke x* 1编辑ppt
x1
8
Short-Run Profit-Maximization
M P 1w p 1 pM P 1w 1
a competitive firm, which is a tiny relative to the market size and takes prices p1,…,pn w1,…,wm as given constants;
编辑ppt
3
Short-run Economic Profit
Suppose the firm is in a short-run circumstance in which x2x ~2. Its short-run production function is
编辑ppt
9
A Mathematical Approach to Short-Run Profit-Maximization
Mathematically, the firm’s short run
problem is: Maximize p y w 1 x 1 w 2 x ~ 2 .
Subject to: y f(x 1 ,x ~ 2 ).
pMP1 is the marginal revenue product of input 1, the rate at which revenue increases with the amount used of input 1. If p M P 1w 1then profit increases with x1. If p M P 1w 1then profit decreases with x1.
编辑ppt
2
Economic Profit
The economic profit generated by (x1,…,xm,y1,…,yn) is
p 1 y 1 p n y n w 1 x 1 w m x m .
Notes: For the time being, w e restrict to the case of
y f(x 1 ,x ~ 2 ).
The firm’s fixed cost is F C w 2 x ~ 2 and its profit function is
p y w 1 x 1 w 2 x ~ 2 .
编辑ppt
4
Short-Run Iso-Profit Lines
An iso-profit line contains all the production plans that yield the same profit level.
y
y f(x 1 ,x ~ 2 )
Slopesw1 p
编辑ppt
x1
7
Short-Run Profit-Maximization
At the short-run profit-maximizing plan, y the slopes of the short-run production
编辑ppt
12
Comparative Statics of Short-Run
Profit-Maximization
y
y f(x 1 ,x ~ 2 )
y* Slopesw1 p
x
* 1
编辑ppt
x1
13
Comparative Statics of Short-Run
Profit-Maximization