Transcript L17

L17
Cost Functions
Producers
 Producers:
have technology
y  f ( K , L)
 Returns
to scale
Constant
Decreasing
Increasing
Returns to Scale (Cobb-Douglass)
Quiz
 Assume
production function
 Doubling
inputs
A) More than doubles output
B) Less than doubles output
C) Doubles output
Profit Maximization and Price taking
 DRS:
 CRS
secrets of happiness
and IRS problem
Cost Minimization



Profit maximization: two stages
 Managers: how much to sell y
 Engineers: How to produce it
K, L
Today: second stage - cost minimization!
Technology + input prices = cost function
Isoquant
y  F ( K , L)
L
y 1
K
Technical Rate of Substitution (TRS)
MPK
TRS  

MPL
L
y 1
K
Isocost map
wK  1, wL  1
COST  K  wK  L  w L
L
K
Secret of Happiness
wK  1, wL  1
L
K
COST  K  wK  L  w L
Example
wK  1, wL  1
F ( K , L)  K  L
y 1
Arbitrary y, (DRS)
1
4
1
4
f ( K , L)  K L
wK  1, wL  1
c( y)  ?
Arbitrary y (CRS)
1
2
1
2
f ( K , L)  K L
wK  1, wL  1
c( y)  ?
Arbitrary y (IRS)
f ( K , L )  KL
wK  1, wL  1
c( y)  ?
Profit Maximization and Cost Minimization
  pF ( K , L )  w K K  w L L
Profit Maximization (DRS)
wK
wL
MPK 
, MPL 
 K * , L* , y *
p
p
Cost Minimization?