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?