chapter 20 cost minimization. basic model: min x1, x2 w 1 x 1 + w 2 x 2 subject to f (x 1, x 2 ) = y...
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Chapter 20Chapter 20
Cost Minimization
Basic modelBasic model: :
min x1, x2 w1 x1 + w2 x2 subject to f (x1 , x2 ) = ygives c ( w1 , w2 , y )
Isocost lines: p351
x2 = C/w2 – w1x1/w2.
Tangency of an isocost line and an isoquant.
– MP1 (x1, x2) / MP2 (x1, x2 )= TRS(x1, x2 ) = – w 1 / w 2
Isocost lines slope= – w 1 / w 2
Isoquant f (x1 , x2 ) = y
Optimal choice
x2*
x2
x1* x1
.
Minimizing costs for
y = min{ax1 , bx2}; 完全互补 y = ax1 + bx2; 完全替代 and y = x1
a x2b. Cobb-Dougl
as
Fixed and variable costs.
(FC and VC)
Total, average, marginal, and average variable costs. (TC, AC, MC and AVC)
MC > (<) AC if and only if AC is increasing (decreasing)
MC cuts AC (AVC) at AC’s (AVC’s) extreme.
MC
AVC
AC
y
ACAVCMC
..
Chapter 21Chapter 21
Cost
Curves
The area under MC
gives VC:
∫MC = VC
MC
Variable costs
MC
y
Division of output Division of output among plants of a firm.among plants of a firm.
MC1
MC2
Typical cost Typical cost curves. curves.
c (y) = y 2 + 1.
Example:
AC MCAVC
y
MC
AVC
AC
The cost curves for c (y) = y 2 + 1
. 2
1
LR and SR cost curves.
y
AC SAC=C(y1, k* )/y
LAC=C(y)/y
. y*
Short-run and long-run average costs
y
AC Short-run average cost curves
Long-run average cost
curves y*
Short-run and long-run average costs
are costs that are not recoverable.
A special kind of fixed costs.
Sunk costs
Chapter 22Chapter 22
Firm Supply
Pure Pure competitioncompetition. .
Price Taker..
The demand curve facing a competitive firm. p380
Q
P
P*
Market price
Demand curve facing firm
Market demand
The supply decision:The supply decision:
FOC: MC ( y* ) = p.
SOC: MC ’ ( y* ) ≥ 0.
The The firm’s supply curvefirm’s supply curve is is the upward-sloping part of MCthe upward-sloping part of MC that lies above the AVC curve. that lies above the AVC curve.
The part of MC is also seen as the inverse supply function.
MC
AVC
AC
y
ACAVCMC
P
y2 y1
firm’s supply curve
Three Three equivalent waysequivalent ways to to measure the producer’s surplus measure the producer’s surplus
( = R – VC =π + FC ).( = R – VC =π + FC ). p389p389
P389 Example:
c ( y ) = y 2 + 1.
LR: p = MC ( y, k ( y ) )LR: p = MC ( y, k ( y ) )
vs
SR: p = MC ( y, k )
Chapter 23Chapter 23
Industry Supply
Horizontal summation Horizontal summation gives gives
the industry supply.
Y
P S1 S2 S1 + S2
Entry and Entry and exit. exit.
The The “zero profit” “zero profit” theorem theorem..
Free entryFree entry vs vs
barriers to entry. barriers to entry.
Economists Economists versus versus lobbyistslobbyists
Rent seeking.Rent seeking.