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 gives c ( w 1, w 2, y )

Isocost lines: p351 x 2 = C/w 2 – w 1 x 1 /w 2.

Tangency of an isocost line and an isoquant. – MP 1 (x 1, x 2 ) / MP 2 (x 1, x 2 ) = TRS(x 1, x 2 ) = – w 1 / w 2

Isocost lines slope= – w 1 / w 2 Isoquant f (x 1, x 2 ) = y Optimal choice x 2 * x2 x2 x 1 * x 1.

Minimizing costs for y = min{ax 1, bx 2 }; 完全互补 y = ax 1 + bx 2 ; 完全替代 and y = x 1 a x 2 b. Cobb- Douglas

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 AVC MC..

Chapter 21 Cost Curves

The area under MC gives VC: ∫MC = VC

MC Variable costs MC y

Division of output among plants of a firm. MC1 MC2

Typical cost curves.

c (y) = y Example:

AC MC AVC y MC AVC AC The cost curves for c (y) = y

LR and SR cost curves.

y AC SAC=C(y 1, 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 22 Firm Supply

Pure competition. Price Taker..

The demand curve facing a competitive firm. p380 Q P P* Market price Demand curve facing firm Market demand

The supply decision: FOC: MC ( y* ) = p. SOC: MC ’ ( y* ) ≥ 0.

The firm ’ s supply curve is the upward-sloping part of MC that lies above the AVC curve. The part of MC is also seen as the inverse supply function.

MC AVC AC y AVC MC P y 2 y 1 firm’s supply curve

Three equivalent ways to measure the producer ’ s surplus ( = R – VC =π + FC ). p389

P389 Example: c ( y ) = y

LR: p = MC ( y, k ( y ) ) vs SR: p = MC ( y, k )

Chapter 23 Industry Supply

Horizontal summation gives the industry supply.

Y P S1S1 S2S2 S 1 + S 2

Entry and exit.

The “ zero profit ” theorem. The “ zero profit ” theorem.

Free entry vs barriers to entry.

Economists versus lobbyists Rent seeking.