Chapter 12 The Partial Equilibrium Competitive Model What is a partial equilibrium? Focus on the market for one good only. Not a complete economy! The market/aggregate demand for good X is the sum of all individual demands for good X . Market demand function: X ( p X ) = ∑ n i = 1 x i ( p X , p Y , m i ) , where x i ( p X , p Y , m i ) is individual i °s demand for good X . X ( p X ) obviously depends p X ( endogenous variable). X ( p X ) also depends on other prices and incomes ( exogenous) . It is the horizontal sum of all individual demand curves. Market demand curve shifts when any exogenous variable changes. For simplicity, denote the market demand as Q D ( p ) = X ( p X ) . Q. Wen (UW) Econ 400 University of Washington 1 / 54
Chapter 12 The Partial Equilibrium Competitive Model Elasticities are de±ned similarly Price elasticity: e Q , p = ∂ Q D ( p ) ∂ p p Q D ( p ) . In general, market demand cannot be written as a function of aggregate income. In short run, the market supply is the sum of all individual ±rm°s supply functions. Short-run market supply: Q S ( p ) = ∑ m i = 1 q i ( p , v , w ) . In short-run, the number of ±rms, m , is ±xed, and use SR supply functions. Example 12.2 A Short-run Supply Function there are 100 identical ±rms, each has supply function q i ( p ) = 10 3 p . The market supply function is Q S ( p ) = 100 ° 10 3 p = 1 , 000 3 p . Q. Wen (UW) Econ 400 University of Washington 2 / 54
Chapter 12 The Partial Equilibrium Competitive Model Equilibrium price determination: Q D ( p ± ) = Q S ( p ± ) . In long run, each ±rm mostly follows its long-run supply function. If the number of ±rms is ±xed exogenously, then the analysis is the same as in short run (non-negative pro±t). If ±rms are free to enter/exist the market. then the number of ±rms is determined endogenously ! When market price is higher than a ±rm°s min average cost, then a typical ±rm will have positive pro±t, and more ±rm will enter the market. the market price decreases, entry stops when it is no longer pro±table. Additional to price and quantity, the number of ±rms varies! Q. Wen (UW) Econ 400 University of Washington 3 / 54
Chapter 12 The Partial Equilibrium Competitive Model Q p Market demand (Blue), MC (Red), 6 ±rms Q. Wen (UW) Econ 400 University of Washington 4 / 54
Chapter 12 The Partial Equilibrium Competitive Model Example 12.4 In±nitely Elastic Long-run Supply (simpli±ed) Market demand: Q D ( p ) = 25 , 000 ² 3 p . A representative ±rm°s cost function: C ( q ) = 40 q 2 + 8 , 000. Average cost function: AC ( q ) = 40 q + 8 , 000 q . Marginal cost function: MC ( q ) = 80 q . To ±nd min AC, set MC ( q ) = AC ( q ) : 80 q = 40 q + 8 , 000 q ) q = 20. So the min of AC is AC ( 20 ) = 1 , 600. A ±rm°s supply function is q ( p ) = ° p 80 when p ³ 1 , 600 , 0 when p ´ 1 , 600 . Q. Wen (UW) Econ 400 University of Washington 5 / 54
Chapter 12 The Partial Equilibrium Competitive Model Example 12.4 In±nitely Elastic Long-run Supply When there are n ±rms, the market supply function is Q S ( p ) = n ° q ( p ) .
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