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Chapter 10. THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL. CONTENTS. Partial Equilibrium Analysis Market Demand Timing of the Supply Response Pricing in the Very Short Run Short-Run Price Determination Shifts in Supply and Demand Curves Mathematical Model of Supply and Demand

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## Chapter 10

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**Chapter 10**THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL**CONTENTS**• Partial Equilibrium Analysis • Market Demand • Timing of the Supply Response • Pricing in the Very Short Run • Short-Run Price Determination • Shifts in Supply and Demand Curves • Mathematical Model of Supply and Demand • Long-Run Analysis • Shape of the Long-Run Supply Curve • Comparative Statics Analysis of Long-Run Equilibrium- industry structure • Producer Surplus in the Long Run**Market Demand**• Assume that there are only two goods (x and y) • An individual’s demand for x is Quantity of x demanded = x(px,py,I) • If we use i to reflect each individual in the market, then the market demand curve is Same price Different distribution**Market Demand**• To construct the market demand curve, PX is allowed to vary while Pyand the incomeof each individual and preferences are held constant • If each individual’s demand for x is downward sloping, the market demand curve will also be downward sloping**Individual 1’s**demand curve Individual 2’s demand curve Market demand curve px* X x1 x2 x2* X* x1* x1* + x2* = X* Market Demand To derive the market demand curve, we sum the quantities demanded at every price px px px x x x**Shifts in the MarketDemand Curve**• The market demand summarizes the ceteris paribus relationship between X and px • changes in px result in movements along the curve (change inquantity demanded) • changes in other determinants of the demand for X cause the demand curve to shift to a new position (change in demand)**Shifts in Market Demand**• individual 1’s demand for oranges is given by x1 = 10 – 2px + 0.1I1 + 0.5py and individual 2’s demand is x2 = 17 – px + 0.05I2 + 0.5py • The market demand curve is X = x1 + x2 = 27 – 3px + 0.1I1 + 0.05I2 + py • If py = 4, I1 = 40, and I2 = 20, the market demand curve becomes X = 27 – 3px + 4 + 1 + 4 = 36 – 3px**Shifts in Market Demand**• If py rises to 6, the market demand curve shifts outward to X = 27 – 3px + 4 + 1 + 6 = 38 – 3px • note that X and Y are substitutes • If I1 fell to 30 while I2 rose to 30, the market demand would shift inward to X = 27 – 3px + 3 + 1.5 + 4 = 35.5 – 3px • note that X is a normal good for both buyers**Generalizations**• Suppose that there are n goods (xi, i = 1,n) with prices pi, i = 1,n. • Assume that there are m individuals in the economy • The j th’s demand for the i th good will depend on all prices and on Ij xij = xij(p1,…,pn, Ij)**Generalizations**• The market demand function for xi is the sum of each individual’s demand for that good • The market demand function depends on the prices of all goods and the incomes and preferences of all buyers**Elasticity of Market Demand**• The price elasticity of market demand is measured by • Market demand is characterized by whether demand is elastic (eQ,P <-1) or inelastic (0> eQ,P > -1)**Elasticity of Market Demand**• The cross-price elasticity of market demand is measured by • The income elasticity of market demand is measured by**From Market Demand Curve to the demand curve faced by the**firm**Timing of the Supply Response**• In the analysis of competitive pricing, the time period under consideration is important • very short run • no supply response (quantity supplied is fixed) • short run • existing firms can alter their quantity supplied, but no new firms can enter the industry • long run • new firms may enter an industry**Pricing in the Very Short Run**• In the very short run (or the market period), there is no supply response to changing market conditions • price acts only as a device to ration demand • price will adjust to clear the market • the supply curve is a vertical line • Perishable goods and antiques**When quantity is fixed in the**very short run, price will rise from P1 to P2 when the demand rises from D to D’ P2 D’ Pricing in the Very Short Run Price S P1 D Quantity Q***A note**• Increasing in quantity supplied need not come only from increased production**Short-Run Price Determination**• What’s short-run? • The number of firms in an industry is fixed • These firms are able to adjust the quantity they are producing • they can do this by altering the levels of the variable inputs they employ**Perfect Competition**• A perfectly competitive industry is one that obeys the following assumptions: • there are a large number of firms, each producing the same homogeneous product, so, each firm is a price taker (its actions have no effect on the market price) • Freedom to entry and exit • information is perfect • transactions are costless**Firm A’s**supply curve sB sA Market supply curve Firm B’s supply curve S P1 q1B Q1 q1A q1A + q1B = Q1 Short-Run Market Supply Curve To derive the market supply curve, we sum the quantities supplied at every price P P P quantity quantity Quantity**Short-Run Market Supply Function**• The short-run market supply function shows total quantity supplied by each firm to a market • Firms are assumed to face the same market price and the same prices for inputs**Short-Run Supply Elasticity**• The short-run supply elasticity describes the responsiveness of quantity supplied to changes in market price • Because price and quantity supplied are positively related, eS,P > 0**Equilibrium Price Determination**• An equilibrium price is one at which quantity demanded is equal to quantity supplied • neither suppliers nor demanders have an incentive to alter their economic decisions • An equilibrium price (P*) solves the equation: The equilibrium price depends on many exogenous factors**D’**Equilibrium Price Determination Price Price Price SMC S q’ d SAC P2 P2 P2 profit q’ P1 P1 P1 profit D d Q1 Q2 Quantity q2 q1 q1 q2 Quantity q’1 output A typical firm The market A typical individual The equilibrium price services two functions: first act to signal for firm to make output decision ; second ration demand for consumer**Shifts in Supply and Demand Curves**• Demand curves shift because • incomes change • prices of substitutes or complements change • preferences change • Supply curves shift because • input prices change • technology changes • number of producers change**Shifts in Supply**Small increase in price, large drop in quantity Large increase in price, small drop in quantity Price Price S’ S’ S S P’ P’ P P D D Quantity Q’ Q Quantity Q’ Q Elastic Demand Inelastic Demand**Shifts in Demand**Small increase in price, large rise in quantity Large increase in price, small rise in quantity Price Price S S P’ P’ P P D’ D’ D D Quantity Q Q’ Quantity Q Q’ Elastic Supply Inelastic Supply**Mathematical Model of Supply and Demand**• Suppose that the demand function is represented by QD = D(P,) • is a parameter that shifts the demand curve • D/ = D can have any sign • D/P = DP < 0**Mathematical Model of Supply and Demand**• The supply relationship can be shown as QS = S(P,) • is a parameter that shifts the supply curve • S/ = S can have any sign • S/P = SP > 0 • Equilibrium requires that QD = QS**Mathematical Model of Supply and Demand**• To analyze the comparative statics of this model, we need to use the total differentials of the supply and demand functions: dQD = DPdP + Dd dQS = SPdP + Sd • Maintenance of equilibrium requires that dQD = dQS**Mathematical Model of Supply and Demand**• Suppose that the demand parameter () changed while remains constant • The equilibrium condition requires that DPdP + Dd = SPdP • Because SP - DP > 0, P/ will have the same sign as D**Mathematical Model of Supply and Demand**• We can convert our analysis to elasticities

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