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Chapter 10

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Chapter 10

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  1. Chapter 10 THE PARTIAL EQUILIBRIUM COMPETITIVE MODEL

  2. 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

  3. Partial Equilibrium Analysis

  4. Partial Equilibrium Analysis

  5. General vs. Partial Equilibrium

  6. General vs. Partial Equilibrium

  7. When is Partial Equilibrium Appropriate?

  8. When is Partial Equilibrium Not Appropriate?

  9. The restriction of supply ?

  10. The Four Types of Market Structure

  11. Profit Maximization

  12. Market Demand

  13. 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

  14. 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

  15. 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

  16. 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)

  17. 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

  18. 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

  19. 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)

  20. 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

  21. 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)

  22. Elasticity of Market Demand • The cross-price elasticity of market demand is measured by • The income elasticity of market demand is measured by

  23. From Market Demand Curve to the demand curve faced by the firm

  24. Timing of the Supply Response

  25. 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

  26. Pricing in the Very Short Run

  27. 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

  28. 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*

  29. A note • Increasing in quantity supplied need not come only from increased production

  30. Short-Run Price Determination

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. Geometric Meaning of es,P

  37. Classification of Elasticity of Supply

  38. 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

  39. 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

  40. Shifts in Supply and Demand Curves

  41. 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

  42. 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

  43. 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

  44. Mathematical Model of Supply and Demand

  45. 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

  46. 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

  47. 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 + Dd dQS = SPdP + Sd • Maintenance of equilibrium requires that dQD = dQS

  48. Mathematical Model of Supply and Demand • Suppose that the demand parameter () changed while  remains constant • The equilibrium condition requires that DPdP + Dd = SPdP • Because SP - DP > 0, P/ will have the same sign as D

  49. Mathematical Model of Supply and Demand • We can convert our analysis to elasticities

  50. Long-Run Analysis