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Chapter 16

Chapter 16. General Equilibrium. General Equilibrium Analysis. To study how markets interrelate, we can use general equilibrium analysis The feedback effect is the price or quantity adjustment in one market caused by price and quantity adjustments in related markets.

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Chapter 16

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  1. Chapter 16 General Equilibrium

  2. General Equilibrium Analysis • To study how markets interrelate, we can use general equilibrium analysis • The feedback effect is the price or quantity adjustment in one market caused by price and quantity adjustments in related markets Chapter 16

  3. Two Interdependent Markets – Moving to General Equilibrium • Scenario • The competitive markets of: • DVD rentals • Movie theater tickets • Changing prices in one market are likely to affect the other market Chapter 16

  4. Two Interdependent Markets – Moving to General Equilibrium • Scenario • Equilibrium price of movies is $6.00 • Equilibrium price of DVD rentals are $3.00 • Government places a $1.00 tax on each movie ticket • Need to look at effect of tax on • Market for DVDs • Feedback effects in Movie market Chapter 16

  5. S*M SM SV $3.50 $6.35 $3.00 D’V $6.00 DM DV QV Q’V Q’M QM Two Interdependent Markets – Movies and DVDs $1 tax on each movie ticket causes supply to fall General Equilibrium Analysis: Increase in movie ticket prices increases demand for videos. Price Price Number of Movie Tickets Number of Videos

  6. $6.82 S*M SM SV $3.58 $6.75 $3.50 $6.35 D*M D*V $3.00 D’V $6.00 D’M DM DV Q*M Q*V Number of Movie Tickets Q”M QV Q’V Q’M QM Two Interdependent Markets – Movies and DVDs The increase in the price of videos increases the demand for movies. General Equilibrium Analysis: The Feedback effects continue. Price Price Number of Videos Chapter 16

  7. Two Interdependent Markets – Movies and DVDs • Observation • Without considering the feedback effect with general equilibrium, the impact of the tax would have been underestimated • This is an important consideration for policy makers. Chapter 16

  8. Reaching General Equilibrium • Must be able to determine the equilibrium price of both movies and DVDs simultaneously • We must simultaneously find two prices that equate quantity demanded and quantity supplied in all related markets • This requires finding the solution to four equations: demand and supply for DVDs and Movies Chapter 16

  9. The Advantages of Trade • Assumptions • Two consumers (countries) • Two goods • Zero transaction costs • James & Karen have a total of 10 units of food and 6 units of clothing. Chapter 16

  10. The Advantage of Trade Chapter 16

  11. The Advantage of Trade • There is room for trade • James values clothing more than Karen • Karen values food more than James • Actual terms of trade are determined through bargaining Chapter 16

  12. The Advantage of Trade • From this analysis we obtain an important result: An allocation of goods is efficient only if the goods are distributed so that the marginal rate of substitution between any pair of goods is the same for all consumers. Chapter 16

  13. The Edgeworth Box Diagram • A diagram showing all possible allocations of either two goods between two people is called an Edgeworth Box Chapter 16

  14. The Edgeworth Box Diagram • Each point describes the market baskets of both consumers • James has 7 units of food and 1 unit of clothing – point A • Karen has 3 units of food and 5 units of clothing – point A from different axis Chapter 16

  15. Karen’s Food 3F James’s Clothing Karen’s Clothing 5C 1C A 7F James’s Food Exchange in an Edgeworth Box 10F 0K 6C The initial allocation before trade is A: James has 7F and 1C & Karen has 3F and 5C. 6C 0J 10F

  16. Karen’s Food 10F 4F 3F 0K 6C James’s Clothing Karen’s Clothing B 2C 4C 5C 1C A 6C 0J 6F 7F 10F James’s Food Exchange in an Edgeworth Box The allocation after trade is B: James has 6F and 2C & Karen has 4F and 4C. +1C -1F Chapter 16

  17. Efficient Allocations • A trade from A to B makes both Karen and James better off • If James’s and Karen’s MRS are the same at B the allocation is efficient. Chapter 16

  18. Efficient Allocations • We can see both parties are better off at point B since they both end up on a higher indifference curve • Although a trade might make both parties better off, the new allocation is not necessarily efficient Chapter 16

  19. Karen’s Food James’s Clothing Karen’s Clothing A Gains from trade UJ1 UK1 James’s Food Efficiency in Exchange 10F 0K 6C A: UJ1 = UK1, but the MRS is not equal. All combinations in the shaded area are preferred to A. 6C 0J 10F Chapter 16

  20. Karen’s Food D UJ3 C UK2 James’s Clothing Karen’s Clothing B UJ2 UK3 A UJ1 UK1 James’s Food Efficiency in Exchange 10F 0K 6C D is also a possible efficient allocation depending on bargaining At point C, MRSs are equal and allocation is efficient Point B is on higher IC but is not efficient 6C 0J 10F Chapter 16

  21. Any move outside the shaded area will make one person worse off (closer to their origin). B is a mutually beneficial trade--higher indifference curve for each person. Trade may be beneficial but not efficient. MRS is equal when indifference curves are tangent and the allocation is efficient. 10F Karen’s Food 0K 6C D Karen’s Clothing James’s Clothing C UJ3 B UJ2 A UJ1 6C UK3 UK2 UK1 0J 10F James’s Food Efficiency in Exchange Chapter 16

  22. Efficiency in Exchange • The Contract Curve • To find all possible efficient allocations of food and clothing between Karen and James, we would look for all points of tangency between each of their indifference curves. • The contract curve shows all the efficient allocations of goods between two consumers, or of two inputs between two production functions Chapter 16

  23. Contract Curve G F E The Contract Curve Karen’s Food 0K E, F, & G are Pareto efficient . James’s Clothing Karen’s Clothing 0J Chapter 16 James’s Food

  24. Contract curve • All points of tangency between the indifference curves are efficient. • MRS of individuals is the same • No more room for trade • The contract curve shows all allocations that are Pareto efficient. • Pareto efficient allocation occurs when further trade will make someone worse off. Chapter 16

  25. Consumer Equilibrium in a Competitive Market • We can show opportunities for trade for many consumers • When prices of food and clothing are equal, we can show the price line, PP’ with a slope of –1 • James buys 2 clothing for 2 food: A to C • Karen buys 2 food for 2 clothing: A to C • Both increase satisfaction Chapter 16

  26. Price Line P C UJ2 A UJ1 P’ UK2 UK1 Consumer Equilibrium in a Competitive Market 10F 0K Karen’s Food 6C Begin at A: Each James buys 2C and sells 2F moving from Uj1 to Uj2, which is preferred (A to C). Begin at A: Each Karen buys 2F and sells 2C moving from UK1 to UK2, which is preferred (A to C). Karen’s Clothing James’s Clothing 6C 0J 10F James’s Food Chapter 16

  27. Consumer Equilibrium in a Competitive Market • The amount of clothing that Karen wanted to sell is equal to the amount of clothing that James wanted to buy • An equilibrium is a set of prices at which the quantity demanded equals the quantity supplied in every market • Also called competitive equilibrium Chapter 16

  28. Consumer Equilibrium in a Competitive Market • In a general equilibrium setting where all markets are perfectly competitive, we can show the same result • Best example of Adam Smith’s invisible hand • Economy will automatically allocate all resources efficiently without need for regulatory control Chapter 16

  29. Consumer Equilibrium in a Competitive Market • Competitive equilibrium • Because the indifference curves are tangent, all MRSs are equal between consumers • Because each indifference curve is tangent to the price line, each person’s MRS is equal to the price ratio of the two goods Chapter 16

  30. Consumer Equilibrium in a Competitive Market • Difficult for efficient allocation with many consumer and producers unless all markets are perfectly competitive • Efficient outcomes can also be achieved by centralized system Chapter 16

  31. Equity and Efficiency • Although there are many efficient allocations, some may be fairer than others • The difficult question is what is the most equitable allocation? • There is no reason to believe that efficient allocation from competitive markets will give an equitable allocation Chapter 16

  32. The Utility Possibilities Frontier • From the Edgeworth box we showed a two person exchange • The utility possibilities frontier represents all allocations that are efficient in terms of the utility levels of the two individuals Chapter 16

  33. OJ L E F H G OK The Utility Possibilities Frontier OJ – James has zero utility OK – Karen has zero utility E, F, G – points on contract curve H – inefficient – can do better in shaded area L - unobtainable Karen’s Utility James’ Utility Chapter 16

  34. OJ E F H G OK The Utility Possibilities Frontier • Are all efficient points equitable? • Efficient points E or F make both persons better off without making one worse off from H • If only possible points are H and G, can argue that one is more equitable to James and one to Karen Karen’s Utility James’ Utility Chapter 16

  35. The Utility Possibilities Frontier • From previous example, we can see that an inefficient allocation might be more equitable than an efficient one. • But how do we define an equitable allocation? Chapter 16

  36. Four Views of Equity Chapter 16

  37. Equity and Perfect Competition • A competitive equilibrium can occur at any point on the contract curve depending on the initial allocation. • Since not all competitive equilibriums are equitable, we rely on the government to help reach equity by redistributing income. • Taxes • Pubic services Chapter 16

  38. Efficiency in Production • We can extend to the efficient use of inputs used for production. • Assume: • Two fixed inputs: capital and labor • Produce same two goods: food and clothing • Many consumers own inputs to production and earn income from selling them • Income allocated between goods Chapter 16

  39. Efficiency in Production • Using the Edgeworth box diagram, we can show efficient use of inputs in production • Labor on horizontal axis • Capital on vertical axis • 50 hours of labor and 30 hours of capital available Chapter 16

  40. Labor in Clothing Production 15L Capital in Clothing Production Capital in Food Production 25K 5K A 35L Labor in Food Production Production in an Edgeworth Box 50L 0C 30K The initial allocation is A. Every combination of labor and capital used to produce two goods is represented as point in box 30K 0F 50L

  41. Production in an Edgeworth Box • Can use production isoquants to show levels of output produced with each combination of inputs • 3 isoquants representing 50, 60 and 80 units of food • 3 isoquants representing 10, 25 and30 units of clothing Chapter 16

  42. Labor in Clothing Production 80F Capital in Clothing Production 25C Capital in Food Production B 30C 50F A 60F 10C Labor in Food Production Production in an Edgeworth Box 50L 15L 0C 30K 3 isoquants representing food production 3 isoquants representing clothing production 25K 5K 30K 0F 35L 50L

  43. Production in an Edgeworth Box • To find efficient production, we must find different combinations of inputs used to produce the two outputs • An allocation of inputs is technically efficient if the output of one good cannot be increased without decreasing the output of another goods Chapter 16

  44. Labor in Clothing Production D 80F C Capital in Clothing Production 25C Capital in Food Production 30C 50F B A 60F 10C Labor in Food Production Production in an Edgeworth Box 50L 15L 0C 30K Can move from A to B or C which increases efficiency. Any place in shaded area will increase efficiency from allocation A. 25K 5K 30K 0F 35L 50L

  45. Production in an Edgeworth Box • Points B and C are efficient allocations and therefore lie on the production contract curve • Curve showing all technically efficient combinations of inputs. • Curve connects the origins, OF and OC • All points on curve are tangencies between two isoquants Chapter 16

  46. Labor in Clothing Production D 80F C Capital in Clothing Production 25C Capital in Food Production 30C 50F B A 60F 10C Labor in Food Production Production in an Edgeworth Box 50L 15L 0C 30K Production Contract Curve 25K 5K 30K 0F 35L 50L

  47. Producer Equilibrium – Competitive Input Markets • If input markets are competitive, an efficient point will be achieved • In competitive input markets • Wage rate, w, will be equal in all industries • Rental rate of capital, r, will be equal in all industries Chapter 16

  48. Producer Equilibrium – Competitive Input Markets • If producers minimize costs, they will choose inputs to the point where the ratio of the marginal products of the two inputs is equal to the ratio of input prices: Chapter 16

  49. Producer Equilibrium – Competitive Input Markets • Ratio of marginal products is the same as the marginal rate of technical substitution of labor for capital: Chapter 16

  50. Producer Equilibrium – Competitive Input Markets • The MRTS is the slope of the isoquant, so competitive equilibrium exists only if: • Slopes of the isoquants are equal to one another • These also equal the ratio of the prices of two inputs • Competitive equilibrium lies on the production contract curve, and the competitive equilibrium is efficient in production Chapter 16

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