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Pareto Optimality

Pareto Optimality. Chapter 2. Learning Objectives. The Pareto criterion General equilibrium First theorem of welfare economics Contract curve Allocation of production and consumption in a perfectly competitive market economy. Pareto Criterion.

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Pareto Optimality

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  1. Pareto Optimality Chapter 2

  2. Learning Objectives • The Pareto criterion • General equilibrium • First theorem of welfare economics • Contract curve • Allocation of production and consumption in a perfectly competitive market economy

  3. Pareto Criterion • A policy change is socially desirable if at least some people are made better off while no one is made worse off • Pareto-optimal allocation (situation): the allocation of commodities cannot be altered without someone being made worse off • Pareto criterion is a core of welfare economics, albeit a weak one • All citizens’ welfare is involved • What if some people are made worse off while the others are made better off? • Pareto ranking of states is incomplete: if even 1 person is made worse off by a policy, it doesn’t pass the Pareto criterion test

  4. Quantity of clams Total utility (utils) Marginal utility per clam (utils) 0 0 15 1 15 13 2 28 11 3 39 9 4 48 7 5 55 5 6 60 3 7 63 1 8 64 –1 9 63 Cassie’s Total Utility and Marginal Utility (a) Cassie’s Utility Function Total utility (utils) 70 60 Utility function 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 Quantity of clams Marginal utility per clams (utils) ( b ) Cassie’s Marginal Utility Curve 16 14 12 10 8 Marginal Utility Curve 6 4 2 0 –2 1 2 3 4 5 6 7 8 9 Quantity of clams

  5. Cassie’s Total Utility and Marginal Utility • Cassie’s total utility depends on her consumption of fried clams. • It increases until it reaches its maximum utility level of 64 utils at 8 clams consumed and decreases after that. • The marginal utility curve slopes downward due to diminishing marginal utility; each additional clam gives Cassie less utility than the previous clam.

  6. The Principle of Diminishing Marginal Utility • The marginal utility of a good or service is the change in total utility generated by consuming one additional unit of that good or service. The marginal utility curve shows how marginal utility depends on the quantity of a good or service consumed. • The principle of diminishing marginal utility says that each successive unit of a good or service consumed adds less to total utility than the previous unit.

  7. Budgets and Optimal Consumption • A budget constraint requires that the cost of a consumer’s consumption bundle be no more than the consumer’s total income. • A consumer’s consumption possibilities is the set of all consumption bundles that can be consumed given the consumer’s income and prevailing prices. • A consumer’s budget line shows the consumption bundles available to a consumer who spends all of his or her income.

  8. Quantity of clams Quantity of potatoes Consumption bundle (pounds) (pounds) A 0 10 B 1 8 C 2 6 D 3 4 E 4 2 F 5 0 The Budget Line Quantity of potatoes (pounds) Unaffordable consumption bundles 10 A 8 B 6 Affordable consumption bundles that cost all of Sammy's income C 4 D Affordable consumption bundles 2 E Sammy’s Budget Line, BL F 0 1 2 4 5 3 Quantity of clams (pounds) The budget line represents all the possible combinations of quantities of potatoes and clams that Sammy can purchase if he spends all of his income. It is also the boundary between the set of affordable consumption bundles (the consumption possibilities) and unaffordable ones.

  9. Sammy’s Utility from Clam and Potato Consumption

  10. Optimal Consumption Choice • The optimal consumption bundle is the consumption bundle that maximizes a consumer’s total utility given his or her budget constraint.

  11. Sammy’s Budget and Total Utility Sammy’s total utility is the sum of the utility he gets from clams and the utility he gets from potatoes.

  12. Optimal Consumption Bundle (a) Sammy’s Budget Line Quantity of potatoes (pounds) The optimal consumption bundle… A 10 B 8 C 6 D 4 E 2 F BL 2 0 1 3 4 5 Quantity of clams (pounds) (b) Sammy’s total utility is maximized at bundle C, where he consumes 2 pounds of clams and 6 pounds of potatoes. This is Sammy’s optimal consumption bundle. Sammy’s Utility Function Total utility (utils) 80 C B D 70 A E 60 Utility function 50 … maximizes total utility given the budget constraint 40 F 30 20 10 2 0 1 3 4 5 Quantity of clams (pounds) 10 8 2 0 6 4 Quantity of potatoes (pounds)

  13. Spending the Marginal Dollar The marginal utility per dollar spent on a good or service is the additional utility from spending one more dollar on that good or service.

  14. Sammy’s Marginal Utility per Dollar

  15. Marginal Utility per Dollar B C B MU / P P C C Total utility (utils) MU / P P P At the optimal consumption bundle, the marginal utility per dollar spent on clams is equal to the marginal utility per dollar spent on potatoes. If Sammy has, in fact, chosen his optimal consumption bundle, his marginal utility per dollar spent on clams and potatoes must be equal. 6 5 4 3 C 2 1 0 1 2 3 4 5 Quantity of clams (pounds) 10 8 6 4 2 0 Quantity of potatoes (pounds)

  16. Optimal Consumption Rule The optimal consumption rule says that when a consumer maximizes utility, the marginal utility per dollar spent must be the same for all goods and services in the consumption bundle.

  17. Utility Effects of Economic Policy Any economic policy changes the allocation of goods Changes in allocation modify utility Call the resulting allocation a state Can we rank the states according to the utilities accruing to different households?

  18. Incompleteness of Pareto Rankings Utility of Household 2 Utility of Household 1 Initial State

  19. Re-cap: Market Demand Curve • Market demand relates commodities’ prices to the sold quantities at those prices • Law of demand: the higher the price, the lower the quantity demanded (sold)downward sloping demand curve

  20. Demand • Quantity demanded • Amount of a good that buyers are willing and able to purchase • Law of demand • Other things equal • When the price of the good rises • Quantity demanded of a good falls

  21. Demand • Demand schedule - a table • Relationship between the price of a good and quantity demanded • Demand curve - a graph • Relationship between the price of a good and quantity demanded • Individual demand • Demand of one individual

  22. Catherine’s Demand Schedule and Demand Curve Price of Ice-Cream Cones 2. . . . increases quantity of cones demanded. 1. A decrease in price . . . $3.00 0.50 1.00 1.50 2.00 2.50 Demand curve 0 11 12 10 7 6 4 3 2 1 9 8 5 Quantity of Ice-Cream Cones The demand schedule is a table that shows the quantity demanded at each price. The demand curve, which graphs the demand schedule, illustrates how the quantity demanded of the good changes as its price varies. Because a lower price increases the quantity demanded, the demand curve slopes downward.

  23. Demand • Market demand • Sum of all individual demands for a good or service • Market demand curve • Sum the individual demand curves horizontally • Total quantity demanded of a good varies • As the price of the good varies • Other things constant

  24. Market Demand as the Sum of Individual Demands The quantity demanded in a market is the sum of the quantities demanded by all the buyers at each price. Thus, the market demand curve is found by adding horizontally the individual demand curves. At a price of $2.00, Catherine demands 4 ice-cream cones, and Nicholas demands 3 ice-cream cones. The quantity demanded in the market at this price is 7 cones. .

  25. Market Demand as the Sum of Individual Demands + = Price of Ice-Cream Cones Price of Ice-Cream Cones Price of Ice-Cream Cones Catherine’s demand Nicholas’s demand Market demand DCatherine DNicholas 1.50 2.00 0.50 $3.00 1.00 2.50 $3.00 0.50 1.00 1.50 2.00 2.50 2.00 $3.00 0.50 1.50 2.50 1.00 DMarket 10 12 11 10 6 7 5 4 3 9 1 1 8 6 5 7 2 18 4 4 8 14 6 2 12 3 16 2 0 0 0 Quantity of Ice-Cream Cones Quantity of Ice-Cream Cones Quantity of Ice-Cream Cones

  26. Demand • Shifts in the demand curve • Increase in demand • Any change that increases the quantity demanded at every price • Demand curve shifts right • Decrease in demand • Any change that decreases the quantity demanded at every price • Demand curve shifts left

  27. Shifts in the Demand Curve Price of Ice-Cream Cones Increase in Demand Decrease in Demand Demand curve, D3 Demand curve, D2 Demand curve, D1 0 Quantity of Ice-Cream Cones Any change that raises the quantity that buyers wish to purchase at any given price shifts the demand curve to the right. Any change that lowers the quantity that buyers wish to purchase at any given price shifts the demand curve to the left.

  28. Demand • Variables that can shift the demand curve • Income • Prices of related goods • Tastes • Expectations • Number of buyers

  29. Shifts in the Demand Curve versus Movements along the Demand Curve (a) A Shift in the Demand Curve (b) A Movement along the Demand Curve Price of Cigarettes, per Pack Price of Cigarettes, per Pack A tax that raises the price of cigarettes results in a movement along the demand curve A policy to discourage smoking shifts the demand curve to the left $2.00 $4.00 2.00 B A D2 A D1 D1 C 10 12 20 20 If warnings on cigarette packages convince smokers to smoke less, the demand curve for cigarettes shifts to the left. In panel (a), the demand curve shifts from D1 to D2. At a price of $2.00 per pack, the quantity demanded falls from 20 to 10 cigarettes per day, as reflected by the shift from point A to point B. By contrast, if a tax raises the price of cigarettes, the demand curve does not shift. Instead, we observe a movement to a different point on the demand curve. In panel (b), when the price rises from $2.00 to $4.00, the quantity demanded falls from 20 to 12 cigarettes per day, as reflected by the movement from point A to point C. 0 0 Number of Cigarettes Smoked per Day Number of Cigarettes Smoked per Day

  30. Supply • Quantity supplied • Amount of a good • Sellers are willing and able to sell • Law of supply • Other things equal • When the price of the good rises • Quantity supplied of a good rises

  31. Supply • Supply schedule - a table • Relationship between the price of a good and the quantity supplied • Supply curve - a graph • Relationship between the price of a good and the quantity supplied • Individual supply • Supply of one seller

  32. Ben’s Supply Schedule and Supply Curve Price of Ice-Cream Cones Supply curve 2. . . . increases quantity of cones supplied. $3.00 2.50 0.50 1.00 1.50 2.00 1. An increase in price . . . 0 11 12 10 7 6 4 3 2 1 9 8 5 Quantity of Ice-Cream Cones The supply schedule is a table that shows the quantity supplied at each price. This supply curve, which graphs the supply schedule, illustrates how the quantity supplied of the good changes as its price varies. Because a higher price increases the quantity supplied, the supply curve slopes upward.

  33. Supply • Market supply • Sum of the supplies of all sellers for a good or service • Market supply curve • Sum of individual supply curves horizontally • Total quantity supplied of a good varies • As the price of the good varies • All other factors that affect how much suppliers want to sell are hold constant

  34. Market Supply as the Sum of Individual Supplies The quantity supplied in a market is the sum of the quantities supplied by all the sellers at each price. Thus, the market supply curve is found by adding horizontally the individual supply curves. At a price of $2.00, Ben supplies 3 ice-cream cones, and Jerry supplies 4 ice-cream cones. The quantity supplied in the market at this price is 7 cones.

  35. Market Supply as the Sum of Individual Supplies Price of Ice-Cream Cones Price of Ice-Cream Cones Price of Ice-Cream Cones + = Ben’s supply Jerry’s supply Market supply SBen SMarket SJerry 2.00 1.50 $3.00 0.50 2.50 1.00 1.50 $3.00 2.50 0.50 2.00 1.00 2.00 $3.00 1.50 2.50 0.50 1.00 10 12 14 18 16 2 8 6 4 7 1 2 6 3 5 7 3 4 2 1 6 4 5 0 0 0 Quantity of Ice-Cream Cones Quantity of Ice-Cream Cones Quantity of Ice-Cream Cones

  36. Supply • Shifts in supply • Increase in supply • Any change that increases the quantity supplied at every price • Supply curve shifts right • Decrease in supply • Any change that decreases the quantity supplied at every price • Supply curve shifts left

  37. Shifts in the Supply Curve Supply curve, S2 Supply curve, S3 Price of Ice-Cream Cones Supply curve, S1 Increase in Supply Decrease In supply 0 Quantity of Ice-Cream Cones Any change that raises the quantity that sellers wish to produce at any given price shifts the supply curve to the right. Any change that lowers the quantity that sellers wish to produce at any given price shifts the supply curve to the left.

  38. Supply and Demand Together • Equilibrium - a situation • Various forces are in balance • A situation in which market price has reached the level where • Quantity supplied = quantity demanded • Supply and demand curves intersect

  39. Supply and Demand Together • Equilibrium price • Balances quantity supplied and quantity demanded • Market-clearing price • Equilibrium quantity • Quantity supplied and quantity demanded at the equilibrium price

  40. The Equilibrium of Supply and Demand Equilibrium quantity Equilibrium Price of Ice-Cream Cones Equilibrium price Supply $3.00 2.50 0.50 1.00 1.50 2.00 Demand 0 12 10 11 7 8 6 5 4 3 2 1 9 Quantity of Ice-Cream Cones The equilibrium is found where the supply and demand curves intersect. At the equilibrium price, the quantity supplied equals the quantity demanded. Here the equilibrium price is $2.00: At this price, 7 ice-cream cones are supplied, and 7 ice-cream cones are demanded.

  41. Supply and Demand Together • Surplus • Quantity supplied > quantity demanded • Excess supply • Downward pressure on price • Movements along the demand and supply curves • Increase in quantity demanded • Decrease in quantity supplied

  42. Supply and Demand Together • Shortage • Quantity demanded > quantity supplied • Excess demand • Upward pressure on price • Movements along the demand and supply curves • Decrease in quantity demanded • Increase in quantity supplied

  43. Markets Not in Equilibrium (a) Excess Supply (b) Excess demand Price of Ice-Cream Cones Price of Ice-Cream Cones Surplus Shortage $2.50 $2.00 2.00 1.50 Quantity demanded Quantity supplied Demand Demand Quantity demanded Quantity supplied Supply Supply 7 7 4 4 10 10 In panel (a), there is a surplus. Because the market price of $2.50 is above the equilibrium price, the quantity supplied (10 cones) exceeds the quantity demanded (4 cones). Suppliers try to increase sales by cutting the price of a cone, and this moves the price toward its equilibrium level. In panel (b), there is a shortage. Because the market price of $1.50 is below the equilibrium price, the quantity demanded (10 cones) exceeds the quantity supplied (4 cones). With too many buyers chasing too few goods, suppliers can take advantage of the shortage by raising the price. Hence, in both cases, the price adjustment moves the market toward the equilibrium of supply and demand 0 0 Quantity of Ice-Cream Cones Quantity of Ice-Cream Cones

  44. Supply and Demand Together • Law of supply and demand • The price of any good adjusts • To bring the quantity supplied and the quantity demanded for that good into balance • In most markets • Surpluses and shortages are temporary

  45. Supply and Demand Together • Three steps to analyzing changes in equilibrium • Decide whether the event shifts the supply curve, the demand curve, or, in some cases, both curves • Decide whether the curve shifts to the right or to the left • Use the supply-and-demand diagram • Compare the initial and the new equilibrium • Effects on equilibrium price and quantity

  46. Three Steps for Analyzing Changes in Equilibrium

  47. Supply and Demand Together • A change in market equilibrium due to a shift in demand • One summer - very hot weather • Effect on the market for ice cream? • Hot weather – shifts the demand curve (tastes ) • Demand curve shifts to the right • Higher equilibrium price; higher equilibrium quantity

  48. 2. …resulting in a higher price . . . 3. …and a higher quantity sold. How an increase in demand affects the equilibrium Price of Ice-Cream Cones 1. Hot weather increases the demand for ice cream . . . Initial equilibrium New equilibrium Supply $2.50 2.00 10 7 D1 D2 Quantity of Ice-Cream Cones 0 An event that raises quantity demanded at any given price shifts the demand curve to the right. The equilibrium price and the equilibrium quantity both rise. Here an abnormally hot summer causes buyers to demand more ice cream. The demand curve shifts from D1 to D2, which causes the equilibrium price to rise from $2.00 to $2.50 and the equilibrium quantity to rise from 7 to 10 cones.

  49. Commodity Demand Functions • Suppose utility F is given by • Then the individual demand function for each good is equal to • Labeling by d total demand by two households, and by d1, d2 the individual demands, total demand for commodity 1 becomes

  50. Aggregate Demand Price of Commodity Demand of household 2 Aggregate (Market) Demand Demand of household 1 Quantity

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