Humphrey and Lauren are splitting 10 gallons of soda and six pounds of popcorn. Let's represent Humphrey's preference with the utility function UH = 3SH + PH and Lauren's preferences with UL = 2SL + 4PL, where SH and SL indicate their soda consumption, while PH and PL indicate their popcorn consumption. Consider the social welfare function W(UH,UL) = UH + UL. According to this social welfare function, which of the following two allocations is better: (1) SH = 1, SL = 9, PH = 2, and PL = 4, or (2) SH = 5, SL = 5, PH = 3, and PL = 3? Which allocation does each consumer prefer? Considering all possible allocations, which is the most socially desirable? [HINT: How is social welfare affected by shifting a gallon of soda between Humphrey and Lauren? What about a pound of popcorn?]
Suppose Humphrey starts out with four pounds of food and seven gallons of water, while Lauren starts out with eight pounds of food and five gallons of water. Draw an Edgeworth box that shows all possible allocations of these goods, and plot the endowment points. Now suppose that both Lauren and Humphrey's preferences correspond to the utility function U(F, W) = min{F, W} (where F refers to pounds of food and W refers to gallons of water). This is a case of perfect complements. Add Humphrey and Lauren's indifference curves to the Edgeworth box. Then draw the contract curve. To which points on the contract curve is each consumer willing to trade?
Humphrey and Lauren are splitting 10 gallons of soda and six pounds of popcorn. Let's represent Humphrey's preference with the utility function UH = 3SH + PH and Lauren's preferences with UL = 2SL + 4PL, where SH and SL indicate their soda consumption, while PH and PL indicate their popcorn consumption. Consider the social welfare function W(UH,UL) = UH + UL. According to this social welfare function, which of the following two allocations is better: (1) SH = 1, SL = 9, PH = 2, and PL = 4, or (2) SH = 5, SL = 5, PH = 3, and PL = 3? Which allocation does each consumer prefer? Considering all possible allocations, which is the most socially desirable? [HINT: How is social welfare affected by shifting a gallon of soda between Humphrey and Lauren? What about a pound of popcorn?]
Suppose Humphrey starts out with four pounds of food and seven gallons of water, while Lauren starts out with eight pounds of food and five gallons of water. Draw an Edgeworth box that shows all possible allocations of these goods, and plot the endowment points. Now suppose that both Lauren and Humphrey's preferences correspond to the utility function U(F, W) = min{F, W} (where F refers to pounds of food and W refers to gallons of water). This is a case of perfect complements. Add Humphrey and Lauren's indifference curves to the Edgeworth box. Then draw the contract curve. To which points on the contract curve is each consumer willing to trade?
