Question

1. Assume a society in which consumers partake of only two goods, bread (B) and wine (W). The price of bread is 4 units per loaf and the price of wine is 2 units per glass. Mr. H, a typical consumer with whom we shall be concerned, has a weekly income of 200 units; the government taxes away entirely any part of that income which he does not spend. There is also a rationing scheme whereby each consumer, Mr. H. included, receives 120 ration "points" each week and must turn in 2 "points" with the purchase of each loaf of bread and 6 "points" with the purchase of each glass of wine. There is no way to buy or sell "points" for money.

1. On graph paper, shade in the region of all feasible combinations of consumption of loaves of bread (B) and glasses of wine (W) for Mr. H.
2. Is it possible for Mr. H's preferred consumption pattern to be such that he exhausts both his income and his "points"? If so draw in a possible highest indifference curve which would bring about this situation; label it XX.
3. Is it possible for Mr. H's preferred consumption pattern to be such that he exhausts his "points' but not his income (the rest of which is of course taxed)? If so, draw in a possible highest indifference curve which would bring about this situation; label it YY.

Answer 1

DARTMOUTH COLLEGEDepartment of EconomicsEconomics 21 Professor GustmanMicroeconomics

Problem Set I1.

This question concerns rent subsidies. Suppose that under a rent subsidy the government will paysome specified proportion of the total rental price. Using an indifference map for "housing" (e.g.rooms of standard quality) and "all other commodities" analyze whether this approach to enhancingdomestic welfare is more or less effective than granting income tax reductions equal in dollaramount to the amount of the rent subsidy? How do these compare to a lump sum $250 per monthsubsidy which must be applied toward rent or it is taken away?

II.

A. Mr. Jones has $15,000 per year of "pocket money." He buys 500 packs of cigarettes at $10.00 per pack. Although he is a heavy smoker cigarettes are not necessary for his survival. Show his budget line and his equilibrium position in a diagram utilizing indifference curves. (Measure packages of cigarettes on the horizontal axis and "pocket money" on the vertical axis.)B. The Anti-Tobacco Alliance threatens to win its fight to have smoking prohibited by law. Wherewould Jones' equilibrium lie if this legislation were passed? Show on the diagram you havedrawn the maximum amount Jones would be willing to pay annually to avoid the ban onsmoking and explain briefly. (Assume that Jones would still pay $10.00 per pack). Show also theminimum amount the U.S. Smokers Compensation Commission (set up to compensate smokersfor the loss of their right to smoke) would have to pay Mr. Jones to compensate him for the lossof his opportunity to smoke.III.

1. Derive a formula for the elasticity of supply so that the elasticity at point E is AX/OX. Use thesame approach to show that any straight line supply curve has unitary elasticity if it goes throughthe origin, is inelastic if it intersects the X axis and is elastic if it intersects the Y axis.2. Draw indifference curves between present consumption (this year) and future consumption (nextyear) and justify the shape you gave them. (Assume that there is just one all purpose commoditythat is used for consumption, investment, etc. Be sure to measure present consumption on the Xaxis.) What does the MRS indicate in this case? Is this related to anything you have learned inother economics courses? Now draw a budget line of any slope. What is the significance of theslope? Is it related to anything you have learned before? Illustrate the determination of

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