6) A number of proposals have been made to institute a "fuel-stamp" program of some kind to reduce the impact of high heating oil prices on low-income homeowners who are dependent on oil for heat. You have been asked by the governor to analyze two such proposals.

Plan 1 would pay 50% of the cost of all heating oil purchased by eligible families and would place no limit on the amount of subsidized oil families could buy.

Plan 2 would give each family 200 free gallons per month during the heating season.

The governor wants you to do the analysis for a "typical" low-income family, which has an income of $2,000 per month. Assume that the poor have preferences defined over heating oil, , and all other goods, . The price of oil is $5 per gallon and the price of all other goods is $1.

6a) Assuming families have convex preferences, illustrate a poor family's budget constraint, indifference curve, and their optimal bundle of heating oil and all other goods when there is no government assistance available. Label the optimal bundle point A.

6b) In a new diagram draw the family's budget constraint from part 6a) and a new budget constraint associated with plan 1. Add indifference curves and show what happens to the family's consumption of heating oil.

6c) Now suppose it is known that under plan 1, a poor family consumes exactly 400 gallons of heating fuel. In a new diagram redraw the family's budget constraint under plan 1 and illustrate their optimal bundle and indifference curve given your knowledge of their consumption of heating fuel. Now add the family's budget constraint under plan 2 to your diagram. Hint: the budget constraints under plan 1 and plan 2 must intersect at 400 gallons of heating oil.

6d) Under which plan does the family consume more heating oil?

6e) Under which plan is the family better off?