Economists often describe local governments as having utility functions (called social

welfare functions) from which indifference curves can be derived that illustrate preferences,

just like for individuals. Suppose the government of Anytown gets utility from two goods,

education for its children and fireworks displays, and its tradeoff for each good is $1 of

educating children can always be sacrificed to gain $1 of additional fireworks (and vice

versa). Currently, Anytown spends $1 million on education and $500,000 on fireworks. The

federal government would like to improve education for Anytown children by giving

Anytown money for education (the federal government does not care about fireworks).

a. Sketch the initial budget constraint facing Anytown, being sure to label the axes, the

slope, the intercepts, and the initial consumption point. Draw an indifference curve

through the consumption point that is consistent with fireworks and education both being

normal goods that are partial substitutes (i.e., in between perfect substitutes and perfect

complements).

b. Sketch the change in the budget constraint facing Anytown if the federal government

gives Anytown a grant of $300,000.

c. Sketch the change in the budget constraint facing Anytown if the federal government

instead gives Anytown a grant of $300,000 that must be spent on education.

d. Sketch the change in the budget constraint facing Anytown if the federal government

instead gives Anytown a "matching grant" of an additional $0.30 for each $1 Anytown

spends of its own money on education.

e. You are an economic advisor to the federal government. Which type of grant would you

recommend they provide to Anytown (recalling that the goal of their spending is to

increase the amount of education spending Anytown children receive)? Explain.

f. If this is instead a grant that will be given to many towns, some of which have much

more money than others, are there any drawbacks to your recommendation?