# Suppose that the State of Washington

November 24, 2016

. Suppose that the State of Washington (that is, the median voter in Washington) has the following preferences of Education E and other goods G:

U(G, E) = α ln G + (1 − α) ln E

The price of education is PE; the price of other goods is 1; the state’ stotal budget is W.

(a)How many units of Education will Washington provide?

(b)What fraction of the budget will be spent on Education – write this as a function of PE and α, and W

(c)Illustrate this graphically.

II. The Federal Government is concerned about the quality of education in Washington, so they are considering a Grant program.First, theyare considering a Matching Grant, that will give the 1 dollar for each dollar they spend on Education.

(a)What is the “effective” price of education under this program?

(b)What is likely to happen to the level E that Washington chooses?Will there be an income effect, a substitution effect, or both?

(c)Illustrate the new situation graphically.

(d)Solve for the new amount of spending mathematically. How much does E rise, and how much does state spending (pre-match) fall?

III. The other possible Grant program is a Block Grant, equivalent is size to the dollars transferred until the matching grant in the previous exercise.

(a)What is the “effective” price of education under this program?Will there be an income effect, a substitution effect, or both?

(b)Solve mathematically for the new level E that Washington will choose.

(c)Explain any difference between the level E you found for this program, and the level you found for the Matching Grant.

IV. Which program would you recommend?

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