Question

The city government of Grantsburg must choose how to allocate the city budget of $90,000 between units of educational quality (E) and all other public goods (G). The city's prefer- ences (i.e., those of the median voter) over E and G are given by: ! U(E,G) = (1/3) - In(E) + (2/3) • In(G) For simplicity, let the unit prices of E and G both equal $1 so that we can interpret E and Gas levels of spending. The city's budget constraint, BC, is depicted below. o 150,000 140,000 130,000 120,000 110,000 100,000 90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 20,000 40,000 60,000 80,000 100,000 120,000 150,000 b. Determine Grantsburg's choice of E and G. Label this choice as point B in the figure. Note: You can answer this with calculus, or by using a property of Cobb-Douglas utility.

Answer 1

rantshnge chace7E = 3000 GE GOOD0 90,000 B (20000, 60000) 60000 BCGE-100007 90,000 30000 In (E)+ 2 ln (G) E,G) 3 Budget line be Et G= 90000 MVaginal Uhidhes of U(E,G) Ju(E.G) JE The ophimal Condi' hon be MUE MRS EG MUG G MUE 3 E MUG PG 3G 2 E Put G=2E in we Gct E= 30000 E 126= 90000 2 E 2 X3000 0 G60000