Calculation of utility maximization on education.

Assume all households have $300,000 for a budget to spend on education (E) and all other goods (G). A unit of education (E) costs $4,000, and its relative price (slope of the constraint) is 0.80. Assume all household utility functions have the form U(E,G)=EαGβ , where α + β = 1.

(a) Let Household A's utility function have α = 0.5 = β. What is the household's utility maximizing bundle?

(b) Elucidate what is the share of Household A's income spent on education?

(c) What is the household's utility if they consume the maximum amt of G allowed by their budget and an amt of free education provided by the government, EF = 20?

(d) Does this household consume more or less education if EF = 20 is provided by the government?

(e) Let Household B's utility function have α = 0.15 and β = 0.85. What is the household's utility maximizing bundle?

(f) Illustrate what is the share of Household B's income spent on education?

(g) Does this household consume more or less education if EF = 20 is provided by the government?

(h) Above what value of beta (β) does a household choose to consume more education when the government provides EF for free?

(i) If you were to conduct a research project looking into the amount of households that would consume more education due to the government providing EF = 20, how might you go about this? Given your answers to (b),(f), and (h)-and the parameters of alpha and beta for each household-what household information might you look at to predict the effect of EF = 20?