Ambrose's brother Augustine has an income of $52 and a utility function U(x₁, x₂)= 18x^1/2₁ + x₂.The price of good 1(nuts)is $3 and the price of good 2(berries)is $1.How many units of berries will Augustine demand?

Question

Quizplus · Accepted Answer

Augustine's marginal utility of income is 18x^-1/2₁. Setting this equal to the price of good 1, we get 18x^-1/2₁ = 3. Solving for x₁, we get x₁ = 9. Substituting this into the utility function, we get U(9, x₂) = 18(9)^1/2 + x₂ = 54 + x₂. Setting this equal to Augustine's income, we get 54 + x₂ = 52. Solving for x₂, we get x₂ = -2. This is not a valid solution, since Augustine cannot consume a negative amount of berries. Therefore, Augustine will demand 0 units of berries.

Ambrose's Brother Augustine Has an Income of $52 and a Utility