Answer to Question #208798 in Microeconomics for Shingirayi

Question

Diogo has a utility function U(B, Z) = AB^αZ^β, where A, α, and β are constants, B is burritos, and Z is pizzas. If the price of burritos, p_B, is $2 and the price of pizzas, p_Z, is $1, and Y is $100, what is Diogo’s optimal bundle?

Answer 1

If Diogo has a utility function$U(B, Z) = AB^{\alpha} Z^{\beta};$ and if the price of burritos, Pb, is N$2 and the price of pizzas, Pz is N$1, and Y is N$100, using the Lagrangian method we can find the optimal bundle:

$Qb = \frac{\beta}{(\alpha+ \beta)}\times\frac{100}{2} = \frac{50\beta}{(\alpha + \beta)}$

$Qz = \frac{100\beta}{(\alpha + \beta)}$