Answer to Question #76838 in Microeconomics for Tomas Nekongo

Question

Mandla has a utility function U(B,Z)=AB^(1/α) Z^(1/β), where A, α and β are constants, B is burritos, and Z is pizzas. If the price of burritos, Pb is 10 and the price of pizzas, Pz, is $5, and Y is $1790, what is Mandla’s optimal bundle?

Answer 1

U(B,Z)=AB^(1/α) Z^(1/β), where A, α and β are constants, B is burritos, and Z is pizzas.
If the price of burritos, Pb is 10 and the price of pizzas, Pz, is N$5, and Y is N$1790, then
John’s optimal bundle is at:
MUb/Pb = MUz/Pz and Pb*B + Pz*Z = Y,
MUb = U'(B) = A*(1/α)*B^(1 - 1/α)*Z^(1/β)
MUz = U'(Z) = A*(1/β)*Z^(1 - 1/β)*B^(1/α)
10B + 5Z = 1790.