Question #76883

John 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 N$5, and Y is N$1790, what is John’s optimal bundle

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, what is John’s optimal bundle

Expert's answer

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.

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.

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