Question

For a given utility level, U₀, derive the Expenditure function E(p_r, p_s, U₀) for U(R,S) = R^0.8S^0.2

Answer 1

We are given

U(R,S)=R^0.8S^0.20

Price of R=p_r

Price of S=p_s

Expenditure=E

Expenditure E is given by

E=R*p_r+S*p_s

Marginal Utility MU_R=0.8R^-0.2S^0.20

Marginal Utility MU_S=0.2R^0.80S^-0.80

For utility maximization, we know that

------------------------------------------(1)

For a given Uo

Put

or

----------------------------------------(2)

From 1, we get

For a given Uo

Put

---------------------------(3)

E=R*p_r+S*p_s