3. A consumer of two goods, x1 and x2, faces positive prices and has a positive income, y. If the consumer exhausts the income in consumption of the two goods and his utility function is given as U(x1, x2) = (x1 – y)b1(x2 – y)b2,
(i) Compute the consumer’s expenditure function.
(ii) Derive his Marshallian demand functions and state their properties.
(iii) What are the properties of the demand functions in (ii) above?
(iv) Derive his indirect utility function and state its properties
(v) Compute his Hicksian demands functions and state their properties.
(vi) If this consumer wants to maintain utility at U0, calculate the minimum cost of attaining this utility and state the properties of this minimum cost.
(vii) Show that the MRS between the two goods is equal to the ratio of their marginal utilities.
