Question 1) Consider the following indirect utility function: v(P, y) = y(Pr1 + Pr2)-1/r Where r = r/(r - 1), pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi(P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity)

Question 1) Consider the following indirect utility function:

v(P, y) = y(P^r₁ + P^r₂)^-1/r

Where r = r/(r - 1), p_i are parametric prices, and y is the consumer’s budget

a) Solve for the Marshallian demand functions x_i(P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity).

b) Derive the Hicksian demand function x^h_i(P, u).

Question 2) Consider Delta, a price-taking single-output, single input firm with following production function:             

                                f(z) = z^4/5

a) Define non decreasing return to scale and non-increasing returns to scale in terms of the production and give conditions under which f(z) satisfies these properties.

b) Suppose that the price of the input z is w = 1. Set up the cost minimization problem and solve for the conditional factor demand correspondence and the cost function.

c) Set up Delta’s profit maximization problem using the cost function you derived in (b) above and solve for the supply correspondence and the profit function.