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Question

Q1. Suppose a consumer has utility function (u) = xy where x and y are amounts of two commodities that this consumer consume. Suppose this consumer's income is $120, price of good x is $1/ unit and the price of good y is $4/ unit.

Maximize utility for this consumer.

Use the bordered Hessian to test the second-order condition.

Q2. Given the total cost function: C = x² + 2xy + 2y² for a firm producing goods x and y. The firm must meet a production quota of 2x + 3y = 40.

Minimize cost for this firm.

Use the bordered Hessian to test the second-order condition.

Q3. A consumer wants to maximize utility u (x,y) subject to the constraint P_xX +P_yY = B where x and y are amounts of two commodities that this consumer consume. Suppose this consumer's income is B, price of good x is P_x and the price of good y is P_y. Assume that the second- order sufficient condition is met so lH¯l = lJl ≠ 0. Find dx/dP_x.