3. A firm has production function Q = a[bk*+ cLB]. (a) Find the marginal rate of technical substitution. (b) Show that the marginal products satisfy the relation K OQ L OQ ay OK By OL = Q.4. A monopolist has cost function TC = 20000 + 60Q. It can sell in two markets with demand functions Pi + 2Q1 = 1000 and P2 + 5Q2 = 2000 respectively. How can the monopolist maximise profit?5. (Exercise 5.5*, Problem 6) A firm wishes to maximise output, Q = KL, subject to a budgetary constraint C(K, L) = 3K + 21 = 900. (a) Use substitution to find the values of K and L which maximise the output. (b) Compute the values of the partial derivatives of the objective function and the con- straint function at the optimal point, and verify that they are in proportion