6. Answer both parts of this question. (a) A firm produces two products, 2, and x2. These products are priced at p, and p2 respectively, and can be divided into sub-units. The demand functions for each product are r1 = 1-p1+ p2 T2 = 1+ -p1 - P2 The firm's total cost function is C(x1, 2) = 2102 + + 12 + 2 (i) Find expressions for p, and pa in terms of a, and 22. Then write down the expression for the company's profit (") as a function of r; and $2. (ii) Find the profit maximizing levels of 1 and ~ making sure to check that the second order conditions for a local maximum are satisfied. (ifi) What will be the prices at the profit maximizing levels of production? (7 marks) (b) Determine an expression for the point elasticity of the following demand equation (q > 0): 1000 P = If q = 156, determine the value of the clasticity. Is demand elastic or inelastic at this point