Question 3 Miss Quaye is an entrepreneur is an entrepreneur who specializes in the production of wig caps from Brazilian virgin hair. She purchase most of her virgin hair from the online trading store Alibaba Express. In order to maximise profit in the short run, she employed an economist to estimate the demand curve for her product, which was used to derive the marginal revenue (MR) function for her product as: MR = 24 - 4Q The economist also derived the marginal cost function (MC) for her product as: MC = 302 19Q +42 To be able to determine the amount of goods she has to produce in order to maximise profit, she employed you at a cheaper cost than the economist, to: a) Find the total revenue function and deduce the corresponding demand equation. b) Find the total cost function if the fixed cost are 10. c) Determine the number of wig caps that maximizes the Miss Quaye's profit using first and second order conditions. d) How much should the Miss Quaye charge for one wig cap? e) Find the total profit at the profit maximizing level of output. Question 4 A monopolistic producer of two goods, G, and G2, has a joint total cost function TC = Q +3Q,Q2 + Q where Q, and Qz denote the quantities of G, and G2 respectively. If P, and P, denote the corresponding prices then the demand equations are 0.5Q. = 25 -0.5P 0.8Q2 = 36 - 0.4P2 a) Find an expression for the firm's profit. b) Determine the firm's pricing policy that maximizes profit using the first and second other conditions. c) Calculate the value of the maximum profit at the profit maximizing level of outputs. d) Now, supposed the firm is contracted to produce a total of 20 goods of either type, find the level of Q, and Q2 that maximises profit. e) Estimate the new optimal profit if the production quota increases to 24 units