Question

QUESTION 2 Muhibah Group manufactures smart phones that can be sold directly to retail outlets or to the Mother Company for further processing and eventual sale by them as a completely different model. The demand function for each of these markets is Retail Outlets: P 60-2Q1 Mother Company: P2-40 -Q2 where P, and P2 are the prices charged and Q, and Q2 are the quantities sold in the respective markets. Muhibah's total cost function for the manufacture of this smart phone is a. Determine Muhibah's total profit function. (1 mark) b. What are the profit-maximising price and output levels for the product in the two markets? (1 marks) e. At these levels of output, calculate the marginal revenue in each market. (2 marks) d. What are Muhibah's total profits if the firm is effectively able to charge different prices in the two markets? (2 marks) e. Calculate the profit-maximising level of price and output if Muhibah is required to charge the same price per unit in each market. What are Mubihah's profits under this condition? (4 marks)

Answer 1

The total profit of the firm in given as pi = TR_1 + TR_2 - TC = P_Q_1 + P_2 Q_2 - 10 - 8 (Q_1 + Q_2) therefore pi = 60 Q_1 - 2 Q_1^2 + 40 Q_2 - Q^2_2 - 10 - 8 (Q_1 + Q_2) therefore pi = 60 Q_1 - 2 Q^2_1 + 40 Q_2 - Q^2_2 - 10 - 8 (Q_1 + Q_2) The FOC for profit maximization is partial differential pi/partial differential Q_4 = 60 - 4 Q_1 - 8 = 0 (1) partial differential pi/partial differential Q_2 = 40 - 2 Q_2 - 8 = 0 (2) From (1): 52 - 4 Q_1 = 0 therefore Q_1^* = 13 therefore P_1^* = 34 From (2): 32- - 2 Q_2 = 0 therefore Q_2^* = 16 therefore P^*_2 = 24 The marginal revenue in each market MR_1 = MR_2 = 8 The total profit is: pi = TR_1 + TR_2 - TC = 442 + 384 - 10 - 232 therefore pi = 584 The market demand can be written as Q_1 = 30 - 0.5 P_1 Q_2 = 40 - P_2 To charge same price, P, total demand therefore Q = Q_1 + Q_2 = 70 - 1.5 P therefore TC = 10 + 8 Q: MC = 8 therefore P = 70/1.5 Q;MR = 70/1.5 - 2/1.5 Q At equilibrium: MR = MC = 8 on, 70/1.5- - 8 = 2/1.5 Q or, 58 = 2 Q: therefore Q^*29 therefore p^* = 27.3