Y9

Question 2 A financial consulting firm has recently begun to give economic advice to its clients by acting as one of the firm's consultants you have estimated the demand curve of a client's firm to be TR=40Q - 3Q2 Where TR is total revenue in thousands of Ghana cedis, and Q is output in units. Your investigation of the client's cost profile shows that marginal cost is given by MC = 16 - 2Q. Where MC is a marginal cost in thousands of Ghana cedis, and Q is output in units. Further investigations by you have shown that the firm's cost when nothing has been produced is GHc 200. Required (a) Derive the marginal revenue and total cost functions. (b) Calculate the output level that maximizes profit. (c) What is the maximum profit? (d) Calculate the price that maximizes profit. (e) Compute the price elasticity of demand for the firm's product at the profit maximizing output level. (f) As a consultant, advise the firm on its pricing policy. (g) The government imposes a per unit tax on the firm, calculate: i. the new profit maximizing level of output. ii. the new maximum profit. Question 3 (i) An economic and financial consultant has estimated the demand and the Marginal Cost functions of your firm as follows: P = 30 - Q and MC = Q + 6 Fixed cost is estimated to be $7 Where Q is quantity, P is the price in $, MC is the marginal cost Required a) Find the level of output that maximises profit. b) What is the maximum profit? c) Calculate the average variable cost at the profit-maximising level of output. d) Compute the breakeven level of output. e) Find the difference between the price that maximises profit and the price at the breakeven point. (ii) An accountant has estimated that the weekly cost of production, TC, is given by the equation: TC = 100 + 23Q + 0.5Q2 Where Q is the number of units of tonnes produced. The weekly revenue equation, TR, is given by TR = 100Q - Q2 (Q<1000) (a) What are the Marginal Cost and Marginal Revenue functions? (b) Find an equation for the demand. (c) Compute the average cost function. (d) Calculate the output level that maximizes profit. (e) What is the maximum profit? (f) Calculate the price that maximizes profit. (g) Compute the price elasticity of demand for the firm's product at the profit-maximizing output level. (h) As a consultant, advise the firm on its pricing policy. (i) The government imposes a per unit tax of GHS30 on the firm, calculate: 1. the new profit maximizing level of output. 2. the new maximum profit.