Question 1 Stonewall receives c250 per year in simple interest from an amount of money he invested in ADB, Barclays and GCB. Suppose ADB pays an interest of 2%, Barclays pays an interest of 4% and GCB pays an interest of 5% per annum and an amount of 350 more was invested in Barclays than the amount invested in ADB and GCB combined. Also, the amount invested in Barclays is 2 times the amount invested in GCB. a) Write down the three linear equations and represent them in the matrix form AX = B. b) Find the amount of money Stonewall invested in ADB. Barclays and GCB using Matrix Inversion Question 2 A manager hires labour and rents capital equipment in a very competitive market. Currently the wage rate is GH2 per hour and capital is rented at GH5 per hour, the unit price of the product is GH0.25 and total cost is 1000. Suppose the firm's production function is as follows: Q = 14540.5 + 10 What is the amount of labour and capital the firm should employ in order to maximize output? | Hint: Maximise the product function subject to the cost constraint] ii. What is the maximum profit? i. 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 = 3Q2 - 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 Ga, has a joint total cost function TC = { +39.02 +02 where Q, and Q, denote the quantities of G and Gz respectively. If , and P, denote the corresponding prices then the demand equations are 0.50,- 25 -0.5P. 0.8Q2 = 36 -0.4P 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 fim is contracted to produce a total of 20 goods of either type, find the level of Q, and Q, that maximises profit c) Estimate the new optimal profit if the production quota increases to 24 units. Question 4 A monopolistic producer of two goods, G, and Go, has a joint total cost function TCQ1 +39.02 + 3 where and Q, denote the quantities of G, and Gy respectively. I Rand P, denote the corresponding prices then the demand equations are 0.5Q. = 25 -0.5P, 0.8Q: = 36 -0.4P 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 fim is contracted to produce a total of 20 goods of either type, find the level of Q, that maximises pros c) Estimate the new optimal profit if the production quota increases to 24 units
