Economics for Mathematicians - Exam 2005 - Statistics and Economics, Exams of Economic statistics

Download Economics for Mathematicians - Exam 2005 - Statistics and Economics and more Exams Economic statistics in PDF only on Docsity! MA309/05 turn over UNIVERSITY OF KENT FACULTY OF SCIENCE, TECHNOLOGY AND MEDICAL STUDIES LEVEL C EXAMINATION ECONOMICS FOR MATHEMATICIANS Thursday, 19 May 2005 : 09.30 – 12.30 This paper contains TEN questions. Candidates should attempt ALL questions. Marks allotted are shown at the end of each question. Graph paper is provided. Approved calculators are permitted. MA309/05 2 1. The linear market demand and supply for a commodity are represented by the following functions: Qd = – P + 40 Qs = 1.5 P – 5 Where Qd = Quantity demanded in thousands of units per year, Qs = Quantity supplied in thousands of units per year, P = Price in £. (a) Determine the equilibrium price and quantity and graph the supply and demand functions. [3 marks] (b) Assume that the government pays the suppliers a subsidy of £2 per unit of the product produced. Determine the new equilibrium price and quantity and graph the new supply function on the diagram in part (a). [4 marks] (c) Show on your diagram, the area corresponding to the amount the government spends on the subsidy and calculate this expenditure. [2 marks] (d) If instead of the subsidy, the government imposes a price floor of £20 on the market, determine the effect on the quantities bought and sold. What should the government do to sustain the price floor? [2 marks] [Total 11 marks] 2. The demand and marginal cost functions for a firm’s product are given by the following functions: Q = 48 – 2P MC = 3Q – 8 Where Q = quantity demanded P = price per unit of the product MC = marginal cost (i) Determine the total revenue and marginal revenue functions. [2 marks] (ii) Determine the profit maximising output and price. [2 marks] (iii) If the fixed cost of production is 25, determine the total cost function, the total cost of producing the profit maximising output and the maximum profit. [3 marks] [Total 7 marks] MA309/05 5 turn over 7. Information about the labour market in a small economy is provided in the following table, where workforce is shown in thousands. Labour force Number in labour force Labour demand Real wage willing to work (£/hour) 125 80 120 4 132 90 110 5 138 100 100 6 146 110 90 7 153 120 80 8 160 130 70 9 (i) If the real wage is fixed at £8 per hour, what are the levels of employment and voluntary and involuntary unemployment? [2 marks] (ii) Assuming that the real wage rate is flexible, what are the equilibrium wage rate, the level of employment and the natural unemployment level? Calculate the labour participation rate in this case. [3 marks] (iii) Briefly describe the factors that influence labour participation. [2 marks] [Total 7 marks] 8. Assume there are only two countries X and Y in the world. Assume further that X and Y are trading partners. The demand and supply for the currency of country X are represented by the following functions: Demand for country X’s currency: E = 2.6 – 0.2 Qd Supply of country X’s currency: E = -1 + 0.4Qs Where E = the exchange rate = country Y’s currency / country X’s currency Qd = demand for country X’s currency Qs = supply of country X’s currency. (i) Sketch the demand and supply functions for country X’s currency and briefly explain how the two schedules arise. [3 marks] (ii) Determine the exchange rate that would prevail under a clean float. What would be the state of the overall balance of payments at this exchange rate? [2 marks] MA309/05 6 (iii) Mr Z has 200 units of country X’s currency, which he wishes to lend for a year. He could lend in country X where the current exchange rate is that determined in part (ii) above and the current market rate of interest is 10 percent per annum, but he could choose to lend his funds in country Y where the current interest rate is 8 percent per annum. If he expects the exchange rate at the end of the year to be 1.20, where should he invest? [4 marks] [Total 9 marks] 9. Explain using appropriate diagrams the determination of the market price and output level of a monopoly. How would the market price and the level of output be determined if a monopoly were to produce a socially optimal level of output? [18 marks] 10. Describe the factors which influence the demand for money. Explain how Keynesians and Monetarists differ in their views on the demand for money. Using an appropriate diagram show the equilibrium in the money market and the determination of interest rates in the economy. [17 marks]