ECS2601 EXAM PACK 2023

SUGGESTED SOLUTIONS FOR MAY/JUNE 2015 QUESTION 1 1a. Consider the following baskets of goods: A B C If preferences satisfy all requirements, is A preferred to C or C to A? Explain your answer. Basket A has more food than basket C. Basket C has more clothing than basket A. Therefore, basket A and C cannot be compared without additional information. 1b. An island economy produces only two goods – coconuts and pineapples. There are five people (A, B, C, D and E) living on the island, with these preferences: A has a strong preference for pineapples. B has a strong preference for coconuts. C doesn’t care for pineapples (assigns no value to them). D doesn’t care for coconuts (assigns no value to them). E will only consume pineapples and coconuts in the fixed proportion of one pineapple to one coconut. For each of these five individuals, construct a representative indifference curve with pineapples on the horizontal axis and coconuts on the vertical axis. Person A: Coconuts A Pineapples Downloaded by Rufaro Chikovore () lOMoARcPSD| Person B: Coconuts B Pineapples Person C: Coconut C Pineapple Person D: Coconut D Pineapple Downloaded by Rufaro Chikovore () lOMoARcPSD| Person E: Coconuts E Pineapples 1c. The diagram below depicts the change in optimal consumption bundles for Kgomotso when the price of bread decreases. Decompose the change into the income and substitution effects. Indicate the total effect, income effect and substitution effect in the diagram. (6 marks) Food bread Downloaded by Rufaro Chikovore () lOMoARcPSD| Food A hypothetical budget line must be constructed to show income effect, substitution effect and total effect. QUESTION 2 2a. A fast-food restaurant currently pays R20 per hour for labour and R40 per hour to rent ovens and other kitchen machinery. The restaurant uses seven hours of labour time per unit of machinery time. (i) Determine whether the restaurant is minimising its cost of production when the ratio of marginal products (capital to labour) is 10. If the firm is minimizing its costs of production, then the MRTS will equal a ratio of prices of inputs. The ratio of prices Pk / PL = R40 / R20= 2 And the MRTS of capital for labour (MPk / MPL) = 10. Since these two ratios are not equal, the firm is not minimizing costs. (ii) If not, what adjustments are called for to improve the efficiency of resource use? (2 marks) To increase efficiency in the use of inputs, the firm should use more capital and use less labour to make the ratios equal. Since these two ratios are not equal, the firm should change the mix of inputs. Downloaded by Rufaro Chikovore () lOMoARcPSD| 2b. (i) The following table contains information for a price taking competitive firm. Complete the table Output Total Cost 0 25 25 25 50 25 25 75 25 25 . 125 25 25 . (ii) Determine the profit maximizing level of output The profit maximizing level of output is where MR = MC. MR = MC at the level of 2. Hence should produce 2 units of output. QUESTION 3 3a. Suppose a firm can practice perfect, first-degree price discrimination. What is the lowest price it will charge, and what will its total output be? (4 marks) First-degree price discrimination is a practice of charging each customer her reservation price. Hence the lowest price it will charge will be marginal cost (i.e. P = MC) and the output will be where MC = AR (ie. the demand curve) 3b A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for his product: Q=200-2P MR=100-Q TC=5Q MC=5 (i) What is the profit maximising level of output? Profit is max when the firm produce at output level where MR = MC Find Q where MR = MC 100 –Q=5 Q=95 What is the profit maximising price Downloaded by Rufaro Chikovore () lOMoARcPSD| Q=200-2P95= 200 – 2p 2p = 105 P = 52.5 (iii) What is the total profit earned? Profit = TR – TC When firm produces 95 units, TR = PxQ = R52.5 x 95 = R4950, while TC = 5 x 95 = 475 Profit = R4987.5 –R 475 =R 4512.5 3b The two leading South African manufacturers of high performance radial tires must formulate their advertising strategies for the coming year. Each firm has two strategies available: maintain current advertising; or increase advertising by 15%. The strategies available to the two firms, A and B, are presented in the payoff matrix below: Firm A increases adveristing Firm A maintains adveristing The entries in the individual cells are profits measured in millions of rands. Firm A’s outcome is listed before the semicolon (;) and Firm B’s outcome is listed after the semicolon (;). (i) Which oligopoly model in the game theory is best suited for analysing this decision? The prisoner’s dilemma model is most appropriate for analysing this situation. (ii) If each firm tries to choose a strategy that is best for it, regardless of the other firm's strategy, which strategy would firm B and firm A choose? Support your choice by using the given firm’s payoffs. (6 marks) Increasing the advertising level is the dominant strategy, since the firm is better off increasing regardless of the rival’s action. For example, if Firm B increases, Firm A earns 18 if it increases and 6 if it does not increase. A is better off to increase advertising. If Firm B doesn’t increase, Firm A earns 24 by not increasing and 30 by increasing. Again, Firm A is better off to increase. It is obvious that no matter what B does, A is better off to increase. The same reasoning works for firm B as well. Increasing the advertising level is also the best strategy for firm B. Downloaded by Rufaro Chikovore () lOMoARcPSD| 2015 MAY/JUNE SECTION B 1. 2 2. 1 3. 2 4. 1 5. 4 6. 4 7. 2 8. 2 9. 1 10. 4 11. 2 12. 2 13. 3 14. 3 15. 5 16. 2 17. 4 18. 3 19. 4 20. 5 21. 2 22. 3 23. 2 24. 3 25. 3 26. 2 27. 4 28. 4 29. 4 30. 5 Downloaded by Rufaro Chikovore () lOMoARcPSD| SUGGESTED SOLUTIONS FOR MAY/JUNE 2014 1a. Consider the following baskets of goods: A B C If preferences satisfy all requirements, is A preferred to B or B to A? Explain your answer A has more food than B. While B has more clothing than A. A and B cannot be compared without additional information. 1b. In the field of financial management it has been observed that there is a trade- off between the rate of return that one earns on investments and the amount of risk that one must bear to earn that return. (i). Draw a set of indifference curves between risk and return for a person that is risk averse (a person that does not like risk). (ii). Draw a set of indifference curves for a person that is risk neutral (a person that does notcare about risk one way or the other). Downloaded by Rufaro Chikovore () lOMoARcPSD| (iii). Draw a set of indifference curves for a person that likes risk. (2 marks) (1c) Lindiwe has a budget of R140. The price of food is R20 and the price of clothes is R10. She maximises her utility by buying 4 units of food and 6 units of clothes. (i) Draw a budget line, with food on the horizontal axis. Clothes 14 7 Food (ii) Suppose an indifference map exists, show her equilibrium point on the diagram above. (2 marks) Downloaded by Rufaro Chikovore () lOMoARcPSD| (iii) Which condition must be satisfied to gain equilibrium? (2 marks) MRS = Pf / Pc Or The slope of the IC = the slope of the budget line Or The IC tangents to the budget line Or MUf / MUc = Pf / Pc (iv) When the income of Lindiwe increases to R180, she then maximise her utility by buying 5 units of food and 8 units of clothes. When the income increases to R260, she buys 8 units of food and 10 units of clothes. From the information given in (i) and (iii), draw an indifference curve map for Lindiwa indicating all equilibrium positions and also derive her income consumption curve. (5 marks) Clothes 26 IC2 IC1 18 14 10 Food 2a. For a producer that uses 6 units of labour at a wage rate of R20 000 per year and R400 000 worth of capital, work out the producer’s total cost of production per year, given an interest rate of 12%. (4 marks) TC = wL + rK = R20 000 X 6 + R400 000 X 12% = R168 000 Downloaded by Rufaro Chikovore () lOMoARcPSD| b. Use an isoquant map with associated isocost curves to explain that when capital is allowed to vary (the long run), a producer can expand and attain a level of output that is the same as when capital is fixed (the short run), however, at a lower total cost. (6 marks) When a firm operates in the short run, its cost of production may not be minimized because of inflexibility in the use of capital inputs. Output is initially at level Q1. In the short run, output Q2 can be produced only by increasing labor from L1 to L3 because capital is fixed at K1. In the long run, the same output can be produced more cheaply by increasing labor from L1 to L2 and capital from K1 to K2. (c) A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product: Q=200-2P MR=100-Q TC = 10Q MC=10 (i) What is the profit maximising level of output? Profit is max when the firm produce at output level where MR = MC Find Q where MR = MC 100 –Q=10 Q=90 Downloaded by Rufaro Chikovore () lOMoARcPSD| (ii) What is the profit maximising price? (3) Q=200-2P 90 = 200 – 2p 2p = 110 P=55 (iii) What is the total profit earned? (3) Profit = TR – TC When firm produces 90 units, TR = P X Q = R55 X 90 = 4950, while TC = 10 X 90 = 900 = 4950 – 900 Profit = 4050 3a (i). Explain the efficiency in production of two industries (the car industry and the computer industry) with two inputs, X and Y. (2 marks) Every producer’s marginal rate of technical substitution between input X and Y are equal to their factor price ratio OR MRTS = Px/ Py Answer the following questions based on the Edgeworth box diagram below. (ii) What is the line joining points C, D and F called? (2 marks) Contract curve. (iii) List any two points where production is inefficient. (2 marks) A and B. 5 Downloaded by Rufaro Chikovore () lOMoARcPSD| (iv) A movement from point A to point D will be to the benefit of which of the two industries? Explain your answer in no more than three sentences. (4) It will benefit computer industry while car industry remains the same. It is because this movement increase the output of computer industry by moving the isoquant outward / to a higher level of isoquant while the isoquant of car industry remains the same. (v) At point C, which of the two industries is dominant? (2) Car industry. 3b (i) The two leading South African manufacturers of high performance radial tires must set their advertising strategies for the coming year. Each firm has two strategies available: maintain current advertising or increase advertising by 15%. The strategies available to the two firms, G and B, are presented in the payoff matrix below. The entries in the individual cells are profits measured in millions of rands. Firm G’s outcome is listed before the comma, and Firm B’s outcome is listed after the comma. Which oligopoly model in the game theory is best suited for analyzing this decision? (2 marks) The prisoner’s dilemma model is most appropriate for analysing this situation. B (ii) Carefully explain the strategy that should be used by each firm. Support your choice by including numbers. (6 marks) Increasing the advertising level is the dominant strategy, since the firm is better off increasing regardless of the rival’s action. For example, if Firm B increases, Firm G earns 27 if it increases and 12 if it does not increase. G is better off increasing. If Firm B doesn’t increase, Firm G earns 45 by not increasing and 50 by increasing. Again, Firm G is better off to increase. It is obvious that no matter what B does, G is better off to increase. Firm B faces the same situation. Downloaded by Rufaro Chikovore () lOMoARcPSD| 2014 MAY/JUNE SECTION B 1. 2 2. 1 3. 2 4. 1 5. 3 6. 3 7. 2 8. 2 9. 1 10. 4 11. 1 12. 2 13. 5 14. 4 15. 5 16. 4 17. 3 18. 3 19. 3 20. 2 21. 1 22. 1 23. 5 24. 2 25. 2 26. 2 27. 1 28. 4 29. 1 30. 1