Exam 2017, questions PDF

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Exam 2017, questions...

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INTERMEDIATE MICROECONOMICS (16ECB002) Summer 2017

3 Hours

Students must answer ALL the questions in Section A and TWO questions in Section B. Section A is worth 40% of the marks, Section B is worth 60% of the marks. Answers to Section A should be given on the OMR answer sheet in pencil. Answers to Section B should be in your answer booklet. Any approved University calculator is permitted.

SECTION A Answer all 20 multiple choice questions. Each question is worth 2 marks. Questions 1-3 consider a consumer choosing between good X and good Y. The consumer’s utility function is U=X0.5+4Y0.5 and her budget constraint is 2X+4Y=M, where M refers to the consumer’s income. 1. What is the consumer’s marginal rate of substitution, −(฀฀฀฀/฀฀฀฀฀฀)/(฀฀฀฀ /฀฀฀฀)? a) −4 b) −4 c) d)

√฀฀ √฀฀ √฀฀

.

.

√฀฀ ฀฀ √฀฀ − ฀฀ . √฀฀ 1 √฀฀ -4 . √฀฀

2. What is the consumer’s optimal ratio? a) b) c) d)

Y*=4X*. Y*=16X*. Y*=32X*. Y*=64X*.

3. At what level of income, M, does the consumer optimally purchase 2 units of good Y. a) b) c) d)

M=72. M=36. M=18. M=9.

Questions 4-5 consider the extension to the planned HS2 high-speed railway. The demand for its usage, Q, is predicted to be as follows where M is predicted average income, p is the predicted price of travel on the HS2, and {pA, pB, pC} are the predicted prices of other modes of transport. Page 1 of 7

Q= 1.5M - 0.6p + 0.2pA + 0.1pB - 0.3pC 4. Which of the following statements is correct? a) b) c) d)

The HS2 is an inferior good and transport mode C is a substitute good to HS2. The HS2 is a normal good and transport mode A is a substitute good to HS2. The HS2 is a normal good and transport mode B is a complement good to HS2. The HS2 is a normal good and transport mode C is a substitute good to HS2.

5. Now suppose M=50 and Q=100. If income rose by 1%, what percentage change would be expected in the demand for HS2? a) +0.25%. b) +0.5%. c) +0.75%. d) -1%. 6. A firm has a marginal cost function, MC(q) = 7q. Which of the following statements is most correct? a) b) c) d)

The firm has a total cost function, TC(q) = 10 + 7q2 . The firm has an average cost function, AC(q) = (10/q) + 7q. The firm has a fixed cost, F=10. Statements a)-c) may all be incorrect.

7. Consider a consumer who receives an income of m1=10 in period one and m2=10 in period two. There is a single composite good which has a price equal to one. The consumer’s utility function defined over period one consumption, c1, and period two consumption, c2, is expressed by U(c1,c2) = c10.5 + c20.5. The consumer can freely borrow or save at an interest rate of 5%. As such, the consumer’s optimisation problem can be written as L = c10.5 + c20.5 - λ (c2 - 10 - 1.05(10 - c1)). What is the consumer’s optimal level of period two consumption? a) b) c) d)

9.50 9.52 10.50 10.52.

Answer: Optimal ratio: from i)/ii), we know c1-0.5/c2-0.5=1.05 such that (c2 /c1)0.5=1.05, and so c2 = c1(1.05)2 = 1.1025c1. Expanding the BC from iii) gives c2 + 1.05c1=20.5. Sub ฀฀฀฀.฀฀ in optimal ratio implies 1.1025c1 + 1.05c1=20.5 and so c1* = ฀฀.฀฀฀฀฀฀฀฀ = 9.52, and c2*=1.1025c2*=10.50. Questions 8-10 refer the following diagram. A perfectly competitive industry starts at market equilibrium e1 with market price, p1, and quantity, q1. However, the government then implements a licensing system that restricts and reduces the number of firms to n’. This causes the market supply curve to move from S1 to S2. As a result, the market equilibrium to moves from e1 to e2 with a new market price, p2, and quantity, q2. Price S2 A p2 p1

B

e2 C

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e1

S1

8. Which of the following reasons best explains why the government policy leads to a movement in the market supply curve from S1 to S2. a) The market supply curve must now only reflect the increasing costs of the n’ existing firms because entry is restricted. b) The policy increases the costs of each individual firm. c) The policy increases input prices. d) The policy increases the costs of the entrants. 9. In terms of the lettered areas on the diagram, what is the loss in total welfare as a result of the policy? a) b) c) d)

A B C We cannot tell.

10. After a period of time, suppose the government puts the licences up for renewal and decides to allocate them to the highest bidders via an auction. If there is an unlimited number of identical potential entrants, how much money could the government raise through such an auction in terms of the lettered areas on the diagram? a) b) c) d)

A B C We cannot tell.

Questions 11-16 refer to the diagram below which show firm 1’s isoprofit lines when marginal cost is zero and inverse demand equals P=50-Q1-Q2, where Q1 and Q2 are output levels of two firms in a duopolistic industry, and P is the market price. 11. Which is the best description of firm 1’s reaction function? a) b) c) d)

The level of profits firm 1 makes as a response to firm 2’s output. The level of output by firm 1 which maximises profits given firm 2’s output. The level of output by firm 2 which maximises profits given firm 1’s output. The level of output by firm 1 which maximises profits given firm 2’s reaction function.

12. Use the diagram to draw in firm 1’s reaction function. When firm 1 is a monopolist, approximately how much output will it produce? Page 3 of 7

a) b) c) d)

16.7 units. 25 units. 12.5 units. Zero units.

13. Firm 2 is symmetric to Firm 1. Use the diagram to also draw in firm 2’s reaction function. If the two firms are Cournot duopolists, approximately how many units will each produce? a) b) c) d)

16.7 units. 25 units. 12.5 units. Zero units.

14. If firm 1 is a Stackelberg leader, how many units will firm 2 produce? a) b) c) d)

16.7 units. 25 units. 12.5 units. Zero units.

15. What will the market price, P, be under Stackelberg duopoly? a) b) c) d)

16.7 per unit. 25 per unit. 12.5 per unit. Zero per unit.

16. If firms pay a fixed cost of £600 each to produce in this industry, but any number of firms are able to enter, how many firms will there be in the industry? a) b) c) d)

None. One. Two. More than two.

Questions 17-19 below refer to a market in used cars. These may either be Peaches (which yield an utility to consumers of £1000) or Lemons (which yield an utility of £0). The probability that a car is a peach is P. The reservation price of the seller is the minimum price at which he is willing to sell. The reservation price for the seller of a Peach is £R (which is less than £1000), while the reservation price for the seller of a Lemon is zero. A purchaser cannot tell whether a used car is a Peach or a Lemon. 17. Which of the following conditions correctly determines the market price? a) If ฀฀ ≤ 1000฀฀, then the market price is between R and 1000P. Otherwise it is zero. b) If ฀ ฀ > 1000฀฀, then the market price is between R and 1000P. Otherwise it is zero. Page 4 of 7

c) If 1000฀฀ ≤ ฀฀ then the market price is between R and 1000P. Otherwise it is zero. d) None of the above. 18. Which of the following is not an effective signalling strategy for a seller of Peaches to differentiate their cars from Lemons. a) b) c) d)

Offering a warrantee for the car. Paying a reputable agent to verify the quality of the car. Installing a poster saying that under no circumstances will he sell for less than £R. Paying a well-known dealer to sell the car.

PTO 19. Which of the following government interventions would not help in stopping the market from disappearing. a) b) c) d)

A tax on sales of used cars. A subsidy on sales of used cars. Compulsory warrantees. Compulsory testing for used cars.

20. A worker’s utility U(Y) is a function of income Y, U(Y)=Y0.5. There are two possible choices. Choice 1 provides an income of £40000 with a 50% chance and zero otherwise. Choice 2 provides an income of £16,000 with certainty. What are the expected utilities for each choice respectively? a) b) c) d)

20000 and 16000. 20000 and 400. 100 and 16000. 100 and 400. SECTION B Answer TWO questions. Each question is worth 30% of the marks.

21. Provide a concise account of four of the following: i) ii) iii) iv) v) vi)

The Slutsky equation. Consumer surplus. Isoquants. The Contract Curve. Risk Neutrality. Pooling Risk.

22. Consider a UK carrot farmer. To produce a given level of output, q, assume that the farmer hires two factors of production: home-based labour, H, at a wage rate of 60, and foreign labour, F, at a wage rate of 30. The farmer’s associated optimisation problem can then be characterised by the following Lagrangian function:

Page 5 of 7

L = 60 H +30 F − λ( H 0.5 + F 0.5 − q) a) Provide an expression for the firm’s production function. Answer: q=H0.5+F0.5 or H0.5+F0.5 (5 marks) Feedback: b) Given the presented Lagrangian, explain whether the farmer’s optimisation problem should be thought of as a maximisation problem or a minimisation problem. Answer: Minimisation. Exploiting the dual of the problem, it is easier to think of the firm as minimising its long run costs subject to supplying a given level of output, rather than maximising its output subject to a given level of costs. (5 marks) Feedback: c) Without making any calculations, provide a detailed, annotated diagram to represent the farmer’s optimisation problem conceptually. Answer: The diagram would be something like this, showing axes, isocosts, isoquants, and optimal minimisation point. (20 marks) Optimal point that minimises costs subject to supplying output q

H

Isocosts, that show possible combinations of H and F that give a given level of total costs

isoquant, showing possible combinations of H and F that yield a given output, q

F Feedback: d) Use the presented Lagrangian to provide the three first order conditions of the optimisation problem. Answer: The FOC’s are provided below and should include (=0). (20 marks). dL/dH=

60 − λ (0.5H −0.5 ) = 0

dL/dF= dL/d λ =

30 − λ(0.5 F −0.5 ) = 0 − ( H 0. 5 + F 0. 5 − q ) = 0

Feedback: e) Calculate the firm’s optimal choice of capital and labour as a function of output, q. Page 6 of 7

Answer: H* = (q2/9) and F* = 4q2/9. Workings: From i) and ii), (60/30)=F0.5/H0.5, 2H0.5=F0.5, and so 4H*=F*. Into iii) H0.5+(4H).0.5 = q, H0.5+2H0.5 = q, 3H0.5=q, H0.5=q/3, H*=q2/9. Then F*=4H** and so F*=4q2/9. (20 marks) Feedback: f) Now, post-Brexit, suppose that the price of foreign labour increases to 90. Calculate and explain the resulting effects on the farmer’s optimal choice. Answer: H** = 3q2/5 and F**=(4q2/15).. Workings: From revised i) and ii), (60/90)=F0.5/H0.5, (2/3)H0.5=F0.5, and so (4/9)H**=F**. Into iii) H0.5+((4/9)H).0.5 = q, H0.5+(2/3)H0.5 = q, (5/3)H0.5=q, H0.5=3q/5, so H**=9q2/25. Then F**=(4/9)H** and so F**=(4/9)(9q2/25) **=(4q2/25). Intuitively, holding q constant, the increase in the relative price of foreign labour has reduced the demand for F and increased the demand for H through the substitution effect. The wage increase would also raise the farmer’s marginal cost. However, it is important to note that these effects are holding q constant and in a broader analysis the wage increase would likely result in a reduction in output which could lead to a reduction in the demand for both factors of production. (30 marks) Feedback:

23. A firm produces output using capital, K, with annual rental cost, r, and labour, L, with wage rate, w. The firm’s production function is Y = K0.5 L0.5 which implies that the firm has constant returns to scale and spends half of its cost expenditure on capital and half on labour. The firm employs 1000 workers each paid £10,000. The firm’s total sales are £30m. a) If the capital rental cost is £1m per machine, how many machines does the firm employ? b) What level of super-normal profit does the firm make? c) Given constant returns to scale, what is the relationship between average cost, AC, and marginal cost, MC? d) Provide values for the marginal cost, MC, and price, P, as a function of output Y. e) Calculate the firm’s Lerner index, (P-MC)/P, and the implied price elasticity of demand. f) Hence comment on whether you would regard it as a perfectly competitive or monopolistic firm. g) What factors might allow a firm with constant returns to scale in production to make a monopolistic profit?

24. Using at least one example, outline the problems involved in simultaneously encouraging innovation and encouraging the efficient use of intellectual property. How well does the current system work?

TH EDWARDS CM WILSON Page 7 of 7...