EC2380 Economics 2: Microeconomics 2020/21
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EC2380
2020/21
Economics 2: Microeconomics
Section A: Answer BOTH questions |
1. Answer true, false or uncertain and provide an explanation. (a) Any separating equilibrium will lead to a larger total surplus for society than a pooling equilibrium. (10 marks) (b) If Andrew’s utility function is denoted by ⃞( = )⃞ ,⃞min show would this ,}⃞4 ;⃞2{ that goods A and B are perfect complements. This would also imply that if there was a change in the price of one of the goods, any change in optimal demands would be entirely due to the income effect. (10 marks) (c) Under the Bertrand model, the Nash equilibrium will always occur where both firms produce where P = MC. (10 marks) |
2. Consider a pack of playing cards, which has 52 cards: 13 are hearts, 13 are clubs, 13 are diamonds and 13 are spades. Barry is deciding whether to play a game, whereby if a heart is drawn, he wins £50, if a club or spade is drawn, he wins £10, but if a diamond is drawn, he loses £10. The cost of playing the game is £10.
(a) Determine the expected value of the game and explain whether we are able to
determine if Barry would choose to play the game. (6 marks)
Barry has a friend called Daria. Both are risk averse and each has A = £100 to spend on consumption. Both put £B on the table, (where B < A) then draw a playing card. If it is a heart or a diamond (a red card), Daria wins everything on the table and if it is a club or a spade (a black card), Barry wins everything on the table. Consider Barry and Daria in the context of an Edgeworth Box, with consumption XR under ‘Red’ on the horizontal and consumption XB under ‘black’ on the vertical axis, with Barry’s origin at the bottom left of the Edgeworth Box.
(b) Construct this Edgeworth Box and by identifying the ‘endowment’ bundle E before
the gamble and the outcome bundle O if they do gamble, determine whether or not it is an efficient decision to gamble. (14 marks)
Section B: Answer ONE question |
3. Consider a consumer called Nadia, who has chosen to optimize by consuming 5 units of good A and 10 units of B, when the price of good A is £10; the price of good B is £4 and her income is £90. (a) Given this information, explain why it is impossible for us to determine the utility function that describes Nadia’s preferences. (4 marks) (b) If Nadia faces a utility function of ⃞ = ⃞ఈ⃞⃞ିఈ and faces prices and incomes of ,⃞ ,⃞⃞ ,⃞⃞find an expression for the Marshall demands. (6 marks) (c) If the price of good X now fell to ⃞, find an expression to show the amount by which income would need to change if we used the Slutsky form of compensation. (10 marks) When a price change occurs, we can use equivalent variation to measure the impact on consumer welfare. |
(d) If there was a fall in the price of good X (measured on the horizontal axis) and Nadia continues to face the utility function as outlined in part (b), illustrate and explain how we would determine the equivalent variation of the price change. (10 marks)
(e) Now assume that Nadia faces a utility function of the form: ⃞ = 8⃞మ + 2⃞ where
good Y is a composite good that represents spending on all other goods. The prices of goods X and Y are ⃞⃞ = 1; ⃞⃞ = 1 and income is £100. The government then imposes a tax on the price of good X, such that its new price is ⃞⃞ = 2. Find the compensating variation. Given your knowledge about the type of preferences that the utility function represents, what can we say about the size of the equivalent variation and consumer surplus? (20 marks)
4.
(a) If we want to find the efficient quantity of a good, why would the approach used be
different depending on whether we have a private good or a public good? Explain the approach used in each case. (8 marks)
(b) Assume that we have a private good, where there are two firms competing in the market. The market demand function is: ⃞ = 272 − 8⃞ and ⃞ = .⃞⃞ + ⃞⃞Both firms face marginal costs of .4 = ⃞⃞Find the Cournot Nash equilibrium and the market output and price. (16 marks)
(c) If firm A’s marginal cost were now above that of firm B’s marginal cost, explain intuitively how this would change the Nash equilibrium. (4 marks)
Assume now that firm B leaves the market and so firm A becomes a monopolist. However, in producing the good, firm A imposes a negative externality on firm B. In order to deal with the negative externality, governments could intervene with a per unit tax on firm A’s output.
(d) Firstly, explain the concept of a negative externality. Then, with the help of a diagram, explain why the tax imposed on firm A would not be set equal to the size of the externality imposed on firm B. (12 marks)
(e) If the government decided against a tax and instead extended property rights to
firm B, explain how the Coase Theorem could enable an efficient point to be reached. (10 marks)
2022-05-11