Microeconomics: Sketch the indifference curves and the initial allocation on an appropriate diagram. In your diagram identify the area where there is scope for a Pareto improvement and explain why this is the case.
Candidates must attempt ALL questions
Question 1
Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B. There are 20 units of X and 20 units of Y in the economy. The preferences of the consumers are represented by the following utility functions:
ππ΄ (ππ΄ππ΄ ) = ππ΄ + 2ππ΄
ππ΅ (ππ΅ππ΅ ) = 3(ππ΅)2 ππ©
a. Suppose that initially consumer A has 10 units of X and 10 units of Y, while consumer B has all the remaining units of the two goods. Is this allocation Pareto efficient? [7 marks]
b. Sketch the indifference curves and the initial allocation on an appropriate diagram. In your diagram identify the area where there is scope for a Pareto improvement and explain why this is the case. [8 marks]
c. Now suppose initially A has all the available units of X and B has all the units of good Y. The price of X is 1 and the price of good Y is 1 as well. Write down expressions for the budget constraints for A and B. How much X and Y will be demanded at these prices? Do these prices and quantities form a general competitive equilibrium?
[10 marks]
[25 Marks]
Question 2
Suppose the inverse demand for a good is given by P = 30 β 2Q, where Q is the total quantity supplied by all firms in the market. Suppose any firm in the market has a constant marginal cost of 14.
a. Assume the market consists of two firms that set their quantities simultaneously. Calculate the duopoly levels of production and the equilibrium price. [7 marks]
b. Now assume firm 1 chooses its production level before firm 2 does. What will be the equilibrium quantities, price and profits in this case? [10 marks]
c. Now suppose that if firm 2 wishes to enter the market then it has to pay a fixed cost of 4. If firm 1 (who again is the first mover) chooses to produce a quantity q1 = 6, what will be firm 2βs profit? What conclusions can you draw concerning firm 2βs entrance decision and firm 1βs profit? [8 marks]
[25 Marks]
Question 3
Suppose the government is considering the provision of traffic lights at three different locations, denoted 1, 2 and ach traffic light costs $600 to install. There are three individuals (A, B, and C). If a traffic light is installed all individuals will be taxed equally to pay for the costs and this information is known to the individuals. The decision whether to install each individual traffic light is taken on the basis of a majority vote; and, for each individual, if the individualβs valuation is greater than or equal to the cost to them then they would vote in favour of provision. The table below gives the value that each individual places on installing a traffic light at each of the locations:
Location Individual A Individual B Individual C
1 170 150 300
2 220 250 180
3 150 220 220
a. Explain which traffic lights will be installed, and whether the outcomes are efficient. [9 marks]
b. Explain for each of the three locations what decisions would be made using a Clark-Groves mechanism, how much each individual would pay and how much revenue would be raised towards the cost. To ease your calculations, you can use a calculator or a computing software such as Excel. [10 marks]
c. What is the main disadvantage of the yes-no majority vote system and what is the main advantage of the Clark-Groves mechanism? [6 marks]
[25 Marks]
Question 4
a. Explain both formally and intuitively, why economic theory predicts that the prices of exhaustible resources rise at the rate of interest. (15 marks)
b. What factors may prevent this from occurring in the real world? How would such factors impact price growth? (10 marks)
[25 Marks]
