Economics 2A, ECON2001 2018
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Degree Exam
Economics 2A, ECON2001
December 2018
Section A
You must answer TWO questions from this section.
Please use ONE WHITE answer sheet per question. If there is not enough space on a white sheet, please raise your hand to request a YELLOW answer sheet in order to continue your answer.
1. [40%]
Suppose that you are in an economy with only two commodities and that you like both commodities. The consumption bundle where you consume x₁ units of commodity 1 and 
2 units of commodity 2 is written as (
1, 
2). The set of consumption bundles such that you are indifferent between (
1, 
2) and (1, 16) is the set of bundles such that 
1 ≥ 0, 
2 ≥ 0 and
2 = 20 − 4√
1 . The set of consumption bundles such that you are indifferent between (
1, 
2) and (36,0) is the set of bundles such that 
1 ≥ 0, 
2 ≥ 0 and 
2 = 24 − 4√
1 .
• In a diagram where commodity 1 is on the horizontal axis, plot your indifference curves passing through the points (1, 16) and (36,0).
• What is the slope of your indifference curve at the point (9, 12). And at the point (4, 16)? Do your indifference curve exhibit diminishing marginal rate of substitution? Explain your answer. Explain the economic meaning of your findings.
• Do you have monotonic preferences? Do you have strictly convex preferences? Explain your answers. Why do economists make the simplifying assumption that consumers have convex preferences?
2. [40%]
Firm 1 and firm 2 are the only firms who compete in a market. Firm 1 has constant average cost 
(
1) = 1 . Firm 2 also has constant average cost equal to 
(
2) = 2. Demand for the product they produce as a function of the price is 
(
) = 12 − 
.
• First assume firms compete in quantity. Calculate the reaction functions and how much each firm produces in a Cournot equilibrium. Draw the reaction functions on a graph, carefully labelling axis and curves. Calculate profits of each firm.
• Now, calculate quantities produced, price and profits if firm 1 is the Stackelberg leader. Comment on the differences between profits of each firm in this sub-question and the previous one.
• If both firms agreed to form a cartel (i.e. first get together and agree on the quantities each produces) to maximize joint profits, how much would each firm produce? What needs to happen so that both firms agree to the cartel?
3. [40%]
Jack owns a bicycle, which he uses to cycle to university every day. The value of the bicycle is 225 pounds. If he crashes while cycling he can sell the parts of his broken bicycle and get
1
25 pounds. Jack’s utility over the value of the bicycle is 
(
) = 
2 , with c being the value of
the consumption of the services of a bicycle that has value c. There is a chance that he
crashes the bicycle (Jack does not get hurt if he crashes).
• Graph Jack’s utility for values of the bicycle between 0 and 225 pounds on a graph that has c on the horizontal axis and the utility of c on the vertical axis. On the graph, indicate the amount of utility he would obtain if he crashed, and if he didn’t crash. What is the expected value of the bicycle (before Jack knows whether he is going to crash or not)? Show this value on the graph. What is Jack’s expected utility (again, before he knows whether he is going to crash or not)? Show this on the (same) graph. What can we say about Jack’s attitude towards risk?
• Imagine that Jack can obtain insurance that pays in case he crashed his bicycle. In particular, the insurance gives him 200 pounds if he crashes his bicycle. The insurance premium is y pounds, which need to be paid whether he crashes his bicycle or not. Please find Jack’s income in both states of the world (this will include y). If he decides to sign this insurance contract, how much risk does Jack face? Will Jack sign this insurance policy if y=40?
• What is the highest level of y for which Jack will still obtain this insurance policy (assume that in the case in which Jack is indifferent he will obtain the insurance policy)? Why might it be hard in reality to obtain an insurance that reimburses you if you crash your bicycle?
4. [40%]
An agricultural firm grows strawberries and operates as a price-taker. The firm’s costs are given by 
(
) = 2
+ 
2 + 
, with F>0 being a positive constant.
• Please find and draw on a chart (quantity q on the horizontal axis and costs on the vertical axis) the marginal cost function and the average variable cost function of this firm.
• What is the profit-maximizing level of output for the firm if the market price is equal to 12? What is the producer surplus for this firm at the profit-maximizing level of output?
• If fixed costs were to decrease, how would the firm change its profit-maximizing level of output? How large can the fixed costs be for the firm to have non-negative profits? What would the firm do if fixed costs were higher than that (imagine the firm knows of these costs but has not incurred them yet)?
Section B
You must now answer ALL sub-questions in question 5 from this section. Please use a new WHITE answer sheet. If there is not enough space on a white sheet, please raise your hand to request a YELLOW answer sheet in order to continue your answer.
5. [20%]
• A perfectly competitive firm sells two goods. The price for the first good is £33. The price for the second good is £17. The total cost for a firm is given by the expression:
TC (Q1, Q2) = 2Q12 + Q1Q2 + Q22 + 5Q1 + 3Q2
Find the maximum profit and the optimal values of Q1 and Q2 .
If the firm cannot produce in total more than 6 units, then what would be the maximum profit and the optimal values of Q1 and Q2? Find an answer using the Lagrange multiplier. Find a value of the Lagrange multiplier. What economic interpretation has the Lagrange multiplier in this context?
• Find the consumer’s surplus at P = 1 for the following demand function:
P = 2 Q-1/4
2021-12-06
Degree Exam