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Degree Exam

Economics 2A, ECON2001

December 2020

QUESTION 1

A firm delivers groceries to people’s homes during COVID restrictions and operates as a price-taker. The firm’s total costs are given by () = 4 + 2 + , where A>0 is a positive constant and q is the number of deliveries.

• Find and draw on a graph (quantity q on the horizontal axis and costs on the vertical axis) the marginal cost, the average variable cost and the average total cost functions of this firm. Provide a short explanation on how you derived them.

• Set up the firm’s maximization problem. What is the profit-maximizing level of output, if the market price is equal to 40? What is/are the variable(s) that the firm can control ? What is the producer surplus at the profit-maximizing level of output? Derive and show the area of producer surplus on a new graph.

• How would the firm change its profit-maximizing level of output if fixed costs were to decrease? Explain briefly.

• How large should the fixed costs be for the firm to have non-negative profits? What would the firm do if fixed costs were higher than that?

(50%)

QUESTION 2

Fatima owns a computer worth 512 pounds. She is using it so much for online learning, so she is afraid that it is possible that the computer will crash. If the computer crashes, she can only sell the parts for 64 pounds. The utility that Fatima gets from using the computer is

() = 3, with c being the value of the computer. Suppose that there is a 10% chance that the computer crashes.

• Plot Fatima’s utility function. On the graph, indicate the utility she would obtain if the computer crashed, and if it didn’t crash. What is the expected value of the computer? What is Fatima’s expected utility? Illustrate both utilities on the graph. What do you conclude about Fatima’s attitude towards risk?

• Imagine that Fatima can purchase an insurance that pays her 400 pounds if her computer crashes. The insurance cost is y pounds, which needs to be paid whether the computer crashes or not. Derive the utility (i.e. in pounds) that Fatima owns in both states of the world when the insurance is available, and the expected value of Fatima’s wealth (which includes computer and insurance payments made and received). Is Fatima facing any risk when buying this insurance policy? Explain in detail.

• How could you find the highest level of y for which Fatima still buys this insurance policy? (you need to only set up the problem, no need to solve it). Discuss one possible reason why in reality we rarely see insurance that fully compensates people for their losses?

(50%)

QUESTION 3

The market for search engines has only two firms, Goo (firm 1) and Gle (firm 2). Goo has constant average cost (1) = 2. Gle has average cost equal to (2) = 2 . Demand for the goods they produce as a function of the price is given by () = 5 − .

• Assume firms compete in quantity. Derive the reaction functions and how much each firm produces in a Cournot equilibrium. Draw the reaction functions on a graph, labelling axis and curves. Calculate profits of each firm. For each step, briefly comment on the logic behind them.

• Now, calculate quantities produced, price and profits if Gle is the Stackelberg leader. Discuss the differences between profits of each firm in the Stackelberg equilibrium and in the Cournot-Nash equilibrium.

• If both firms agreed to form a Cartel to maximize joint profits, how much would each firm produce? Assuming that the firms are sure that the cartel is stable, would the firms agree to let another firm enter the market (and the cartel)? Why or why not?

(50%)

QUESTION 4

A market is characterised by a monopoly. The firm’s total cost function for producing X units

of the good is () = 1 2 . Assume that the monopolist faces the demand function =

15 − .

• On a graph, show the inverse demand, marginal revenue and marginal cost curves. Set up the profit maximization problem that the firm faces. Derive the profit maximizing price, quantity and the resulting profit of the monopolist, including all the intermediate steps. Show the equilibrium price and quantity on the graph. What is the socially optimal price? Derive and explain.

• Calculate the consumer surplus, producer surplus and deadweight loss (DWL) from the monopoly and show it on the graph. Show all your calculations. Discuss why monopoly causes inefficiency.

• Consider that the government wants to correct the inefficiency and maximize the total surplus. How can the government achieve this? Be specific using your previous calculations. Discuss the government’s challenges in implementing such policies.

(50%)