QUESTION 1

Suppose a large steel manufacturing industry consists of D identical firms and the market demand curve is 𝑃𝑃 = 𝑘𝑘 − 𝑚𝑚𝑚𝑚. Each firm’s total cost is 0.5𝑐𝑐2 + 1.

(a) Find the Cournot equilibrium quantity per firm. (5 marks) (b) Find the Cournot equilibrium market quantity and price. (3 marks) c) Find the Monopoly market quantity, markup, and elasticity of demand. (3 marks) d) Find the Duopoly market quantity, markup, and elasticity of demand. (3 marks) e) Find in the perfectly competitive markets, the markup and elasticity of demand.
(3 marks) f) Assume that D-1 Firms merged into Firm 1, as a leader produces quantity M. Whereas the unmerged firm becomes Firm 2, a follower producing quantity Z. The inverse market demand curve is given by 𝑃𝑃 = 280 – 2(M + Z). Firms 1 and 2 have marginal costs equal to 40, respectively.
(i) Assuming duopoly, find the reaction function, equilibrium output and price. Plot the reaction function and show the equilibrium quantities. (7 marks) (ii) Find the Stackelberg equilibrium quantities and price. (4 marks) (iii) Using well annotated diagram show the Stackelberg equilibrium in (i). (3 marks)

QUESTION 2

a) In the reward program of leading fast fast-moving consumer goods market there are only two firms. Firms A and B should decide whether to offer a frequent buyer program to their customers. The annual profits of Firms A and B associated with each strategy are summarized in the following table below.

Frequent buyer

Firm B
Frequent buyer program

No frequent buyer program

Firm A
program 400 ; 320 680 ; 160
No Frequent buyer
program 320 ; 280 480 ; 400

i) Determine whether each firm has a dominant strategy. (4 marks) ii) Find the Nash equilibrium in this game. (3 marks) iii) Can you describe this game as an example of the prisoners’ dilemma? Explain.
(3 marks)
iv) If Firm A could move first, determine sequential, the optimal strategy. (4 marks)

b) Anna is employed by a manufacturing company, but because of the predictions of low economic growth and high inflation from the end of 2022 to 2023, is unsure if she will keep her job. Her income (Y) from her current job is R90,000. There is an 80% probability that she will keep her job and earn this income. However, there is a 20% probability that she will be laid off and will be out of work for a long time. The lay-off will force her to accept a lower-paying job. In this case, her income is R10,000.
1) Show that Anna`s expected value of her income is thus R74,000.
2) If Anna`s utility function has the formula 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 − 𝟏𝟏. 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟐𝟐
i) Determine the value of the insurance required to the purchase insurance policy ii) Interpret the value in (i).

QUESTION 3

Suppose you are a consultant working for an economic advisory company which is working on an assignment in the electric car battery manufacturing industry using Lithium. The client has provided your manager with the information needed to complete the assignment. The market demand curve in the lithium electric car battery manufacturing industry is given Q = 200 – 2P. The industry is dominated by a large firm with a marginal cost of R4 per kilogram. There is a competitive fringe of 12 price- taking firms, each of which has a total cost function 𝑇𝑇𝑇𝑇 = 3𝑞𝑞2 + 20𝑞𝑞. To complete the report your manager requires the information below.

a) Find the supply function of the fringe firms. (3 marks)
b) (i) Find the output and price of the dominant and fringe firms. (3.5 marks) (ii) Find the dominant firm`s profit, markup and elasticity of demand. (3.5 marks) c) Graph your answer to part (b). (4 marks)

d) Calculate the welfare effects of a dominant firm. (2 marks)

e) Determine the effects on dominant and fringe when
(i) the total market demand doubles. (3.5 marks) (ii) the marginal costs double (3.5 marks) f) Give a recommendation based on results in b) and e). (3 marks)

g) With the aid of a well-annotated diagram, determine the effects of doubling the fringe supply on dominant and fringe equilibrium conditions in comparison to (b). (8 marks)

Answers to Above Questions on Economics

Answer 1: The Cournot equilibrium quantity per firm is calculated as follows:

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