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Free response question

Microeconomics · Hard · 30 marks

IEO past paper: 2024 International Economics Olympiad, open questions

Open Question 4. Competition with the Leader In country B, the market for beer is organized as follows: There is a major brewery, Brewery A, and numerous (potentially very many) microbreweries and craft beer producers. Brewery A is the market leader and sets the price for a bottle that others follow as price-takers. After Brewery A sets the price, each price-taking firm decides how much beer to produce (if any). Any demand not met by these firms is satisfied by Brewery A. Assume the market parameters are as follows: - beer is a homogenous product, but the production technologies may differ across firms; - the demand function is $D(p) = 20{,}000 - 3p$ ; - the marginal cost of Brewery A is constant and equal to $MC_A = 30$ ; - the marginal cost of price-taking firm number $i$ is $MC_i = 3i + q_i$ , where $i = 1, 2, 3, \dots$ , and $q_i$ is the amount of beer produced by firm $i$ . Also, just in case you forgot, $1 + 2 + 3 + \dots + n = \dfrac{n(n+1)}{2}$ .

(a)Determine the supply function of a price-taking firm

i

. Don't forget to specify the supply level under all prices.[5](b)How many price-taking firms will produce beer under different prices set by Brewery A?[5](c)What is the profit-maximizing price that firm A should set?[10](d)You are the economic advisor to the President of Country B. The President believes that to improve consumers' welfare, the government needs to cease operations of Brewery A because it has enormous power in setting prices, which is always bad for consumers. If this policy is implemented, the market becomes perfectly competitive with only price-taking firms (

i = 1, 2, 3, \dots

). What advice would you give regarding such a policy?[5](e)Now assume that instead of shutting down Brewery A, the government orders it to become one of the price-taking firms. That is, the market becomes perfectly competitive with Brewery A and some other firms. How many firms will there be in the market in equilibrium? Compare this situation with (c) from the perspective of: (1) market concentration, (2) consumers' welfare.[5]

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