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:
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beer is a homogenous product, but the production technologies may differ across firms;
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the demand function is $D(p) = 20,000 - 3p$ ;
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the marginal cost of Brewery A is constant and equal to $MCA = 30$ ;
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marginal cost of price-taking firm number i is $MCi = 3i + qi$, where $i = 1, 2, 3,...$, and qi is the amount of beer produced by firm i
Also, just in case you forgot, $1 + 2 + 3 +... + n = n(n+1)/2$.
(a) (5 rp) Determine the supply function of a price-taking firm i. Don't forget to specify the supply level under all prices.