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Firm A has no costs of production and sells its production i

Firm A has no costs of production and sells its production in two buyers. Buyer 1's demand function is
p1 = 90 - 10y1
and Buyer 2's demand function is
p2 = 60 - 5y2
Assuming that the firm can engage in ordinary price discrimination, find the profit maximizing prices.

What is firm A's profit?
Now suppose that the firm cannot price-discriminate.
First find the firms aggregate demand function.
Then find its marginal revenue function.
Find its profit maximizing price, and compute its profit

Solution Preview

p1 = 90 - 10y1

Total Profit = 90y1 - 10y1^2

dprofit / dy1 = 90 - 20y1

y1 = 4.5 (substituting dprofit /dy1 = 0 for profit maximization)

total profit from p1 = 90x4.5 - 10 (4.5)^2 = ...

$2.19