4. Two companies, Firm 1 and Firm 2 sell the same product y. The market demand f

Question

4. Two companies, Firm 1 and Firm 2 sell the same product y. The market demand for the good y is given by y = 200-2p. Denote by ci the marginal cost of Firm 1 and c2 the marginal cost of Firm 2. Let yi be the quantity produced by Firm 1, v2 be the quantity produced by Firm 2, pi be the price of Firm 1, and p2 be the price of Firm 2. The firms compete à la Bertrand (a) What are yi and y2 when pi p2? prices. (c) (Bonus question) Assume that c,-2 and c2 0, Find the equilibrium prices. Now suppose that they sell competing products. These products are substitutes, so that the number of units that either company sells is a decreasing function of its own price and an increasing function of the other product's price. The demand function for each product is given by yi = 132-2P1 + P2 U2 102-2p2 +pi For the following assume that C1 = C2 =0. d) Write an expression for the total revenue of Firm 1, as a function of pi and p2. e) Find the best response function of Firm 1. (Hint: Find the revenue-maximizing p as a function of p2.) (f) Find the best response function of Firm 2. (g) (Bonus question) Find the equilibrium prices.

Explanation / Answer

a) Since p1<p2 and given that te goods are homogeneous/same, this will lead consumers to go to the low charging firm thus the output of firm 2 y2 will be zero while y1 = 200-2p1. When p1>p2, we have y1 = 0 and y2 = 200-2p2.

b) At c1 = c2 = 0, the prices will be p1 = p2 = 0. This is because charging a higher price will bring down the market share of the firm charging higher price.

c) At c1 = 2 and c1 =0, the firm 1 will charge a price p2 = 2-e, e being very small. Firm 2 will charge c1 = 2. Charging any less will cause losses to firm 1 thus the firm 2 caters to all the demand in the market and y1 = 0.

d) Total revenue for firm 1 = p1*y1 = (132-2p1+p2)p1 = 132p1 -2p1^2 +p2*p1

*For other parts please post as aseparate question mentioning the parts to be done.We are supposed to do only four sub-parts

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