Question

91 = Two firms compete in a market by selling differentiated products. The demand equations are given by the following equations: P2 75 – P1 + 75 – P2 + 2. assume that each firm has a marginal cost (and average costs) of 0. a. What market model do we use if each firm competes by simultaneously choosing price? P 92 = b. Are the two goods substitutes? C. Solve for firm 1's best response function. d. Solve for the equilibrium price and quantity. e. Would firm 1 still be able to compete in the market if their marginal costs increased while firm 2's remained at 0?

Answer 1

a. Bertrand model is used when firm competes by simultaneously choosing price.

b. Yes, they are substitites because we can see from each demand function that if price of other good increases then its own demand will increase which means that they are substitutes.

c. MC = 0
Firm 1: Profit = TR - TC = q1*p1 - 0 = (75 - p1 + p2/2)*p1 = 75p1 - p1² + p1p2/2
d(Profit)/dp1 = 75 - 2p1 + p2/2 = 0
So, 2p1 = 75 + 0.5p2
So, p1 = 75/2 + 0.5p2/2
So, p1 = 37.5 + 0.25p2
This is the best response function of firm 1.

d. As their demand functions are similar, so, we can write firm 2's best response function as:
p2 = 37.5 + 0.25p1
Substituting the value of p1 into this, we get,
p2 = 37.5 + 0.25p1 = 37.5 + 0.25(37.5 + 0.25p2) = 37.5 + 9.375 + 0.0625p2
So, p2 - 0.0625p2 = 0.9375p2 = 46.875
So, p2 = 46.875/0.9375 = 50

So, p2 = p1 = 50

q1 = 75 - p1 + p2/2 = 75 - 50 + 50/2 = 25 + 25 = 50
So, q1 = q2 = 50

e. Firm 1 will not be able to compete because the products are subtitutes so as MC of firm 1 increase, its price will have to increase which will decrease the demand for its product.