Question

2. Consider two Bertrand competitors in the market for brie, Jason and Kayal. The cheeses of Jason and Kayal are differentiated, with the demand for Jason's cheese given by qt = 30 - py + px, where qt is the quantity Jason Sells, py is the price Jason charges, and px is the price charged by Kayal. The demand for Kayal’s cheese is similarly given by qt = 30 - px + py. Assume the marginal cost of producing cheeses is zero for both producers.

a) Find the Bertrand equilibrium prices and quantities as well as the profits for these two competitors.

b) Now consider a situation in which Jason sets his price first, and Kayal responds, Solve for profit-maximizing price and quantity and the level of profit for each competitor.

c) Based on (i) and (ii), was Jason's attempt to seize the first-mover advantage worthwhile?

Answer 1

Part A

Jason's Marginal revenue is,

Kayal's Marginal revenue is,

Here given that the marginal cost is zero, Then the firms reaction curve is,

Now the equilibrium prices are,

Part B

if Jason sets his price first, then

  

  

Now equating the marginal cost with the marginal revenue, then

If the price is $45, then profit is

Kayal's profit maximizing quantity is,

  

And, the price is,

The profit is,

Part C

If Jason be the first mover, the advantage was not worthwhile as his profit decreased.