Consider two Bertrand competitors in the market for brie, Franc ois and Babette.
ID: 2495892 • Letter: C
Question
Consider two Bertrand competitors in the market for brie, Franc ois and Babette. The cheeses of Fran cois and Babette are differentiated, with the demand for Fran cois’ cheese given by qF = 30 pF + pB , where qF is the quantity Fran cois sells, pF is the price Fran cois charges, and pB is the price charged by Babette. The demand for Babette’s cheese is similarly given as qB = 30 pB + pF . Find the equilibrium price, quantities, and profits for Fran cois and Babette. (Assume the marginal cost for both is zero.)
Explanation / Answer
Ans:- Francols’s marginal revenue is MRF = 30-2PF+PB
Babette’s marginal revenue is MRB = 30-2PB+PF
Assuming that the marginal cost is zero, we can find the firm’s reaction curve:
MRF = 30-2PF+PB = 0 = MC
PF = 15+0.5PB
PB = 15+0.5PF
The equilibrium prices are;
PF = 15±0.5PB = 15+0.5(15+0.5PF) = 22.5+0.25 PF
= $30
PB = 15+0.5PF = $30
The equilibrium quantities are;
qF = 30-PF+PB = 30
qB = 30-PB+PF= 30
For Profit Francois
qF = 30-PF+(15+0.5PF) = 45-0.5PF
PF= 90-2qF
Equalling the marginal revenue with the marginal cost, we obtain
MRF = 90-4qF =0=MC
qF = 22.50
The price PF is $45. His profit is
TRF - TCF = $45*22.50-0 = $1012.5
For Profit Babette’s profit maximizing quantity is
qB = 30-PB+PF = 75- PB
MRB = 75-2qF =0=MC
qF = 37.50
The price is PB = 75 - qB = $37.50
His profit is
TRB – TCB = $37.50*$37.50-0 = $1406.25