Answer to Question #264805 in Microeconomics for manuewrz

Question

a.) Suppose the demand for Pepsi-Cola is Qn = 54 - 2 Pn + Pc. The demand for Coca-Cola is Qc = 54 - 2 Pc + 1Pp. Each firm faces a constant marginal cost of zero. Determine the Bertrand equilibrium prices, output and profit for each firm.[10 marks] b.) What happens to the Bertrand equilibrium prices and profits if increased differentiation causes the demand for Pepsi-Cola to become Qn = 104 - 2 Pn + 1Pc while the demand for Coca-Cola remains unchanged ? c.) Suppose the demand for Pepsi-Cola is Qn = 50 - 2 Pp + 1 Pc. The firm faces a constant marginal cost of "m", and "pc" denotes the price of Coca-Cola. Assuming Bertrand behavior, derive Pepsi-Cola's best-response function and explain how the firm changes price in response to changes in its own marginal cost and changes in Coca-Cola's price. [5 marks]

Answer 1

Demand for pepsi:

$q_p=54-2pp+1pc$

$q_c=54-2pc+1pp$

$MC=0$

For pepsi profit maximization:

$\frac{\delta x}{\delta pp}=54-2pp+pc=0$

For coke profit maximization:

$\frac{\delta x}{\delta pc}=54-2pc+pp=0$

Both firms set price at 18.

When pepsi shifts demand curve,

New profit maximization:

$\frac{\delta x}{\delta pp}=104-4pp+pc$

Then pepsi charges:

$P=31.33$

$C=21.33$