Two portrait painters compete in a Bertrand market structure with differentiated products. The demand curve for the first is given by
where p_F is the price for a portrait from the first and p_S is the price from the second. The demand curve for the second painter's portraits is given by
The two painters' cost functions are C_F = q_F and C_S = q_S, respectively. Use calculus for the following:
a. Identify the first painter's profit function and its reaction function.
b. Identify the second painter's profit function and its reaction function.
c. Identify the equilibrium prices charged for portraits by the two painters.

Question

Two portrait painters compete in a Bertrand market structure with differentiated products. The demand curve for the first is given by

where p_F is the price for a portrait from the first and p_S is the price from the second. The demand curve for the second painter's portraits is given by

The two painters' cost functions are C_F = q_F and C_S = q_S, respectively. Use calculus for the following:
a. Identify the first painter's profit function and its reaction function.
b. Identify the second painter's profit function and its reaction function.
c. Identify the equilibrium prices charged for portraits by the two painters.

Quizplus · Accepted Answer

The Answer of Two portrait painters compete in a Bertrand market structure with differentiated products. The demand curve for the first is given by where p_F is the price for a portrait from the first and p_S is the price from the second. The demand curve for the second painter's portraits is given by The two painters' cost functions are C_F = q_F and C_S = q_S, respectively. Use calculus for the following: a. Identify the first painter's profit function and its reaction function. b. Identify the second painter's profit function and its reaction function. c. Identify the equilibrium prices charged for portraits by the two painters.

Two Portrait Painters Compete in a Bertrand Market Structure with Differentiated