Two Portrait Painters Compete in a Bertrand Market Structure with Differentiated

question 119

Essay

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.

---

Definitions:

Realities

The state of things as they actually exist, as opposed to an idealistic or notional idea of them.

Marital Burnout

The gradual deterioration of love and ultimate loss of an emotional attachment between partners.

Slowly

At a leisurely or reduced pace, allowing for careful progression or appreciation.

Quietly

In a manner that makes little or no noise; silently or softly.