What is the bertrand equilibrium

Question

Problem

Consider again the situation described above, but now imagine that each firm sets a price, selling as many units of the good as it can at that price. Each firm is aware that

• It will not be able to sell any goods if its price exceeds the other firm's price, because every consumer will prefer to buy from the other firm.
• If the two prices are the same, total purchases will be determined by the demand equation, and each firm will sell an equal quantity of goods.
• If its price is lower than the other firm's price, every consumer will prefer to buy from it rather than the other firm, and its total sales will be determined by the demand equation.

A Bertrand equilibrium in this environment is a pair of prices (p₁, p₂) such that, when firm 1 charges p₁ and firm 2 sells p₂, neither firm can raise its own profits by unilaterally changing its price. What is the Bertrand equilibrium?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.