Gotcha, the Only Seller of Stun Guns, Faces the Inverse

question 59

Essay

Gotcha, the only seller of stun guns, faces the inverse market demand curve P = 400 - 12Q, where Q measures the number of stun guns per day and P is the price per stun gun. The marginal cost is constant at $64.
a. What is Gotcha's profit-maximizing price and quantity?
b. Suppose a new firm, Ouchy, enters the stun gun market. Ouchy's marginal cost is also constant at $64. Gotcha and Ouchy decide to form a cartel and evenly split the market output. What is the market price? How much output does each firm produce?
c. Now suppose that Ouchy no longer abides by the cartel agreement; it decides to produce and sell 5 additional stun guns per day. What happens to the market price and market output?

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Definitions:

Central Nervous System

The part of the nervous system consisting of the brain and spinal cord, responsible for processing information and controlling responses.

Binge Drinking

The consumption of an excessive amount of alcohol in a short period of time, often defined as five or more drinks for men and four or more for women in about two hours.

Stimulant Use Disorder

A mental health condition characterized by the problematic use of substances that stimulate the central nervous system, leading to significant impairment or distress.

Brain's Reward Centers

Regions of the brain, including the nucleus accumbens, responsible for processing rewards and pleasure.