The Inverse Demand for Coffeemakers Is Given by P =

question 165

Essay

The inverse demand for coffeemakers is given by P = 80 - 0.02Q, where P is the price and Q is the total number sold in the local market. There are two manufacturers operating in the local market. Firm 1's cost function is given by C₁ = 0.01q₁², where q₁ is the number brought to market by firm 1. Firm 2's cost function is given by C₂ = 0.02q₂², where q₂ is the number brought to market by firm 2. The two firms are Cournot competitors that compete by setting output so that Q = q₁ + q₂. Use calculus for the following.
a. Write firm 1's profit function and identify firm 1's reaction function to firm 2's output.
b. Write firm 2's profit function and identify firm 2's reaction function to firm 1's output.
c. Identify the equilibrium price and output of each firm.

---

Definitions:

Being Single

A state of not being in a marriage or a romantic relationship, focusing on individual autonomy and self-reliance.

Stigmatized

Labeled or regarded as worthy of disgrace or disapproval.

Maternity

The period during pregnancy and shortly after childbirth.

Child Support

Financial contributions legally required to be made by a non-custodial parent, aimed at supporting the wellbeing and expenses of their children.