The Inverse Demand for Shampoo Is Given by P =

Essay

The inverse demand for shampoo is given by P = 30 - 0.03Q, where P is the price per bottle in dollars and Q is bottles brought to market in hundreds. There are two manufacturers in the local market. Firm 1's cost function is given by C₁ = 0.05q₁², where q₁ is the number of bottles it brings to market. Firm 2's cost function is given by C₂ = 0.03q₂², where q₂ is the number of bottles it brings to market. The two firms are Cournot competitors who set 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.