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. In equilibrium, firm 1 will earn $ ____ in profit.

Question

Quizplus · Accepted Answer

The correct answer is A because firm 1's profit is given by π₁ = Pq₁ - C₁ = (30 - 0.03Q)q₁ - 0.05q₁² = 30q₁ - 0.03q₁² - 0.05q₁² = 30q₁ - 0.08q₁². To find the equilibrium output for firm 1, we take the derivative of π₁ with respect to q₁ and set it equal to zero: dπ₁/dq₁ = 30 - 0.16q₁ = 0. Solving for q₁, we get q₁ = 187.5. Substituting this back into the profit function, we get π₁ = 30(187.5) - 0.08(187.5)² = $1,741.37.

The Inverse Demand for Shampoo Is Given by P =