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, the market price is $____.

Question

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In a Cournot equilibrium, each firm maximizes its profit given the output of the other firm. Solving the reaction functions for both firms and substituting into the inverse demand function gives the equilibrium price.

The Inverse Demand for Shampoo Is Given by P =