The inverse demand for tacos is given by P = 10 - 0.02Q, where P is the price per taco and Q is the total number of tacos brought to market. There are two taco shops in the local market. Shop 1's cost function is given by C₁ = 0.01q₁², where q₁ is the number of tacos it brings to market. Shop 2's cost function is given by C₂ = 0.01q₂², where q₂ is the number of tacos it brings to market. Assume the two shops compete by setting output (Cournot). Let Q = q₁ + q₂. Shop 1 produces ____ to maximize profit.

Question

Quizplus · Accepted Answer

Given the inverse demand function P = 10 - 0.02Q and identical cost functions for both shops (CS = 0.01q^2), we can find the quantity produced by each shop to maximize profit in a Cournot competition by first finding the reaction functions for each shop. The reaction function is derived by maximizing profit given the output of the other firm. Since both firms have identical cost functions and face the same demand, they will produce the same quantity in equilibrium. Setting the derivative of the profit function with respect to quantity equal to zero and solving for q gives us the equilibrium quantity for each firm. In a symmetric equilibrium, Q = 2q, and substituting the demand function into the profit maximization condition leads to the equilibrium quantity of 125 tacos for each shop.

The Inverse Demand for Tacos Is Given by P =