If the inverse demand for bean sprouts were given by P(Y)= 940 - 5Y and the total cost of producing Y units for any firm were TC(Y)=40Y and if the industry consisted of two Cournot duopolists, then in equilibrium each firm's production would be
A)90 units.
B)45 units.
C)30 units.
D)60 units.
E)47 units.

Question

Quizplus · Accepted Answer

In a Cournot duopoly, firms choose quantities to maximize their profits, taking into account the quantity produced by the other firm. The inverse demand function is P(Y) = 940 - 0.5Y, where Y is the total quantity produced by both firms, and the total cost function for producing Y units is TC(Y) = 40Y. To find the equilibrium quantity produced by each firm, we first determine the marginal cost (MC) from the total cost function, which is the derivative of TC(Y) with respect to Y, giving MC = 40. Then, we set up the reaction functions for each firm, considering that the total quantity Y = Y1 + Y2, where Y1 and Y2 are the quantities produced by firm 1 and firm 2, respectively. Solving the system of equations derived from the reaction functions typically involves substituting the expressions into the inverse demand function and solving for the quantities. In this case, without going through all the algebraic steps, the correct equilibrium quantity for each firm in a Cournot duopoly with the given demand and cost functions is 60 units, indicating that each firm will produce 60 units to maximize their profit in equilibrium.

If the Inverse Demand for Bean Sprouts Were Given by P(Y)=