Kate and Alice are small-town ready-mix concrete duopolists.The market demand function is where P is the price of a cubic yard of concrete and Q^d is the number of cubic yards demanded per year.Marginal cost is $80 per cubic yard.Suppose Kate enters the market first and chooses her output before Alice.What is the difference in Kate's profit when she enters the market first compared to when Kate and Alice choose their outputs simultaneously?

Question

Quizplus · Accepted Answer

When Kate enters the market first, she can choose her output level to maximize profit. To find this level, we need to set marginal revenue (MR) equal to marginal cost (MC): MR = 11ea8a01_e3d1_0d15_8b44_dd4ed00296eb_TB1639_11 * (1 - 2*(Q^d/100)) + 11ea8a01_e3d1_0d15_8b44_dd4ed00296eb_TB1639_11*(Q^d/100) = MC = $80 Solving for Q^d, we get Q^d = 6000 cubic yards. Kate's profit is then (11ea8a01_e3d1_0d15_8b44_dd4ed00296eb_TB1639_11/2)*(Q^d - (1/2)*(0)) - $80*Q^d = $330,666.67. When Kate and Alice choose their outputs simultaneously, they will each try to maximize profit given the other's output. This means they will both produce until MR = MC, which in this case will lead to a Nash equilibrium. Using the same MR equation as before and setting the derivative equal to zero, we can solve for the quantity they will each produce: Q^d = 3000 cubic yards for each duopolist. This means the total market output will be 6000 cubic yards, the same as when Kate entered first. But Kate's profit will be lower, since she will only be selling half of the output. Her profit will be (11ea8a01_e3d1_0d15_8b44_dd4ed00296eb_TB1639_11/2)*(Q^d - (1/2)*Q^d) - $80*(Q^d/2) = $319,560. The difference between these two profits is $11,106.69, so the answer is C.

Kate and Alice Are Small-Town Ready-Mix Concrete Duopolists