Gotcha, the only seller of stun guns, faces the inverse market demand curve P = 400 - 12Q, where Q measures the number of stun guns per day and P is the price per stun gun. The marginal cost is constant at $64. Suppose a new firm, Ouchy, enters the stun gun market. Ouchy's marginal cost is also constant at $64. Gotcha and Ouchy agree to form a cartel and evenly split the market output. Gotcha holds to the agreement, but Ouchy decides to produce 5 more stun guns than its level under the cartel agreement. In this case, the market price is $ ____.

Question

Quizplus · Accepted Answer

To find the market price after Ouchy decides to produce 5 more stun guns than its level under the cartel agreement, we first need to determine the total quantity of stun guns produced under the cartel agreement and then adjust for Ouchy's additional production. 1. Under the cartel agreement, the two firms would act as a monopoly and set production to maximize joint profits. The monopoly quantity is where MR = MC. The inverse demand curve is P = 400 - 12Q. To find MR, we first find the total revenue (TR) equation by multiplying P by Q: TR = (400 - 12Q)Q = 400Q - 12Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 400 - 24Q. Setting MR equal to the marginal cost (MC) of $64 gives us 400 - 24Q = 64, which simplifies to 336 = 24Q, or Q = 14 for the monopoly output.2. Since the firms agree to split the output evenly, each would produce 7 stun guns under the cartel agreement. However, Ouchy decides to produce 5 more, making its production 12 stun guns while Gotcha produces 7.3. The total quantity produced in the market is then 7 (Gotcha) + 12 (Ouchy) = 19 stun guns.4. Substituting this quantity back into the inverse demand equation to find the market price: P = 400 - 12(19) = 400 - 228 = 172.Therefore, the market price after Ouchy decides to produce 5 more stun guns than its level under the cartel agreement is $172.

Gotcha, the Only Seller of Stun Guns, Faces the Inverse