A monopolist owns two plants in which to produce a product which has inverse demand $P =$ $( 770 / 3 ) - 3 Q$. The monopolist has marginal cost curves of $M C _ { 1 } = 20 + 3 Q _ { 1 }$ and $M C _ { 2 } = 10 + 6 Q _ { 2 }$ in the two plants, respectively. Which of the following represents the optimal outputs in the two plants, $Q _ { 1 }$ and $Q _ { 2 }$ and the market price?

Question

Quizplus · Accepted Answer

To find the optimal outputs and market price, we first determine the total quantity $Q = Q_1 + Q_2$ and then use the inverse demand function to find the price. The monopolist's goal is to maximize profit, which involves equating the marginal revenue (MR) to the marginal cost (MC) of production. The marginal cost curves are given for each plant, and we need to find the quantity where the marginal revenue equals the sum of the marginal costs from both plants. The solution provided in option A correctly reflects the outcome of this optimization process, taking into account the given demand and marginal cost functions.

A Monopolist Owns Two Plants in Which to Produce a Product