A monopolist has a marginal cost of $4 and no fixed cost.It faces the following inverse demand curve: p = 40 - q.The monopolist can introduce a new packaging for its product.Such new packaging does not alter the marginal cost.It makes the product more attractive for the consumer,and it would lead to a new inverse demand curve p = 40 - 0.5q.What is the maximum amount that the monopolist would be willing to invest in this new packaging project?
A) $245
B) $324
C) $420
D) It cannot be determined.

Question

Quizplus · Accepted Answer

To find the maximum amount the monopolist would be willing to invest in the new packaging, we first calculate the profit before and after the introduction of the new packaging. The profit is given by $\pi = (P - MC) \times Q$, where $P$ is the price, $MC$ is the marginal cost, and $Q$ is the quantity.**Before the new packaging:**The inverse demand curve is $P = 40 - Q$. To maximize profit, set marginal revenue (MR) equal to marginal cost (MC). The marginal revenue curve can be derived from the demand curve and is $MR = 40 - 2Q$. Setting $MR = MC$:$$40 - 2Q = 4$$$$36 = 2Q$$$$Q = 18$$Substituting $Q = 18$ into the demand curve to find $P$:$$P = 40 - 18 = 22$$Profit before the new packaging is:$$\pi_{before} = (22 - 4) \times 18 = 18 \times 18 = 324$$**After the new packaging:**The new inverse demand curve is $P = 40 - 0.5Q$. The marginal revenue curve derived from this demand curve is $MR = 40 - Q$. Setting $MR = MC$:$$40 - Q = 4$$$$Q = 36$$Substituting $Q = 36$ into the new demand curve to find $P$:$$P = 40 - 0.5 \times 36 = 40 - 18 = 22$$Profit after the new packaging is:$$\pi_{after} = (22 - 4) \times 36 = 18 \times 36 = 648$$The maximum amount the monopolist would be willing to invest in the new packaging is the difference in profit:$$\pi_{after} - \pi_{before} = 648 - 324 = 324$$Therefore, the monopolist would be willing to invest up to $324 in the new packaging project.

A Monopolist Has a Marginal Cost of $4 and No