Question

In a competitive market for dry-cleaning, the inverse market demand function is given by: \[ P = 100 - Q \] where \( P \) denotes price and \( Q \) denotes quantity. The (private) marginal cost (MC) of production for all the dry-cleaning firms together is given by: \[ MC = 20 + 2Q \] The market pollution generated by the dry-cleaning processes of all firms creates external damages given by the marginal external cost (MEC): \[ MEC = 2Q. \] The socially efficient output of dry-cleaning is _________ (in integer).

Hint:

To find the socially efficient output, set the marginal social cost equal to the marginal benefit and solve for quantity. This accounts for both private and external costs.

Answer 1

Correct Answer: 16

The socially efficient output occurs when the marginal social cost (MSC) is equal to the marginal benefit (MB). The MSC is the sum of the private marginal cost and the marginal external cost: \[ MSC = MC + MEC = (20 + 2Q) + 2Q = 20 + 4Q. \] The marginal benefit is the price function, so we equate the MSC to the demand curve to find the socially efficient output: \[ P = MSC \quad \Rightarrow \quad 100 - Q = 20 + 4Q. \] Solving for \( Q \): \[ 100 - 20 = 4Q + Q \quad \Rightarrow \quad 80 = 5Q \quad \Rightarrow \quad Q = 16. \] Thus, the socially efficient output of dry-cleaning is: \[ \boxed{16}. \]