Question

Illustrating private vs social marginal costs and benefits using oversimplified examples. (a) The PMB of getting the annual flu shot can be approximated by P=50− q/2. The PMC of flu shots is a constant $30 (note: a constant MC just means that each additional flu shot produced always costs an extra $20 ). There are positive consumption externalities of getting flu shots (for ex., older people, for whom the flu shot is not very effective and who are at most risk of serious illness, benefit from having fewer exposures). Suppose that positive consumption externality was calculated to be MB=$20.

i. What is the SMB? (In the absence of an externality on the production side, PMC=SMC of producing flu shots)
ii. What is the privately optimal quantity?
iii. What is the socially optimal quantity?
iv. Graph these curves out, along with the private and social optima. Shade in the area corresponding to DWL.
v. What is the $ amount of deadweight loss?

Answer 1

The SMB is the sum of the MPB and the positive consumption externality. The privately optimal quantity is where the PMC equals the MPB. The socially optimal quantity is where the PMC equals the SMB.

Step-by-step explanation:

The SMB (Social Marginal Benefit) is the sum of the marginal private benefit and the positive consumption externality. In this case, the SMB is equal to the MPB + MB, which is $50 - q/2 + $20 = $70 - q/2.

The privately optimal quantity is where the PMC (Private Marginal Cost) equals the MPB. In this case, $30 = $50 - q/2, so solving for q gives us q = 40.

The socially optimal quantity is where the PMC equals the SMB. In this case, $30 = $70 - q/2, so solving for q gives us q = 80.

The graph of these curves will show the MPB, PMC, SMB, and the private and social optima. The area corresponding to deadweight loss will be shaded in. The deadweight loss is the difference between the privately optimal quantity and the socially optimal quantity, multiplied by the difference in prices. In this case, the deadweight loss would be ($80 - $40) * ($50 - $30) = $40 * $20 = $800.