Suppose that the marginal private benefit of a new vaccine could be measured as $M P B = 10 -$ $Q$. Suppose that the marginal social benefit could be measured as $M S B = 12 - Q$. Suppose that the private marginal cost curve could be measured as $M P C = Q$. If there is no subsidy in this market,:
A) society will over-consume this product by 2 units.
B) society will over-consume this product by 1 unit.
C) society will under-consume this product by 2 units.
D) society will under-consume this product by 1 unit.

Question

Quizplus · Accepted Answer

To find the socially optimal level of output, we can set MSB = MSC:

12 - Q = Q

Solving for Q, we get Q = 6.

Therefore, the socially optimal level of output is 6.

However, the market only takes into account the private benefit and cost, so it will only produce where MPB = MPC:

10 - Q = Q

Solving for Q, we get Q = 5.

Therefore, in the absence of a subsidy, the market will under-consume the vaccine by 1 unit (producing 5 instead of the socially optimal 6). To maximize social welfare, we want to produce at the quantity where marginal social benefit (MSB) equals marginal social cost (MSC).

Setting MSB = MSC, we get:

$$12 - Q = Q$$

Solving for Q, we get:

$$Q = 6$$

Thus, the socially optimal quantity to produce is 6 units of the vaccine.

However, in the absence of a subsidy, the private market will only produce up to the point where marginal private benefit (MPB) equals marginal private cost (MPC):

Setting MPB = MPC, we get:

$$10 - Q = Q$$

Solving for Q, we get:

$$Q = 5$$

Thus, the private market will only produce 5 units of the vaccine.

Since 5 < 6, society will under-consume this product by 1 unit. Therefore, the answer is D.

Suppose That the Marginal Private Benefit of a New Vaccine MPB=10−M P B = 10 -MPB=10−

Suppose That the Marginal Private Benefit of a New Vaccine $M P B = 10 -$