Question

5. Suppose economists estimated the following total social cost and total social benefit functions associated with hand sanitizers:

TSB = 75Q – 0.4Q²

TSC = 25Q + 0.85Q²

Find the market efficient quantity of vaccines and the price of the vaccine.

What is the consumer surplus and producer surplus of the vaccine? Economic surplus?

If the government decides to make a price ceiling of $42 per unit, what does this action affect the market?

Answer 1

MSB = dTSB/dQ = 75 - 0.8Q

MSC = dTSC/dQ = 25 + 1.7Q

(a) Efficiency condition is MSB = MSC.

75 - 0.8Q = 25 + 1.7Q

2.5Q = 50

Q = 20

P = 75 - (0.8 x 20) = 75 - 16 = $59

(b)

From MSB function, when Q = 0, MSB = 75 (Vertical intercept).

Consumer surplus (CS) = Area between MSB curve & price = (1/2) x $(75 - 59) x 20 = 10 x $16 = $160

From MSC function, when Q = 0, MSC = 25 (Vertical intercept).

Producer surplus (PS) = Area between MSC curve & price = (1/2) x $(59 - 25) x 20 = 10 x $34 = $340

Economic surplus (ES) = CS + PS = $(160 + 340) = $500

(c)

When ceiling price = $42,

From MSB function: 42 = 75 - 0.8Q, or 0.8Q = 33, or Q = 41.25

From MSC function: 42 = 25 + 1.7Q, or 1.7Q = 17, or Q = 10

Since MSB > MSC, there is a market shortage equal to (MSB - MSC) = 41.25 - 10 = 31.25 units at this price.