Consider a market where demand is P=10-2Q. There is a negative production extern

ID: 1122623 • Letter: C

Question

Consider a market where demand is P=10-2Q. There is a negative production externality of $2.50 per unit of consumption. Supply is equal to P=Q/2.

a. What is market equilibrium?

b. What is the socially optimum quantity and price?

c. If the government uses a tax to get producers to internalize the externality, what is the net price received by producers?

d. Calculate the total surplus in the market equilibrium.

e. Calculate the total surplus at the social optimum.

f. Calculate the total surplus with the tax.

Demand: P = 10 - 2Q

Supply: P = Q/2 = 0.5Q

Marginal social cost (MSC) = Supply price + Externality cost = 0.5Q + 2.5

(a) In market equilibrium, demand price equals supply price.

10 - 2Q = 0.5Q

2.5Q = 10

Q = 4

P = 4 x 0.5 = $2

(b) In social optimal, demand price equals MSC.

10 - 2Q = 0.5Q + 2.5

2.5Q = 7.5

Q = 3

P = 10 - (2 x 3) = 10 - 6 = $4

Market supply price = 0.5 x 3 = $1.5

This is the net price received by producers.

(d) In market equilibrium, P = $2 & Q = 4

From demand function, when Q = 0, P = $10 (Reservation price)

Consumer surplus (CS) = Area between demand curve and market price = (1/2) x $(10 - 2) x 4 = 2 x $8 = $16

From supply function, when Q = 0, P = 0 (Minimum acceptable price)

Producer surplus (PS) = Area between supply curve and price = (1/2) x $(2 - 0) x 4 = 2 x $2 = $4

Total surplus (TS) = CS + PS = $(16 + 4) = $20

NOTE: As per Chegg answering policy, 1st 4 parts are answered.

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