Question

1.) Assume the Indian market for textiles is described as:

PMC = 2 + Q P

(Sidenote: PMC is private marginal cost)

MB = 46 - 3Q

Assume units on Q is “1000s of spools” and Price is in “dollars.”

a. What is the market price and quantity for textiles?

b. What is the consumer and producer surplus in this market? (include the units)

c. Now assume the factories producing these textiles produce effluent which is dumped into a large lake. The damages done by the factories can be described as “MD = 0.4Q.” What is the socially optimal Q that should be produced as a result?

d. Calculate the total damages when producing at the socially optimal Q and the private optimal Q.

e. Find the optimal tax or subsidy that will allow the market to reach the socially optimal Q.

Answer 1

(a)

Setting MB = PMC,

46 - 3Q = 2 + Q

4Q = 44

Q = 11 (thousand)

P = 2 + 11 = $13

(b)

When Q = 0, MB = 46/3 = 15.33

Consumer surplus = (1/2) x (15.33 - 13) x 11 = 5.5 x 2.33 = $12.815 (thousand)

When Q = 0, PMC = 2

Producer surplus = (1/2) x (13 - 2) x 11 = 5.5 x 11 = $60.5 (thousand)

(c)

In social optimal, MB = PMC + MD

46 - 3Q = 2 + Q + 0.4Q

46 - 3Q = 2 + 1.4Q

4.4Q = 44

Q = 10 (thousnad)

P = 46 - 3 x 10 = 46 - 30 = $16

(d)

Total damage (TD) = MD x Q = 0.4Q x Q = 0.4Q2

With private outcome, TD = 0.4 x 11 x 11 = $48.4 (thousand)

With optimal outcome, TD = 0.4 x 10 x 10 = $40 (thousand)

(e)

A marginal damage means a tax should be imposed.

When Q = 10, Unit tax = MD = 0.4 x 10 = $4