Question

Q1) The government seeks to reduce the emissions of gunk through a tax. The marginal benefits of reducing gunk emissions are: MB = 30 – 1/3 Q Two firms emit gunk from their factories. The marginal costs of reducing emission of gunk for firms one and two are the following: MC1 = 4q1 and MC2 = 2q2 where q1 and q2 are, respectively, the amount of emissions reduced by the first and second firms. a) What are the total industry costs of pollution control (for both firms combined) if a uniform emission standard is utilized to achieve an aggregate reduction (for both firms combined) of 9 tons of emissions? b) What is the cost effective allocation of control when a total reduction of 9 units is required? c) If the firms are charged a tax per unit of gunk emitted in order to reach this target reduction of 9 units, what should the tax be set at? d) Derive (calculate) the aggregate MC function. ( MARKS) e) What is the efficient level of pollution control, Q*? f) What is the efficient tax that would produce this result? g) If you were speaking with a policy-maker, how would you explain the difference between he result you obtained in part (b) versus the result you obtained in part (e)? What new or different information are you relying on? What result would prefer from an economic perspective?

Answer 1

A) q1 and q2 are, respectively, the amount of emissions reduced by the first and second firms

Aggregate reduction in emissions required = 9 tons

q1+q2=9

Since a uniform emission standard is utilized, then both the firms have to reduce the emission by same amount. This means q1=q2 = 4.5

We are given the individual marginal costs of both the firms, MC1 = 4q1 and MC2 = 2q2. The total marginal costs to the industry when both the firms reduce emission levels by 4.5 = MC1+MC2 = 4*4.5 + 2*4.5 = $27

If the marginal cost of firm 1 is 4q1, then the total cost can be found out by integrating MC with q1

Total industry cost = TC1+TC2 = $60.75

B) For cost-effective allocation, divide the reduction in emission in such a way that both the firms have same MC.

MC1 = MC 2 and q1+q2=9 (q2= 9-q1)

4q1=2q2

4q1 = 2(9-q1)

4q1 = 18-2q1

q1 = 3 units and q2 = 9-3 = 6 units

C) If the firms are charged a tax per unit of gunk emitted in order to reach this target reduction of 9 units, what the tax be should be set at

Tax = MC1 = MC2

MC1 = 4q1 = 4*3 = $12/unit

Therefore, tax should be set at $12/unit of emissions

D) MC1 = 4q1

q1 = MC1/4

MC2=2q2

q2 = MC2/2

Q = q1+q2 = MC/4+MC/2 = 3MC/4

MC = 4Q/3

The aggregate MC function is given by MC =4Q/3

As per the guidelines, the first four subparts are to be answered. Thanks!