Question

You can use graphs or simple algebra to answer this question; either way, be sure

to show all of your work and/or explain your reasoning.

Two firms can reduce emissions of a pollutant at the following marginal costs:

MC1 = $3 q1

MC2 = $1 q2

where q1 and q2 are, respectively, the amount of emissions reduced by the first

and second firms. Total pollution-control cost functions for the two firms are

Respectively:

TC1 = $100 + $60 (q1)2                                                                                     

TC2 = $100 + $20 (q2)2                                                                                    

Assume that with no control at all, each firm would be emitting 10 units of emissions (for aggregate emissions of 20 tons), and assume that there are no significant transaction costs.

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 6 tons of emissions?

TC1 =                                                                                                                        

TC2 =                                                                                                               

TC = TC1 + TC2 =

b.         What are the marginal costs of pollution control for firm #1 and for firm

#2 under the standard considered in part a?

MC1 =

MC2 =

c.         Compute the cost-effective reduction by each of the two firms if a total

reduction of 10 tons of emissions is necessary.

Note:

(MC1 = MC2) and

(q1 + q2 = 10)

d.         What is the total industry cost of reduction (for both firms combined) for

the scenario above in part (c)?

TC1 =                                                                                                               

TC2 =

TC = TC1 + TC2

e.         What is the cost-effective reduction by the two firms with a tradable

permit approach if both firm #1 and firm #2 are freely allocated 7 tons of

emissions permits?

How will the cost-effective reduction be affected by a change in the initial allocation?

q1 =

q2 =

f.          If the authority chose to reach its objective of 6 tons of aggregate

Reduction with an emission charge, what per-unit charge should be

Imposed? How much government revenue will the tax system generate, if

the tax is levied on all units of emission?

Emissions charge = MC1 [= MC2]

Tax revenue =

g.         Which policy instrument ? taxes, tradable permits, or a uniform

standard ? would you expect private industry as a whole to prefer

(assuming the same target for aggregate emission reductions in each

case)? Why?

Answer 1

(a) Here aggregate reduction is given 6 ton of emissions so we assume q1=q2=3. Then,

TC1= $100+$60(q1)2

= $100 + $60 (3)2

= $100 + $360

= $460

TC2= $100 + $20 (q2)2

= $100 + $20 (3)2

= $100 + $120

= $220

TC = TC1 + TC2

= $460 + $220

= $680

(b) MC1= $3q1

= $3(3) [ from (a) ]

= $9

MC2 = $1q2

= $1(3) [ from (a) ]

= $3

(c) Given,

MC1 = MC2 & q1+ q2 =10

Therefore, $3q1 = $1q2

Now, putting q2 = 3q1 in q1+ q2 = 10

q1+ 3q1 = 10

4q1 = 10

q1 = 2.5

So, q2 = 3q1

= 3(2.5)

= 7.5

(d) Taking value of q1= 2.5 & q2 = 7.5 from (c)

TC1 = $100 + $60(2.5)2

= $100 + $300

= $400

TC2 = $100 + $20(7.5)2

= $100 + $300

= $400

TC = TC1 + TC2

= $400 + $400

= $800