Exercise 1

(a)

If the emissions in the area are left unregulated then the two factories will emit as much as they can, which means there will be zero abatement (MAC=0). So we have: Factory A: MACA=0 4000-EA=0 EA=4000

Factory B: MACB=0 4000-4EB=0 EB=1000

For the socially optimal level of emissions we have:

MACA=4000-EA EA=4000-MACA

MACB=4000-4EB EB=1000-0,25MACB

By adding the above by parts we get:

E=5000-1,25MAC MAC=4000-0,8E

The socially optimal level of emissions is where MAC equals MD, therefore: MAC=MD 4000-0,8E*=1,7E* 4000=2,5E* E*=1600

(b)

First, we must find the excess demand for permits for each factory. In order to do this, we must assume 2 prices for each factory. Factory A:

If PE=0 then factory A will emit:

MACA=PE 4000-EA=0 EA=4000

But factory A owns half of the total emission permits, which means EA=800 , so the excess demand for permits in this case will be: QAE=4000-800=3200 (permits buyer)

Now if PE=4000 then factory A will emit:

MACA=PE 4000-EA=4000 EA=0

Factory B owns half of the total emission permits, which means EA=800 , so the excess demand for permits in this case will be: QAE=0-800=-800 (permits seller)

So we have the following table:

PE| 0| 4000|

QAE| 3200| -800|

Assuming that there is a linear relationship between Q and P (QAE=a+bPE), we get the following system: 3200=a+b(0)-800=a+b (4000)

We solve the system:

3200=a + (0)b a=32000

-800=a +4000b -800 =3200 +4000b 4000b= -4000 b=-1

And we finally come to the following function:

QAE=a+bPEQAE=3200-PE

Factory B:

If PE=0 then factory B will emit:

MACB=PE 4000-4EB=0 EB =1000

But factory B owns half of the total emission permits, which means EA=800 , so the excess demand for permits in this case will be: QBE=1000-800=200 (permits buyer)

Now if PE=4000 factory B will emit:

MACB=PE 4000-4EB=4000 EB=0

Factory B owns half of the total emission permits, which means EA=800 , so the excess demand for permits in this case will be: QBE=0-800=-800 (permits seller)

So we have the following table:

PE| 0| 4000|

QBE| 200| -800|

Assuming that there is a linear relationship between Q and P (QAE=a+bPE), we get the following system: 200=a+b(0)-800=a+b (4000)

We solve the system:

200= a + b(0) a=200

-800= a + b(4000) -800=200 +4000b 4000b=-1000 b=-0,25

And we finally come to the following function:

QAE=a+bPEQAE=200-0,25PE

The equilibrium permit price can be found by setting the total excess demand for the two factories equal to zero: QAE+QBE=0

3200-PE+200-0,25PE 3400=1,25PE PE=2720

(c)

Factory A:

For the price we found in (b), PE=2720 , factory A will emit: MACA=PE 4000- EA = 2720 EA =4000- 2720 = 1280

But factory A has the rights for EA=800 , so the excess demand for permits will be: QAE=1280-800=480 (permits buyer)

And graphically:

So the cost of compliance for factory A is b (the cost of buying 480 more permits from factory B) plus c (the abatement cost for factory A at the 1280 level of emissions). Therefore: TCA=b+c=1280-8002720+4000-1280(2720)2=4802720+2720×27202=1305600+3699200=5004800 Factory B:

For the price PE=2720 factory B will emit:

MACB=PE 4000- 4EB=2720 4EB=1280 EB = 320

But factory B has the rights for EA=800 , so the excess demand for permits will be: QBE=320-800=-480 (permits seller)

And graphically:

So the cost of compliance for factory B is b+d (the cost of abatement, when factory B emits 320), minus b+c (the revenue for factory B by selling 480 permits to factory A). Therefore: TCB=b+d-b+c=d-c=1000-8004000-4×8002+800-3202720-(4000-4×800)2=200×8002-480×(2720-800)2=80000-460800=-380800 Note that TCB<0 , which means that factory B has bigger profits from selling the permits than its abatement costs at the level of 320 emissions.

Exercise 2

(a)

If the emissions in the area are left unregulated then the two tanneries will emit as much as they can, which means...