Environmental Economics Exam

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Take-Home Exam
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...
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