Environmental Economics Exam

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