# Environmental Economics Exam

1139 Words5 Pages
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
So, we have:
MAC=MD 360- 65 E = 0,3E* 360 = 310 E* + 1210 E* E*= 1015×360 E*=240 units.
(b)
In order for the two tanneries to be cost-efficient, two conditions need to be in force:
EA+EB=E
MACA=MACB
So, we have:
EA+EB=240 EA= 240-EB
MACA=MACB 360-2EA=360-3EB 360-2(240- EB) =360- 3EB 5EB=480 EB=96
And EA= 240-EB EA= 240-96 EA=144
So, Firm A should emit EA=144 units and Firm B EB=96.

For EA=144 we have:
MACA=360-2(144) =360-288=72
So:
TACA=180-144×722=25922=1296

For EB=96 we have:
MACB=360-3(96) =360-288=72
So:
TACB=120-96×722=17282=864
(c)
Since, the government sets an emission tax, in order to find the units that each firm will be willing to emit under this tax we set MAC=tax, because each tannery will choose to emit until its MAC becomes equal to the tax. So, we have:
Tannery A will emit: MACA=66 360- 2EA=66 2EA=294 EA=147 units
Tannery B will emit: MACB=66 360 -3EB=66 3EB=294 EB=98 units

Under this policy of taxing we have:

For tannery A the cost of compliance is:
TCA=TACA+(t×EA)
TACA=12×180-14766\$=1089\$
So: