1
Department of Agricultural and Resource Economics
EEP101/ECON125
University of California, Berkeley
David Zilberman
Solutions to Problem set 2
1.
Uncertainty (Weitzman’s model, see Chapter 6, pp11-16).
We know that MSC = 2 + x,
MB = 20 – 0.5 x,
Thus social optimal outcome is when MSC = MB
Î
2 + x = 20 – 0.5 x
Î
x* = 12
.
If government believe that MB
H
= 30 – 0.5 x, they will choose output standard such that
MSC = MB
H
Î
2 + x = 30 – 0.5 x
Î
x
H
= 18.7
.
If the government like to use tax, and they believe that the optimal outcome should be
18.7 as calculated above, then tax rate t* =
MSC (x
H
) = 2 + 18.7 = $20.7.
Since the true
demand is MB = 20 – 0.5 x, by t* = MB = $20.7
Î
x
H
TAX
= (20 – 20.7) * 2 = -1.4 < 0,
thus the outcome will be
x
H
TAX
= 0
(nonnegativity constraint).
If government believe that MB
L
= 10 – 0.5 x, they will choose output standard such that
MSC = MB
L
Î
2 + x = 10 – 0.5 x
Î
x
L
= 5.3
.
If the government like to use tax, and they believe that the optimal outcome should be 5.3
as calculated above, then tax rate t* =
MSC (x
L
) = 2 + 5.3 = $7.3.
Since the true demand
is MB = 20 – 0.5 x, by t* = MB = $7.3
Î
x
L
TAX
= (20 – 7.3) * 2 = 25.4
.
(a)
Under direct control policy, if the government overestimated the demand, the output
is 18.7; if the government underestimated the demand, the output is 5.3.
The social
optimal output level is 12, thus the deviation is +/- 6.7.
Under tax policy, if the government overestimated the demand, the output is 0; if the
government underestimated the demand, the output is 25.4.
The social optimal output
level is 12, thus the deviation is –12 and + 13.4.
Conclusion, direct control policy is more desirable
as it leads less deviation from the
social optimum.
(b)
If true demand is MB = 20 – 3 x,
Î
x* = 4.5
High demand is MB
H
= 30 – 3 x,
Î
x
H
= 7, x
H
TAX
= 3.7
Low demand is MB
H
= 10 – 3 x,
Î
x
L
= 2, x
L
TAX
= 5.3
Now tax policy
is more desirable
because it leads less deviation from the social