L. Karp
November 25, 2007
Solution to Problem Set 4
Some of the
f
gures that are needed to provide "graphical proofs" appear
rather complicated, making the arguments appear di
ﬃ
cult. This apparent
complication is a disadvante of graphical arguments, relative to mathematical
arguments. For the latter, the sequential nature of the proof is apparent: one
thing comes before another. In contrast, with a graph, "everything appears
a
tthesamet
ime"
. Onewaytoov
e
rcometh
i
sd
i
ﬃ
culty is to use lots of
graphs, so that the reader can see the development of the argument. I have
tried to do that, but there is no substitute for "thinking with a pencil". As
you read the text of the argument, you should draw the
f
gure, and compare
your drawings with the ones in the answer key.
Case I (Constraint on food consumption)
a) Under free trade the equilibrium consumption of food is
F
T
>F
∗
so
the constraint is violated. (Figure 1)
b) The optimal policy is a consumption tax/subsidy. The domestic con-
sumer price equals slope of the tangent to indi
f
erence curve at point A,
f
gure
2, denoted
p
d
. The ad valorem consumption tax on food,
t,
solves
p
d
=
p
w
1+
t
.
You can write the tax in terms of the slopes of lines
p
d
and
p
w
.T
h
e
f
rst
best consumption tax/subsidy leads to consumption at A and utility
U
1
.
Imposition of the constraint leads to a lower level of utility compared to free
trade: there are points on the balance of payments constraint, above point
A, that result in higher utility. (The indi
f
erence curve
U
1
is not tangent to
the BOP line.) Note that the consumption tax does not alter the production
point nor the BOP constraint.
c and d) First consider the production policy. I’ve drawn the constraint
as the dashed line at
F
∗
in
f
gure 3. If a production tax/subsidy is used, the
consumer price equals the world price, so consumption must be on
IEP
(
p
w
)
.
This fact, and the fact that the constraint is binding, means that consump-
tion must occur at point

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*f
rst best policy. Production must be at point
C
, in order to satisfy the BOP
equilibrium. Note that growth cannot alter the consumption point (which is
uniquely determined by the IEP curve and the constraint) so growth neither
increases nor decreases welfare.
Growth can change the production point
(e.g. growth may result in production shifting away from point C); growth
cannot shift the consumption point along the line at
F
∗
when a production
policy is used. Therefore, growth cannot be immiserizing if a production
policy is used - but neither can it lead to an increase in welfare.
Now consider the trade policy. Note that point A gives the highest feasi-

This is the end of the preview.
Sign up
to
access the rest of the document.