More on Intertemporal Trade

More on Intertemporal Trade
This appendix contains a more detailed examination of the two-period intertemporal
trade model described in the chapter. First consider Home, whose intertemporal production
possibility frontier is shown in Figure 6A-1. Recall that the quantities of present
and future consumption goods produced at Home depend on the amount of present
consumption goods invested to produce future goods. As currently available resources
are diverted from present consumption to investment, production of present consumption,
falls and production of future consumption, rises. Increased investment
therefore shifts the economy up and to the left along the intertemporal production
possibility frontier.
The chapter showed that the price of future consumption in terms of present consumption
is where r is the real interest rate. Measured in terms of present consumption,
the value of the economy’s total production over the two periods of its existence is
therefore
Figure 6A-1 shows the isovalue lines corresponding to the relative price for different
values of V. These are straight lines with slope (because future consumption is
on the vertical axis). As in the standard trade model, firms’ decisions lead to a production
pattern that maximizes the value of production at market prices Production
therefore occurs at point Q. The economy invests the amount shown, leaving available
for present consumption and producing an amount of future consumption when the firstperiod
investment pays off.
Notice that at point Q, the extra future consumption that would result from investing
an additional unit of present consumption just equals It would be inefficient
to push investment beyond point Q because the economy could do better by
11 + r2.
QF
QP
QP + QF /11+ r2.
- 11 + r2
1/11 + r2
V = QP + QF /11 + r2.
1/11 + r2,
QP, QF,
Future
consumption
Isovalue lines with slope – (1 + r)
Q
Intertemporal
production
possibility
frontier
Present
consumption
Investment
QP
QF
Figure 6A-1
Determining Home’s Intertemporal
Production Pattern
At a world real interest rate of r,
Home’s investment level maximizes
the value of production
over the two periods that the
economy exists.
CHAPTER 6 The Standard Trade Model 135
lending additional present consumption to foreigners instead. Figure 6A-1 implies
that a rise in the world real interest rate r, which steepens the isovalue lines, causes
investment to fall.
Figure 6A-2 shows how Home’s consumption pattern is determined for a given
world interest rate. Let and represent the demands for present and future
consumption goods, respectively. Since production is at point Q, the economy’s consumption
possibilities over the two periods are limited by the intertemporal budget
constraint:
This constraint states that the value of Home’s consumption over the two periods (measured
in terms of present consumption) equals the value of consumption goods produced in
the two periods (also measured in present consumption units). Put another way, production
and consumption must lie on the same isovalue line.
Point D, where Home’s budget constraint touches the highest attainable indifference
curve, shows the present and future consumption levels chosen by the economy.
Home’s demand for present consumption, is smaller than its production of present
consumption, so it exports (that is, lends) units of present consumption
to Foreigners. Correspondingly, Home imports units of future consumption
from abroad when its first-period loans are repaid to it with interest. The intertemporal
budget constraint implies that so trade is intertemporally
balanced.
Figure 6A-3 shows how investment and consumption are determined in Foreign.
Foreign is assumed to have a comparative advantage in producing future consumption
goods. The diagram shows that at a real interest rate of r, Foreign borrows consumption
goods in the first period and repays this loan using consumption goods produced in the
second period. Because of its relatively rich domestic investment opportunities and its relative
preference for present consumption, Foreign is an importer of present consumption
and an exporter of future consumption.
DF - QF = 11 + r2 * 1QP - DP2,
DF - QF
QP, QP - DP
DP,
DP + DF /11 + r2 = QP + QF /11 + r2.
DP DF
Future
consumption
Present
consumption
Exports
Q
D
Imports
Indifference curves
QP
QF
DP
DF
Intertemporal
budget constraint,
DP + DF /(1 + r)
= QP + QF /(1 + r)
Figure 6A-2
Determining Home’s
Intertemporal Consumption
Pattern
Home’s consumption places it
on the highest indifference curve
touching its intertemporal budget
constraint. The economy exports
units of present
consumption and imports
units of future consumption.
DF - QF = 11 + r2 * 1QP - DP2
QP - DP
136 PART ONE International Trade Theory
The differences between Home and Foreign’s production possibility frontiers lead to
the differences in the relative supply curves depicted in Figure 6-11. At the equilibrium
interest rate Home’s desired export of present consumption equals Foreign’s
desired import of present consumption. Put another way, at that interest rate, Home’s
desired first-period lending equals Foreign’s desired first-period borrowing. Supply and
demand are therefore equal in both periods.
1/(1 + r 1),
Future
consumption
Present
consumption
Exports
Q*
D*
Imports
QP
QF*
DP
DF
Intertemporal
budget constraint,
DP + DF /(1 + r)
= QP + QF /(1 + r)
*
* *
* *1
* *
Figure 6A-3
Determining Foreign’s
Intertemporal Production and
Consumption Patterns
Foreign produces at point and
consumes at point , importing
units of present
consumption and exporting
units of future consumption.
QF * - DF * = 11 + r2 * 1DP * - QP * 2
DP * - QP *
D*