Intertemporal Trade and Current Account Balance

- inviduals, households and firms
- individuals + macro relations
- welfare after a macro shock
- justify demand-determined output

Resource exchanges across time
- Measured by current account of balance of payments
- Model is entirely real (no money

1) small open economy
2) SINGLE GOOD
3) agents have perfect foresight
4) agents are identical and population size is unity
5) no investment

_ Marginal rate of substitution equals price of future consumption in terms of present consumption

OR $u'(c_1^i) = (1 + r) \beta u'(c_2^i)$

- At maximum utility, the consumer cannot gain from feasible shifts of consumption between periods

If $\beta < \frac{1}{1 + r}$ --> $c_1^i > c_2^i$ ie discount factor is less than the price of future consumption

If $\beta > \frac{1}{1 + r}$ --> $c_1^i < c_2^i$

If $\beta = \frac{1}{1 + r}$, the consumer chooses a flat consumption path $c_1^i = c_2^i$ and there is common consumption in both periods

We can identify per capita quantity variables with national aggregate quantities, thus $c^i = C$ and $y^i = Y$

The representative agent model

That $CA_2 = -CA_1$

- Net foreign debt cannot be positive at the end of period 2 because of the foreign agent maximisation problem
- Net foreign assets cannot be positive as it needs to be maximised within the two-period time frame

$CA_2 = B_3 - B_2 = -B_2$
$CA_1 = B_2 - B_1 = B_2$

so $CA_2 = -CA_1$

Along the indifference curve, utility is maximised and there would be no consumer gain from feasible shifts of consumption between periods. So following $u'(C_1) \Delta C_1 + \beta u'(C_2) \Delta C_2 = 0)$, $\frac{\Delta C_2}{\Delta C_1} = -\frac{u'(C_1)}{\beta u'(C_2)}$.

At point B, $\frac{u'(C_1)}{\beta u'(C_2)}$ = $1+r$ (both usually in minus) (hitting the budget line) so $u'(c_1^i) = (1 + r) \beta u'(c_2^i)$ (EULER EQUATION)

- Future consumption is relatively cheap in the home economy (present consumption is relatively expensive)
- Therefore, the home will “import” present consumption from abroad in the first period by running a current account deficit, and “export” future consumption later by repaying its debt

- The home will “export” present consumption and “import” future consumption
- Still gains from intertemporal trade --> Regardless of the sign of the initial current account balance, there is a utility gain
- If $r^A = r$, there is no gain

Countries can borrow to finance investments
Output is now a function of capital $Y = F(K)$ where F'(K) > 0
Capital good is created from consumption and vice versa, relative price of K goods in terms of C goods is unity

net foreign asset accumulation

The PPF is tangent to the highest indifference curve reached without intertemporal trade. The common slope at the equilibrium is $-(1+r^A)$ where $r^A$ is the real autarky interest rate

A: autarky EQ, Euler equation satisfied in terms of $r^A$
- marginal product of investment > world interest rate
- I1 goes up corresponding to the horizontal disztance between A and B; Notice F(K1) = C1 + I1 so that fall in C1 corresponds to the rise in I1
- Horizontal difference between B and C; current account deficit in period 1.
- UTILTY GAIN - There is an additional source of gain (i.e., not only smoothing the time path of consumption but also changing the production point)

- also a gain when $r^A < r$, but a first-period current account surplus