The Relative Price of Foreign Goods as an Endogenous Variable

In the previous section, investors behaved mysteriously. When they want American assets, the relative cost of foreign goods falls. When they do not want our assets, then we must pay more for foreign goods.

In a complete macroeconomic model, the relative cost of foreign goods is endogenous. That is, the relative cost of foreign goods is determined by other variables in the model. A key variable is the real interest rate, r, which we already have used as a determinant of investment.

When the real interest rate is high, the demand for our assets will be high, which means that the relative cost of foreign goods will fall. Thus, an increase in our real interest rate will make our exports less competitive, which will reduce net exports and therefore reduce aggregate demand. This helps to strengthen monetary policy.

Recall that if monetary policy is used to raise the interest rate, this will reduce investment and reduce demand. Now, we see that with a higher interest rate, the trade sector also will swing toward deficit, reducing demand. So monetary policy is even more effective when we take the trade sector into account.

Here is a set of equations that describes an economy with an endogenous trade balance (X) and an endogenous relative price of foreign goods (e).

[1] (accounting identity) Y = C + I + G + X[2] (consumption function) C = c

[3] (tax function) T = T

[4] (investment function I = I

[5] (trade balance function) X = x

[6] (price-of-foreign-goods function) e = e

- Name the 6 endogenous variables in this macro model.
- Name the five parameters in the model that are intercept terms (also called constant terms).
- Name the two exogenous variables in the model.
- Name the five paramters in the model that are slope coefficients.

The model has two interest-sensitive sectors--investment and the trade balance. Putting the two together, and substituting equation [6] for the price of foreign goods in equation [5], we have

[7] (replaces [4]-[6]) I + X = I_{0} + X_{0} - (h + fx)r

In this model, the interest rate determines investment and the trade balance. Those variables, along with government spending, will determine income, taxes and consumption using equations [1] - [3].

In a more sophisticated model, the simplification of [7] would not be possible. That is because investment can depend on output, Y. As aggregate demand goes up, firms invest more. Also, the trade balance can depend negatively on Y. As demand goes up, more of it is satisfied by imports. Those real-world relationships make the model considerably more complex. It becomes a fully simultaneous 6-equation system, which takes a lot of work to solve.