Final answer:
If the world interest rate falls, domestic investment in a small open economy will likely increase, and net exports will decrease, due to cheaper borrowing costs and currency depreciation, respectively.
Step-by-step explanation:
If the world interest rate falls, then, holding other factors constant, in a small open economy the amount of domestic investment will increase, and net exports will decrease.
When the world interest rate falls, cheaper capital becomes available. This makes borrowing less expensive, which encourages firms and individuals to invest more domestically. Therefore, domestic investment rises. However, a lower interest rate also tends to weaken the currency because foreign investors might seek higher returns elsewhere, reducing demand for the currency. As a result, domestic goods can become more expensive for foreign buyers, which can lead to a decrease in exports. Conversely, foreign goods become cheaper for domestic buyers, which can lead to an increase in imports. Consequently, net exports (exports minus imports) will likely decrease.
The national savings and investment identity for a small open economy can be represented by the equation: S + (T - G) = I + (X - M), where S is private savings, T is taxes minus transfer payments, G is government spending, I is investment, X is exports, and M is imports. In the case of a fall in the world interest rate, the identity implies a rise in I and a potential decrease in (X - M), holding S and (T - G) constant.