Final answer:
When domestic investment increases without an increase in domestic savings, the trade deficit will increase to supply the necessary capital for additional investment, reflecting the need for more capital from abroad.
Step-by-step explanation:
If domestic investment increases and there is no change in the amount of private and public saving, the size of the trade deficit must increase. This is because the trade deficit is essentially the gap between a country's savings and its investment. When domestic investment rises with no corresponding increase in domestic savings, the country will require more capital from abroad, which is reflected as an increase in the trade deficit. In other words, if a country invests more than it saves domestically, it must borrow the difference from foreigners, leading to a larger trade deficit.
To put it in the form of an equation, one might look at the national saving and investment identity, which is Savings + (trade deficit) + (government budget surplus) = Investment. Since the level of savings remains constant (no change in the amount of private and public saving) and investment increases, the trade deficit must also increase to balance the equation.
As an example, imagine that the domestic savings of a country remain at a fixed amount, while the level of domestic investment increases. According to the equation, the trade deficit would need to widen to supply the necessary capital for this additional investment. This concept underscores the interplay between domestic financial factors and international trade.