Principles of Macroeconomics / Unit 15 MAC 1403 worked example, 60 to 90 seconds
Applying the Identity
The idea
Given a rise in government borrowing, work out what must adjust. Write the identity, put the starting figures in, change the borrowing term, and then see what the other terms have to do. Something must move, and the identity says which candidates exist without saying which one it will be.
In practice
Start with private saving of 1,400, a net inflow from abroad of 300, investment of 1,500 and government borrowing of 200. The left side is 1,700 and so is the right, so the identity holds. Now let government borrowing rise to 500. If saving and the inflow do not change, the left side is still 1,700, so investment must fall to 1,200: that is crowding out in full. If instead households save an extra 300, the left side becomes 2,000 and investment stays at 1,500. If instead the inflow from abroad rises by 300, the left side is again 2,000 and investment stays at 1,500.
Where people slip
All three outcomes are consistent with the same identity, which is exactly the point. An identity constrains the possibilities; it does not predict which one occurs. Anyone claiming that government borrowing must reduce investment is asserting something the identity alone cannot deliver, and the next entries are about which adjustment actually tends to happen.
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