Why are the multiplier and MPS inversely related?

If net exports increase, is this a leakage or an injection?

The multiplier and MPS (marginal propensity to save) are inversely related because MPS is the fraction of additional income that households choose to save instead of spending. The multiplier measures the overall impact on aggregate demand (total spending) resulting from an initial change in spending or investment.

To understand the relationship, you'll need to know the formula for the multiplier:

Multiplier = 1 / MPS

Since the multiplier is the inverse of MPS, an increase in MPS will lead to a decrease in the multiplier, and vice versa. In other words, if households save a larger portion of their income (higher MPS), it means they are spending less, and the overall impact on aggregate demand will be smaller (lower multiplier).

Now, let's talk about net exports. Net exports represent the difference between a country's exports and imports. When net exports increase, it means the country's exports exceed its imports, resulting in a positive value.

In terms of the national income model, net exports are considered an injection. An injection is any addition to the circular flow of income that boosts aggregate demand. In this case, an increase in net exports represents an injection of spending into the economy because foreign buyers are purchasing more goods and services from the domestic market, increasing overall spending and income.

So, to answer your question directly, if net exports increase, it is considered an injection into the economy, not a leakage.