Q.Why is the open economy autonomous expenditure multiplier smaller than the closed economy one?

The autonomous expenditure multiplier indicates how much equilibrium income changes for a given change in autonomous expenditure.

In a closed economy, the multiplier is determined by the marginal propensity to consume (MPC). An increase in autonomous expenditure leads to successive rounds of spending within the domestic economy, with each round diminishing by the amount saved.

In an open economy, in addition to saving, a portion of any increase in income is spent on imports. This is captured by the marginal propensity to import (MPM). Imports represent a leakage from the domestic circular flow of income, similar to saving. When domestic income rises, some of the increased spending is directed towards foreign goods and services, rather than being re-spent within the domestic economy.

This additional leakage due to imports reduces the amount of money recirculating domestically in each subsequent round of spending. Consequently, the overall expansion of income for a given initial autonomous expenditure is smaller in an open economy compared to a closed one.

The autonomous expenditure multiplier describes how a change in autonomous spending (like investment, government spending, or autonomous consumption) leads to a larger change in equilibrium national income. The core idea is that an initial injection of spending creates income for someone, who then spends a portion of that income, creating income for someone else, and so on, in a continuous chain. However, at each step, some income "leaks" out of this domestic spending stream.

In a closed economy, which has no international trade, the leakages from the circular flow of income are primarily savings and taxes. When an individual receives additional income, they save a portion of it (determined by the Marginal Propensity to Save, MPS) and pay taxes on another portion (determined by the Marginal Propensity to Tax, MPT). These portions are not re-spent within the domestic economy in the next round, thus reducing the multiplier effect. The formula for the autonomous expenditure multiplier in a closed economy, assuming a simple model with income-dependent taxes, is:

Alternatively, if we consider the Marginal Propensity to Consume (MPC) and a tax rate $t$, the leakages are $(1-MPC)$ for savings and $MPC \times t$ for taxes. The denominator represents the sum of all marginal propensities to withdraw (leakages).

Now, consider an open economy. An open economy engages in international trade, meaning it imports and exports goods and services. In addition to savings and taxes, there is an additional leakage: imports. When domestic residents receive additional income, they not only save a portion and pay taxes on a portion, but they also spend a portion of it on imported goods and services. This spending on imports represents income flowing out of the domestic economy to foreign producers. It does not contribute to further rounds of domestic spending and income generation.

The Marginal Propensity to Import (MPM) measures the fraction of additional income that is spent on imports. Because this spending leaves the domestic economy, it further reduces the amount of income available for re-spending domestically, thereby dampening the multiplier effect even more than in a closed economy. The formula for the autonomous expenditure multiplier in an open economy is: