The open economy autonomous expenditure multiplier is smaller than the closed economy multiplier due to the additional leakage caused by imports.

In a closed economy, the multiplier is given by 1/(1-c), where c is the marginal propensity to consume. In an open economy, the multiplier becomes 1/(1-c+m), where m is the marginal propensity to import. Since m is greater than zero, the denominator becomes larger, resulting in a smaller multiplier value.

The reason lies in the multiplier process. When autonomous expenditure increases, it has a direct effect on income and an induced effect on consumption. In a closed economy, all induced consumption creates demand for domestic goods. However, in an open economy, a proportion of the induced effect on consumption becomes demand for foreign goods rather than domestic goods.

This increase in imports per unit of income constitutes an additional leakage from the circular flow of domestic income at each round of the multiplier process. As a result, the induced effect on demand for domestic goods, and hence on domestic income, becomes smaller.

For example, if c = 0.8 and m = 0.3, the closed economy multiplier would be 1/(1-0.8) = 5, while the open economy multiplier would be 1/(1-0.8+0.3) = 2. Thus, if autonomous demand increases by 100, output increases by 500 in a closed economy but only by 200 in an open economy.