The fluctuations in the incomes taxes along with imports directly affects the multiplier size and realize the same into a smaller fraction than the size it will originally be. One can understand the statement with an example of increasing investment. One can notice the increasing expenditure in consumption when the GDP in increased because of the increased investment. The increase in the expenditure can also be realized on import of services and goods in the country. Taking an example of US economy, the expenditure of goods and services produced in U.S alone can increase the real GDP of U.S.
We can also say that when the marginal propensity towards import is larger, the real GDP of U.S. is smaller. On the other hand, the multiplier is also affects by the income taxes. With income taxes, the multiplier is resulted into a smaller fraction than it should originally be. Considering the same example of increasing investment in U.S.; we can say that when the income tax rate is higher, the change in the real G.D.P of U.S is smaller than expected.
The multiplier is determined by import marginal propensity and marginal propensity of consumption added with income tax rate which in turn determines curve AE slope as a combination. Furthermore, the change in tax rates along with marginal propensity of consumption and import; it changes the value of multiplier too. And therefore, the prediction of change in multiplier becomes really hard. Though the prediction is tough, it does not affect the statement which is a fundamental fact stating a change at an initial stage in autonomous expenditure leads to the magnifying change of real GDP along with aggregated expenditure.