# If the marginal propensity to save is 0.15 the mariginal tax rate is 0.21 and the mariginal propensity to import is 0.1, what is the value of the complex multiplier.

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The change in the autonomous expenditure or income in an economy is not directly proportional to changes in autonomous expenditure, consumption, net exports and other macroeconomic factors.

A simple multiplier can be derived from the changes in individual expenditure or saving, the change in the rate of taxation by the government and a change in net imports. If all the simple multipliers derived are combined a complex multiplier can be arrived at.

This is given as a simple expression: k = 1/(MPS + MPT + MPM) where MPS denotes the marginal propensity to save, MPT is the marginal propensity to tax and MPM is the marginal propensity to import.

In the question the marginal propensity to save is 0.15, the marginal tax rate is 0.21 and the marginal propensity to import is 0.1. This gives the value of the complex multiplier as 1/(0.15 + 0.1 + 0.21) = 2.17

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