In an economy, out of every 100 of national income, 20 is taken by the government, 20 is saved, 10 is spent on imports. The national income at equilibrium is $1 000. What is the value of the multiplier?

Given that for every $100 of national income:

• $20 is taken by the government (taxes)
• $20 is saved
• $10 is spent on imports

The marginal propensity to tax ($t$) is: $t = \frac{\text{Taxes}}{\text{National Income}} = \frac{\$20}{\$100} = 0.2$ The marginal propensity to save ($s$) is: $s = \frac{\text{Savings}}{\text{National Income}} = \frac{\$20}{\$100} = 0.2$ The marginal propensity to import ($m$) is: $m = \frac{\text{Imports}}{\text{National Income}} = \frac{\$10}{\$100} = 0.1$

The marginal propensity to withdraw is the sum of all marginal propensities to leak from the circular flow of income.

$$\text{MPW} = t + s + m$$ $$\text{MPW} = 0.2 + 0.2 + 0.1 = 0.5$$

The multiplier ($k$) is given by the formula:

$$k = \frac{1}{\text{MPW}}$$ $$k = \frac{1}{0.5}$$ $$k = 2$$

The national income at equilibrium ($1000) is additional information not required to calculate the multiplier itself.

The value of the multiplier is 2. This corresponds to option A.
The final answer is $\text{A}$.