Find the multiplier in an open economy if out of one rupee income, 80 paise goes to domestic…

Out of each rupee of income, $0.80$ is spent on domestic consumption ($c_d = c - m = 0.80$) and $0.10$ is spent on imports ($m = 0.10$), which implies a total marginal propensity to consume of $c = 0.80 + 0.10 = 0.90$ and a marginal propensity to save of $s = 1 - 0.90 = 0.10$. Therefore, the open-economy multiplier is $k = \frac{1}{s + m} = \frac{1}{0.10 + 0.10} = \frac{1}{0.20} = 5$ (equivalently, $k = \frac{1}{1 - c_d} = \frac{1}{1 - 0.80} = 5$).