If β1 is the marginal propensity to consume of taxpayers and β2 is the marginal propensity to consume…

When an increase in tax revenue ($\Delta T$) is used to finance an equal increase in government purchases of goods and services ($\Delta G = \Delta T$), and the marginal propensity to consume of taxpayers ($\beta_1$) differs from that of the recipients of government expenditure ($\beta_2$), the balanced-budget multiplier is given by $\frac{\Delta Y}{\Delta T} = \frac{1 - \beta_1}{1 - \beta_2}$. When $\beta_2 > \beta_1$ (with $0 < \beta_1 < \beta_2 < 1$), the numerator $1 - \beta_1$ exceeds the denominator $1 - \beta_2$, so $(\Delta Y / \Delta T) > 1$.