Suppose that for a particular economy, investment is equal to 200, government purchases are 150, net taxes (that is lump-sum taxes minus transfers) is 100 and consumption is given by C = 100 + 0.75Y,
- What is the level of equilibrium income?
- Calculate the value of the government expenditure multiplier and the tax multiplier.
- If government expenditure increases by 200, find the change in equilibrium income.
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I = 200 G = 150 T = 100 C = 100 + 0.75 Y So, C (Autonomous consumption) = 100 And, MPC (c) = 0.75
$=\frac{1}{1-0.75}(100-0.75\times100+200+150)$
$\frac{1}{0.25}\times375$
$\frac{375}{25}\times100=\text{Rs.}1500$
$\frac{1}{25}\times100$
$=4$
$\text{Tax multiplier }=\frac{\Delta\text{Y}}{\Delta\text{T}}=\frac{-\text{c}}{1-\text{c}}$
$=\frac{-0.75}{1-0.75}=\frac{-0.75}{0.25}$
$=-3$
$=\frac{1}{1-\text{c}}[\bar{\text{C}}-\text{cT}+\text{I}+\text{G}+\Delta\text{G}]$
$=\frac{1}{1-0.75}[100-0.75\times100+200+150+200]$
$\frac{1}{0.25}\times575$
$\frac{100\times575}{25}=\text{Rs.}2300$
Therefore, change in equilibrium income = 2300 − 1500 = Rs 800.
- Equilibrium level of income
$=\frac{1}{1-0.75}(100-0.75\times100+200+150)$
$\frac{1}{0.25}\times375$
$\frac{375}{25}\times100=\text{Rs.}1500$
- Government expenditure multiplier
$\frac{1}{25}\times100$
$=4$
$\text{Tax multiplier }=\frac{\Delta\text{Y}}{\Delta\text{T}}=\frac{-\text{c}}{1-\text{c}}$
$=\frac{-0.75}{1-0.75}=\frac{-0.75}{0.25}$
$=-3$
- $\Delta\text{G}=200$
$=\frac{1}{1-\text{c}}[\bar{\text{C}}-\text{cT}+\text{I}+\text{G}+\Delta\text{G}]$
$=\frac{1}{1-0.75}[100-0.75\times100+200+150+200]$
$\frac{1}{0.25}\times575$
$\frac{100\times575}{25}=\text{Rs.}2300$
Therefore, change in equilibrium income = 2300 − 1500 = Rs 800.
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