Calculating income-expenditure multiplier? If planned aggregate expenditure in an economy can be written as: PAE = 5000 + 0.8Y, what is the income-expenditure multiplier in this economy?


My Attempt:

Y = 5000 + 0.8Y
Y - 0.8Y = 5000
0.2Y = 5000
Y = 25000


Since the marginal propensity to consume (MPC) is equal to ΔC / ΔY, where ΔC is change in consumption, and ΔY is change in income.

25000 / 20000 = 1.25


Do I take this further using multiplier = 1 / (1 - MPC) = 1 / (1-1.25) = 4
No, that is not correct. In the Keynesian model, the only variable that reacts to output is consumption. Other components of the aggregate demand do not.

For instance, in a closed economy, aggregate demand is $C+G+I$. Here, $C=c_0 + c_1Y$, where $c_0$ is autonomous consumption and $c_1$ is the MPC. 

Hence, planned expenditure is 

$$ Y^e = c_0 + G + I + c_1Y$$

which can be condensed to 

$$ Y^e = a + bY $$

This is the equation you are given. Thus, the MPC is 0.8. This is actually the slope of the PAE curve in the Keynesian Cross diagram. It is usually lower than one. Calculation of the multiplier goes as normal.