Answer to Question #214095 in Macroeconomics for geoffrey

Question

A simple closed economy with an mpc equal to 0.5. Investment spending has suddenly fallen, reducing aggregate demand and output to a level that is 100 million below Y*.

                   i.           If the government decide to try to get the economy back to full employment using only an increase in government spending, by how much would G need to be increased?

Answer 1

$Y = C + I + G$

where Y = national income, C = consumption expenditure, I = investment expenditure and G = government expenditure

$C = a + bY' and Y' = Y - T + R$

where a = autonomous consumption, b = marginal propensity to consume, Y' = disposable income, T = taxes, and R = transfers.

so $C = a + b(Y - T + R) = a + bY - bT + bR.$

Substituting C in the original national income equation.

$Y = a + bY - bT + bR + I + G\\ or\\ Y - bY = a - bT + bR + I + G\\ or$

$Y=\frac{1}{1-b}(a-bT+bR+I+G)$

Y changes with respect to change in G or government spending, we will simply differentiate Equation 1 wrt G

$\frac{dY}{dG}\frac{d(\frac{1}{1-b}(a-bT +bR+I+G))}{dG}=\frac{1}{1-b}$

govenment multiplier (GM)$=\frac{dY}{dG}=\frac{1}{1-b}=\frac{1}{1-0.5}=2$

Now the needed change in national income is 100 million, so as to bring it to the level of full employment equilibrium. We are given three cases. Let's approach each individually.

Earlier we have calculated GM = 2. And GM = change in Y / change in G = 2. When change in Y = 100, change in G = 50. Thus, government spending must increase by 50 million, to increase national income by 100 million.