Answer to Question #211472 in Macroeconomics for Shubham

Question

For a single model of the expenditure sector with government and income taxes, derive the expenditure multiplier and explain how it changes as the marginal propensity to save increases.

Answer 1

$Y= C + I + G + NX....... (1)$

Where

Y is the income,C is consumption, I is investment,G is government spending, and NX is net exports,

$C = C0 + MPCx(Y — T).....(2)$

Where

C0 = autonomous consumption

MPC = marginal propensity to consume

T = Taxes on personal income.

Here MPC is positive

Thus $MPC+MPS=1$

MPS is the marginal propensity to save

Inserting equition 2 into equition 1 we get

$Y = C0 + MPCx(Y — T) + I + G + NX\\$

we can group them together with C0 under the same fixed term A, as shown 

$Y = C0 + MPCxY — MPCxT + I + G + NX = MPCxY + A\\Y — MPCxY = A\\(1 — MPC)xY = A\\Y = {1÷(1—MPC)}xA\\$

The term inside the brackets is the multiplier: 1÷(1—MPC)

The expenditure multiplier shows how changes in marginal propensity to save affects the economy. The smallest the marginal propensity to consume the the larger the multiplier and economic impact on government expenditures.