Question

Given a macaroni economic model:

C=200+2/3yd

G=500

I=300

X=100

M=20+1/10y

T=15+1/20y

Required: determine equilibrium income, consumption exp, total tax, the multiplier

Answer 1

In the income-expenditure model, the equilibrium occurs at the level of GDP where aggregate expenditures equal national income (or GDP).

Aggregate expenditure function (AE) equals National Income (Y) 

Y= C+I+G+X-M

$Y=200+2/3(Y-15-1/20Y)+300+500+100-20-1/10Y$

$Y=200+2/3(19/20Y-15)+880-1/10Y$

$Y=1070+32/60Y$

$Y-32/60Y=1070$

$28/60Y=1070$

$Y=2,293$ Equilibrium Income.

Consumer Expenditure

$C=200+2/3(Y-15-1/20Y)$

$C=200+2/3(2293-15-(1/20*2293)$

$C=200+2/3(2163.35)$

$C=1,642.23$

Total Tax

$T=15+1/20Y$

$T=15+1/20*2,293$

$T=129.65$

Multiplier

$\alpha$=$1/(1-c)$)

c=0.67

$\alpha$= $1/(1-0.67)$

$\alpha$= 3.00