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

equilibrium income

$Y=C+I+G-M=200+2/3(Y-T)+I+G-M$

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

$Y=200+2/3(19Y/20-15)+780-1Y/10=38Y/60+1Y/10=970$

$7Y/15=970$

$Y=2078.57$

consumption expenditure

$C=200+2/3Y_d=200+2/3(2078.57-15-1/20\times 2078.57)=200+1959.64=2159.64$

total tax

$T=15+1/20Y=15+1/20\times 2078.57=118.93$

$multiplier=1/(1-MPC)$ ,$MPC=C/Y=2159.64/2078.57=1.039$

$Multiplier=1/(1-1.039)=-1/0.039=-25.639$