Question

a)     A hypothetical economy is given by the following identities:

C = 3000

I = 2000

G = 2500

T = 0.2Y

MPC = 0.5

X=6500

Z=5500 + 0.2Y

                   i.           Find the equilibrium level of income.

                 ii.           If investment expenditure decreases by 100, what will be the change in Y?

               iii.           Using the initial values, if G increases by 300 what will be the new level of Y?

Answer 1

I)

$Y=3,000+0.5(Y-0.2Y)+2,000+2,500+6,500-5,500-0.2Y\\Y=3,000+0.4Y+2,000+2,500+6,500-5,500-0.2Y\\ Y=14,000-5,500+0.2Y\\ Y=8,500+0.2Y\\ 0.8Y=8,500\\ Y=10,625$

ii)

$Y=3,000+0.5(Y-0.2Y)+1900+2,500+6,500-5,500-0.2Y\\Y=3,000+0.4Y+1900+2,500+6,500-5,500-0.2Y\\ Y=13900-5,500+0.2Y\\ Y=8,400+0.2Y\\ 0.8Y=8,400\\ Y=10,500$

iii)

$Y=3,000+0.5(Y-0.2Y)+2,000+2,800+6,500-5,500-0.2Y\\Y=3,000+0.4Y+2,000+2,500+6,500-5,500-0.2Y\\ Y=14,300-5,500+0.2Y\\ Y=8,800+0.2Y\\ 0.8Y=8,800\\ Y=11000$