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?

 iv.           Using initial values, what will the new level of Y be if the tax rate rises to T=0.3Y?

 v.           Calculate the budget deficit/surplus using the initial values.

 vi.           Calculate the trade balance using the initial values

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)

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

iv)

The rise in the tax rate to 0.3Y would result in the equilibrium level of value of income to be as follows:

$Y=3,000+0.5(Y-0.3Y)+2,000+2,500+6,500-5,500-0.2Y\\ Y=3,000+0.35Y+2,000+2,500+6,500-5,500-0.2Y\\ Y=14,000-5,500+0.15Y\\ Y=8,500+0.15Y\\ 0.85Y=8,500\\ Y=10,000$

v)

The budget deficit would be the difference between the tax and the government expenditure and thus 

Budget Surplus=Tax-Government Expenditure

            $=0.3\times (10,000)-2,500\\ =3,000-2,500\\ =500$

vi)

The trade balance would result in the net exports

Trade Balance=Exports-Imports

           $=6,500-5,500-0.2Y\\ =6,500-5,500-0.2\times(10,000)\\ =6,500-5,500-2,000\\ =6,500-7,500\\ =-1,000$

Thus, trade balance would be a trade deficit and a budget surplus.