Question

As a part of the stimulus package ($93 billion) was paid out in the form of tax credits . Use the parameters given in the table below and the equation of IS Curve to answer the following questions:

Autonomous Consumption (C) = $1.3 trillion mpc = 0.6

Autonomous Investment (I) = $1.2 trillion c = 0.1

Government Spending (G) = $3.0 trillion d = 0.2

Tax Revenue (T) = $3.0 trillion x = 0.1

Net Exports (NX) =1.3 trillion financial frictions (f) = 1

a) Calculate the goods market equilibrium output ( Hint: Use equation for IS Curve)

b) Calculate the good market equilibrium if there is tax cut of $93 billion. Interpret your result and provide economic intuition to support your result.

Answer 1

(a)Since we know that equation for IS model or the product market for 3 sector model is given by-

I+G=S+T

Where, I=investment, S=savings, T=taxation and G= government expenditure.

However,the question to us is for an open economy but it has also asked only for the equilibrium of goods market so we will be ignoring the role of Net exports as it will be included in the money market.

Now the equations for our model will be-

C=1.3+0.6(Y-T)

S= -1.3+0.4(Y-T) this is so because Y=C+S and MPS=1-MPC

I=1.2-0.1i

G=3+0.2d and

T=3

So for equilibrium we have-

I+G=S+T

1.2-0.1i+3+0.2d= -1.3+0.4(Y-T)+3

4.2-0.1i+0.2d=1.7+0.4(Y-3)

2.5-0.1i+0.2d+1.2=0.4Y (by opening up bracket and taking values to the left hand side of the equation)

Or, 0.4Y=3.7-0.1i+0.2d

Or, Y=9.25-0.25i+0.5d is the required equation.

The values of output will vary with the changing values of 'i' and 'd'.

(b) Here the only change will be of Taxation. So converting the value of trillion into billion requires the division of 93 billion by 3 trillion and we will get 0.031 as the answer.

Hence, we will only be replacing the value of taxes (T).

So our model will now become-

1.2-0.1i+3+0.2d=-1.3+0.4(Y-0.031)+3

4.2-0.1i+0.2d=1.7+0.4Y-0.0124

4.2-0.1i+0.2d-1.6876=0.4Y

Or, 0.4Y=2.5124-0.1i+0.2d

Or, Y=6.281-0.1i+0.2d

Or, Y=6.3-0.25i+0.5d is the required equation.