Question

Consider the following example of the IS-LM model:

C = 300 + 0.5(Y–T)

I = 400 – 1000(r + x)

G = 250           T = 200
x=0.03

                       

π^e = 0.02

1. Derive the IS equation.
2. Suppose that the nominal interest rate is 4% (i = 0.04). Find the equilibrium value of Y.
3. Suppose that the risk premium x has increased to x=0.1.
4. 1. Suppose that the Fed wants to maintain the equilibrium value of Y at the value of Y in part (2). What is the real interest rate required to achieve this goal?
   2. 1. Does this real interest rate satisfy the zero lower bound constraint?

Answer 1

as given that T = 200

We know that real interest rate if nominal interest rate less expected inflation. So,

πe  

πe = 0.04 - 0.02 = 0.02



IS Equation : It is a relation between interest rate and income such that goods market is in equilibrium.

This is the IS equation.

When i = 0.04, equilibrium value of Y is given by:

Therefore equilibrium value of

A) Now the risk premium x has increased to 0.1 and Fed wants to maintain equilibrium value of income at 1600, so the required real interest rate is:

So, the real interest rate required to achieve equilibrium income of 1600 is -5 %.

B) Zero lower bound constraint means that interest rate cannot fall below zero i.e. interest rate cannot reach negative values. It means that there is lower limit of 0% on interest rates.

Here, the real interest rate in part (a) does not satisfy zero lower bound constraint as it falls below zero to maintain the equilibrium income.