Assignment 3:

A IS-LM model:

We consider a economic system, where our GDP, which is given by:

Z = C(Y T) + G + I(r),

C(Y T) = C0 + C1(Y T),

I(r) = I0 I1r,

Where Z is planned expenses, our Y is our GDP, T our taxes, G is our government purchases, I is our investments, r is interest rates.

C0, C1, I0, I1 > 0 are all paramters and C1 < 1.

Our T and G is Exogenous variables. Also in this part of the assignment r is Exogenous

We are adding the following equations to our model:

M^d (Y, r) = M0 + M1Y M2r

Md = M P ,

Where M and P is exogenous variables and M0, M1, M2 > 0. and Md is money / liquidity savings in the economy.

Explain why M1 and M2 both are positive, and deduce the LM curve ie. deduce Y as a fuction off r and M/P?

M1 and M2 both are positive as they include various modes of money and transactions that occur in daily life.M1 includes cash, checkable deposits, and traveler's checks. On the other hand, the M2 includes savings and time deposits, certificates of deposits, and money market funds in addition to M1.

The Lm curve equation is the following:

Y=M1PMM1M0+M1M2r

Explanation:

An explanation for the new question:

There are two definitions of money based on their liquidity according to the Federal Bank, M1, and M2.M1 money is very liquid in nature; it includes cash, checkable deposits, and traveler's checks. On the other hand, the M2 moneyis less liquid in nature and it includes savings and time deposits, certificates of deposits, and money market funds in addition to M1. Both cannot be negative as these are the money circulating in the economy on daily basis.

The equation of money demand is:

M^d (Y, r) = M0 + M1Y M2r

Here, M0 is the money that is in circulation. A positive sign before the M1Y denotes the positive relationship between money demand and income. Whereas, the negative sign before M2r represents the negative relationship between money demand and rate of interest. When the interest rate is higher, the demand for money in the economy reduces and vice versa.

In the money market, at equilibrium money demand is equal to the money demand.

So, from the given equations, we can derive the Y as the function of r and M/P.

Md=PMM0+M1YM2r=PMM1Y=PMM0+M2rY=M11(PMM0+M2r)Y=M1PMM1M0+M1M2r

The above equation of Y as the function of r and M/P represents the LM curve equation.

Do not take r as exogenous anymore.

The new question is now:

Find out how much the centralbank shall increase the money supply with to compensate for the fallen C0 ie. Find dM/dC0 under the condition that GDP is unchanged.