Question

1. Suppose you have the following equations:

MP curve: r = 2 + 0.5π

IS curve: Y = 1000 − 20r

(a) Obtain the equation for the aggregate demand curve

(b) Make graphs for the MP, IS, and AD curve (c) Suppose the yearly inflation rate rises from 3% to 5%. What will be the central bank’s response in terms of setting the real interest rate, and what will be the change in real GDP (Y)?

(c) Suppose the yearly inflation rate rises from 3% to 5%. What will be the central bank’s response in terms of setting the real interest rate, and what will be the change in real GDP (Y)?

Answer 1

a).

Consider the given problem here the IS and MP schedules are “r = 2 + 0.5*A” and “Y = 1000 – 20*r”, where “r=rate of interest rate” “A=inflation rate” and “Y=income”.

So, the AD shows the simultaneous equilibrium of goods and money market, => the equation of AD curve is given below.

=> Y = 1000 – 20*r = 1000 – 20*(2 + 0.5*A), => Y = 1000 – 40 - 10*A.

=> Y = 960 – 10*A, be the equation of AD.

b).

The following fig shows the IS, MP and AD curves.

Here the IS shows the negative relationship between “Y” and “r”, on the other hand MP curve is completely independent of “Y”, => it is horizontal.

Now, the AD shows the simultaneous equilibrium of goods and money market, => its shows the negative relationship between “A” and “Y”.

c).

Here the AD equation is given by.

=> Y = 960 – 10*A, => if “A1=3%”, => Y = 960 – 10*3 = 930, => Y1 = 930. Now, as the inflation rate increases to “A2=5%”, => the corresponding income is “Y2=960-10*5 = 910”. So, as the inflation rate increases the level of income decreases. So, here the central bank should reduce the interest rate in order to increase income back to “Y=930”.