demand function for money

[neha.neu]

Q : If demand function for money is L = kY-hr (where k>0, h>0,Yis income & r is rate of interest), an increase in the autonomous money supply, ceteris paribus will shift the LM curve
Solution choices are a) rightward by change in M / h
b) leftward by change in M/h
c) rightward by change in M/k
d) leftward by change in M/k

What would be the equatiom of Lm curve in this case and certainly what would be the answer?

 

[nehapodar]

This same question is asked by Madhuri Kumar named IAI nov 2005..the ans is
The LM curve shows the combinations of r and Y that keep the money market in equilibrium, ie where Ms = Md. Assuming the money supply is fixed, an increase in Y would cause an increase in Md and hence an increase in r. Hence the LM curve slopes upwards. There is a different LM curve for every possible level of the money supply - the higher the money supply, the further to the right the LM curve will be.

For this question, we know that the LM curve will shift to the right - the question is, by how much? If the LM curve shifts to the right, there will be a higher Y at every given r. We have to work out the increase in Y at a given r.

For equilibrium, Md = Ms. At the original equilibrium kY1-hr = M1. At the new equilibrium kY2-hr=M2. Therefore k x change in Y = change in M. Therefore, the change in Y (ie the amount by which the LM curve shifts to the right) = change in M / k.