demand function for money

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?

 

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.