Question

Frank likes to play his stereo loudly which gives him marginal benefits per hour of

MBF = 30 - 2H

where H is hours per week. Mike, Frank's neighbor, doesn't like stereo noise and has a willingness to pay for quietness (marginal benefit of stereo noise avoided, Q = - H)

MBM = 20 - 1.5Q

What is the total gain in Mike's welfare at H* compared to the maximum playing time of H =15 hours?

Answer 1

With MBF=30-2H and MBM=20-1.5Q, the equilibrium H* is given by:

MBF=MBM

30-2H*=20-1.5Q

30-2H*=20-1.5*(-H*)

30-2H*=20+1.5H*

3.5H*=10

H*=2.857143

MBM=20-1.5*(-2.857143)=24.28571

When H=15,

MBM=20-1.5Q

=20-1.5*(-15)

=20+22.5

=42.5

Thus, total gain in welfare at H* compared to maximum playing time of H=15 is:

=2.857143*(42.5-24.28571) + (1/2)*(42.5-24.28571)*(15-2.857143)

=162.6276