Answer to Question #96756 in Microeconomics for Sumanjeet Kaur

Question

Three neighbors share a road to their rural cabins. This road requires lots of maintenance and each hour of maintenance costs whoever does the work $120. Family A enjoys using rustic vehicles and doesn’t mind if the road isn’t maintained well but the other two neighbors prefer more comfortable vehicles. Family A’s demand for maintenance is: QdA=50-P/2 (i.e. TBA=100Q-Q2) Family B and C are: QdB=50-(1/5)P (TBB=250Q-5Q2/2) and QdC=50-P/8 (TBC=400Q-4Q2)
a. Suppose Family B was the first to open their cabin this season and performed what it felt was adequate maintenance for itself. Then Family A opens their cabin. Knowing what Family B has already done, would Family A do any further work? How much? Then Family C arrives. Knowing what Company A and B have already done, would Family C do any more work? How much?
B. Given the total amount of work done by all three families, how much net benefit will each company get?

Answer 1

Solution:

Suppose Family B was the first to open their cabin this season and performed what it felt was adequate maintenance for itself.

$$250Q- 5/2 Q^2=120Q$$

$$130Q-2,5Q^2=0$$

                                                                                     Q=52

So, the part of Family B is Q=52.

Then Family A opens their cabin. Knowing what Family B has already done, would Family A do any further work? How much?

$$100Q-Q^2=120Q$$

                                                                                 

$$Q^2-20Q=0$$

 Q=20

So, the part of Family A is Q=20.

Then Family C arrives. Knowing what Company A and B have already done, would Family C do any more work? How much?

$$100Q-Q^2+250Q-5/2 Q^2+400Q-4Q^2=0$$

$$1500Q-15Q^2=0$$

                                                                          Q=100

Total work Q=100

Family C do 100-(52+20)=28.

B. Given the total amount of work done by all three families, how much net benefit will each company get?

Family A: $120·20=$2400

Family B: $120·52=$6240

Family C: $120·28=$3360