Question

SECTION C All work is to be done in the spaces provided.

1. (Chapter 3) Corduroy Island is very rocky and very dangerous for passing ships. The island’s citizens have decided to build lighthouses to alert passing ships to the contours of the island and to avoid environmental disaster. Those on the west side of the island (“westerners”) have an inverse demand function for lighthouses given by P = 36 – 4Q and those on the east side of the island (“easterners”) have an inverse demand function for lighthouses given by P = 14 – 2Q. The total cost of building/maintaining lighthouses on the island is TC = 20Q.

a. Calculate is the marginal cost of a lighthouse.









b. If the westerners act on their own, calculate how many lighthouses they will build.









c. Calculate the westerners’ consumer surplus in part (b).









d. If the easterners act on their own, calculate how many lighthouses they will build.

Answer 1

a) Marginal cost=$20

Calculations---

TC=20Q

MC = derivative of TC

MC= 20$

b) If the westerners act on their own,the number of lighthouses they will build= 2

Calculations----

The equilibrium/ profit maximising quantity will be determined where -----

MR=MC

Finding MR-------

P=36-4Q

TR=PQ= 36Q-4Q2

MR= derivative of TR,so-----

MR= 36-8Q

At equilibrium______

36-8Q=20. ( MC=20$)

Q=2

C) CONSUMER surplus C(cs) of westerners=$ 8

Calculations-------

CS is difference between the price ,what the consumer's are willing to pay and the equilibrium price.

Formula-----

1/2(Q)(wTP-Ep). = 1/2(2)(36-28)

1/2*2*8=$8

d) If Easterners act on their own,the number of lighthouses they will build--------zero

Calculations--------

P=14-2Q

TR=PQ=14-2Q2

MR=14-4Q

At equilibrium-----

14-4Q=20

Q=-3/2

So, the westerners shouldn't build any lighthouse.