Answer to Question #196645 in Microeconomics for Neeraj Tushar Gadk

Question

The demand for the services provided by the Tikho Marina in Novorossyisk is Q = 100 − 2P and the marginal cost of providing these services is MC = −110 + 2Q, where Q is the number of yachts in the marina. Assume that all yachts require the same services. If a two-part tariff pricing system is used,

1. what is the optimal daily entry fee for the marina?

2. how many yachts will visit the Tikho Marina ?

Answer 1

$$solution$$

1. Considering the above example, the firm will set the usage fee (per-unit price) equal to marginal cost: Where;

$MC=-110+2q\\ But, to\ obtain\ the\ MR\ then;\\ Get\ TR=P*Q\\ p(100-2p)=100p+2p^2\\ MR=100+4P\\ At\ the\ optimal\ price\ fee\ MC=MR\\ 100-4p=110+2Q\\ Q=5+2P\\ But,\ q=100-2p\\ substitute : 5+2p=100-2p\\ p=23.75\\ Q^*=5+2(23.75)\\ =52.5\\$

Hence, The firm will set the usage fee (per-unit price) equal to marginal cost $p^*=MC=5$ At this price, the quantity sold is found by substitution of the price into the inverse demand function. Next, the firm will determine the entry fee (fixed price), by calculating the area of consumer surplus at this price.

$CS=0.5(23.5)(52)\\ =611$

Therefore, the firm sets the usage fee: T = 611

2 .The yachts to visit Tikho Marina will be 53