A small island near a major city has a beautiful beach. The company that owns the island sells day passes for the beach, including travel by ferry to and from the beach. Because the beach is small, the company does not want to sell more than 200 excursion tickets per day. The company knows there are two kinds of visitors: those who are willing to buy tickets a month in advance and those who want to buy on the day of the trip. Those willing to buy in advance are typically more price sensitive. The demand curve for advance purchase excursion tickets is described by P1 = 100 – 0.2Q1, where Q1 is the number of advance purchase tickets sold at a price of P1. The demand schedule for tickets by day-of-travel excursions is represented by P2 = 200 – 0.8Q2, where Q2 is the number of tickets sold at a price of P2.
a) Suppose the marginal cost of the ferry trip and use of beach is 50 per customer. What prices should the firm charge for its excursion tickets?
b) If the marginal cost were high enough, the firm would want to sell fewer than 200 tickets. Suppose the marginal cost of the ferry trip and use of beach is 80 per customer. What prices should the firm charge for its beach excursion tickets?
Concept The company owns an island, its an example monopoly. In monopoly, equilibrium is attained when marginal revenue is equal to the marginal cost. Because if marginal revenue would be less than marginal cost, company would run into losses and when marginal revenue is greater than marginal cost its demand will go down. Solution Marginal cost per customer=$50 MR1= MC Total revenue=p1xq1? =100q1-0.2q1^2 MR1=100-0.4q1 MR1=MC 100-0.4q1=50 q1=125 p1=75 For day of travel ticket Total revenue=p2xq2? =200q2-0.8q2^2 MR2=200-1.6q2 MR2=MC 200-1.6q2=50 q2=93.75 p2=125 Answer- The price of advance…
ets excursion is $75. The price of day of travel tickets excursion is $125. b) Marginal cost per customer=$80 MR1=Mc 100-0.4q1=80 q1=50 p1=90 For day of travel ticket? MR2=MC 200-1.6q2=80 q2=75 p2=140 ? Answer- The price of advance ticket excursion is $90. The price of day of travel excursion is $140. When the marginal cost increases, price of excursions also increases and quantity sold will decrease.