The market for round trip airline travel from Madison to Cleveland over the Memorial Day holiday consists of two types of customers. Let X1 denote the demand for airline tickets by students, and let X2 denote the demand for airline tickets by non-student adults. Let the price of a round trip ticket be denoted by Px, and suppose that everyone who purchases a ticket pays the same price. The demand functions of the two customer groups has been determined as follows
X1 = 9000 – 30Px
X2 = 39600 – 90Px
(a) What is the total market demand for airline tickets, as a function of by Px? Keep in mind that the total demand is the sum of the group demands (students plus non student adults.)
(b) Suppose that the price-elasticity of demand by students, at the price by
Px, is -2. What is the price for the non-student adult?
(c) At what price is the total revenue (for the entire market) maximized?
A. Total market demand= X1+X2=9000-30Px+39600-90Px= 48600-120Px
-2=-30(P/X)
15P=X
X=9000-30P=15P
P*=9000/45= 200
Price is same for students and non students.
Price for non student adults=$200
c) X=48600-120Px
Total revenue=Px*X= 48600Px-120Px^2
To find the price where total revenue is maximum. Differentiate total revenue with respect to price then equate it to zero.
dTR/dPx= 48600-240Px=0
Px= 48600/240= $202.5
When Price= $202.5 Total revenue is maximum.
The market for round trip airline travel from Madison to Cleveland over the Memorial Day holiday...
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