Hi k9queen!
Here are your answers:
A) Since the airline has commited to do the flights, it faces a fixed
cost schedule. It doesn't matter (regarding costs) wether there are 1
or 300 people in an airplane, since the fuel and maintenance costs are
the same. In other words, all of the airline costs are fixed costs.
The cost of adding more passengers to the plane can be said to be zero
(even though the airline may serve meals during the flight, the cost
of these meals, compared to the other costs, can be neglected). So,
since the airline only has fixed costs, it must now maximize its
income: in this case, this will be equivalent as maximizing profits,
since variable costs are zero.
B) The formula for elasticity can be found at the following link:
Price Elasticity
http://ingrimayne.saintjoe.edu/econ/elasticity/Elastic1.html
As you can see, the formula is:
e = (percentage change in quantity) / (percentage change in price)
Let's compute then the price elasticity for business travelers:
Price Quantity Elasticity Revenue
$150 2,100 315000
200 2,000 4.76%/33.33% = 0.142 400000
250 1,900 5.00%/25.00% = 0.2 475000
300 1,800 0.26 540000
400 1,600 0.3333 640000
500 1,500 0.25 750000
(the revenue is not necessary to compute the elasticity, I included it
for the next questions)
The elasiticities were computed as follows: at price $200, the percent
change in price from 150 to 200 is 33.33%. The percent change in
quantity from 2100 to 2000 is -4.76%; so the proportion is 0.142 (in
absolute value). Even though the elasticities should be negative,
since it's understood that for demand elasticity is negative (higher
price - lower quantity), it's customary to use the absolute value.
For vacation travalers, the elasticites are:
Price Quantity Elasticity Revenue
$150 1,000 150000
200 800 0.6 160000
250 600 1 150000
300 400 1.66 120000
400 100 2.25 40000
500 25 3 12500
Therefore, for business travalers, demand is always inelastic (it's
always less than one in absolute value). That is, a one percent change
in price causes a less than on epercent change in quantity. For
vacation travalers, demand is inelastic between $150-$200, and elastic
between $300-$500. Why is demand elasticity greater for business
travelers than for vacation travelers? The idea is that of a low
elasticity is that, no matter the price, the demand is more or less
the same (of course is lower at high prices, but not "much" lower).
Since businessmen HAVE to travel, because they have to conduct their
business, they will be less sensitive to changes in prices. If one day
the price of the airplane ticket rises, since they have to travel for
work, most of them will travel anyway. This is not so true for
vacation travelers: they might want to substitue the airplane for
another transport, or not go on vacation at all and just rest at home.
This is usually not possible for businessmen.
C) The total demand curve would be:
Price Quantity Revenue
150 3100 465000
200 2800 560000
250 2500 625000
300 2200 660000
400 1700 680000
500 1525 762500
where the quantity is the sum of the business demand plus vacation
demand. Since total revenue is maximized at price $500, that's the
price the airline should charge if it were to charge the same price to
everyone.
D) If the airline can charge a different price for each, it should
choose the prices that maximize the revenue for each group separately.
From the tables shown above, we see that, for business, revenue is
maximized at $500 (revenue is $750,000). For travelers, revenue is
maximized at $200 (revenue is $160,000). Therefore, those are the
prices the airline should charge (which partially explains why
airplanes have a "business class" and "tourist" sections, with
different prices). Total revenue is 750000+160000=$910,000, which is
higher than if the airline charges the same price to everyone.
Google search strategy
arc-elasticity formula
://www.google.com.ar/search?hl=es&ie=UTF-8&oe=UTF-8&q=arc-elasticity+formula&btnG=B%C3%BAsqueda+en+Google&meta=
I hope this helps! If you have any doubt regarding this answer, please
request a clarification before rating it. Otherweise I await your
rating and final comments.
Best wishes!
elmarto |
