Hi cpc1!
Here are the answers to your questions.
1. First of all, recall that definition of price elasticity of the demand is:
%Change in Quantity
-------------------
%Change in Price
if all else (such as per capita income and competitors' prices) is
left equal. When using the "arc" formula there's a specific way of
calculating the percentage changes. You'll find the formula at the
following link:
Arc Elasticity
http://www.ecoteacher.asn.au/Demand/elastsli/e16.htm
Answering points 1, 2 and 3 will be just a matter of applying this
formula to different variables.
* Own-price Elasticity of Demand
Notice than in months 4 and 5, United's price and per capita income is
the same; and only American's price changes. So we'll use these two
months to calculate the own-price elasticity.
American's price in month 4 was $109 and in month 5 was $108, so we'll
set P0=109 and P1=108 (actually, the arc elasticity formula is built
in such a way that doesn't matter which one is P0 and P1). Also, we
have that Q0=70 and Q1=72. So as expected, when price falls, demand
increases. Plugging these values in the formula shown in the link
above gives that the own-price arc elasticity is -3.056. So for every
1% increase in price, demand falls 3.05%, and viceversa
* Income Elasticity of Demand
We choose here months 2 and 3, since American's price and United's
price remain constant while per capita income changes.
Let's call Y0 and Y1 to the per capita income in months 2 and 3. We
have Y0=1900 and Y1=2100. Also, checking the quantities, we have Q0=62
and Q1=70. Now, in order to find the income elasticity, we again plug
these values into the formula. Notice that the Y0 and Y1 should be
plugged where the "P0" and "P1" are in the formula, because what we
want to calculate here is:
%Change in Quantity
-------------------
%Change in INCOME
So we shoould enter the income data in the denominator. We get here
that the income elasticity is 1.21. So, for every 1% increase in
income, demand increases 1.21%
* Cross Price Elasticity of Demand
We're interested here in the reaction to American's demand when United
changes its prices. Thus, we use months 1 and 2, where American's
prices and per capita income are fixed, while United's price changes.
Using the same procedure as before, we have here P0=112, P1=110, Q0=65
and Q1=62. So, as we would expect, when United lowered its prices,
demand for American tickets decreased. Plugging those values into the
formula, we get that the cross-price elasticity is 2.62. Therefore,
when United increases its prices by 1%, demand for American tickets
increases by 2.62%.
2. Here's a definition of what inferior and normal goods are:
"In consumer theory, an inferior good is one for which demand
decreases when income rises, unlike the more common normal goods, for
which the opposite is observed."
Inferior Good
http://encyclopedia.laborlawtalk.com/Inferior_good
Using the results found in the previous question, we conclude that
economy class tickets in the Chicago-Columbus market are a normal
good, because when income increases, demand also increases. (In other
words, if income elasticity is positive, the good is normal; if it's
negative, then the good is inferior)
3. United appears to be a very close substitute of American in the
Chicago-Columbus Market, because we've seen from the cross-price
elasticity that when United decreases its prices by 1%, this hurts the
demand for American's economy class tickets, which is reduced by more
than 2%. If these companies were not close competitors, we would
expect the cross-price elasticity to be very close to zero; so that
price changes in one company would not affect demand for tickets in
the other one. Since this is not happening, we conclude that American
and United are close substitutes of each other.
4. We need to consider what would happen to total revenue and total
cost in order to decide how to set the price. Since the own-price
elasticity is approximately -3, increasing the price by 1% reduces the
number of tickets sold by 3%. Now, since revenue is Price*Quantity,
it's clear that increasing the price would only reduce the revenue,
because the quantity sold would experience a higher fall than the rise
in price. So, in order to increase total revenue, we should actually
reduce prices, because reducing prices by 1% increases demand by 3%.
So again, in this case the increase in quantity sold more than
compensates the lower price American charges, thus increasing total
revenue.
Regarding costs, there is no data. However, a good guess would be
that, at these levels of load factor, costs don't change when changing
prices. We concluded in the previous paragraph that price should be
reduced and quantity increased in order for the revenue to rise. This
would mean that more people will be travelling with American. However,
the table shows us that only about 60% of the seats are filled, while
the rest are empty. So, increasing the quantity of tickets sold would
not require to add more flights (thus increasing the fuel and
maintenance costs), and the new customers could just be added to
existing flights. The extra costs of adding these "new" customers is
negligible (probably just the cost of some extra food and cleaning).
So there are good reasons to think that total costs would not change
if price is lowered.
Finally, we conclude that in order to increase profits, American
should lower its prices, as this will clearly increase the total
revenue while leaving total costs almost unchanged.
5. It would probably be larger. Own-price elasticity is said to be
greater as the time in which it is measured increases. This is due to
the fact that in the long run there is more flexibility to move to
substitutes than in the short-run. In the short-run, if American rises
its prices, people would probably still buy almost as many tickets as
before, be it because they are "used to" that company, they have
almost got a free ticket because of the mileage points program, or
they just don't know how good the other companies. However, in the
long run these effects are not as important, and people will have more
time to adjust and switch to American's competitors if prices remains
high for years. Therefore, we conclude that the own-price elasticity
would have been greater (in absolute value) if we had conducted the
survey over a period of 5 successive years rather than over 5
successive months.
Google search terms
arc elasticity
://www.google.com/search?hl=en&q=arc+elasticity
inferior good
://www.google.com/search?hl=en&lr=&q=inferior+good
I hope this helps! If you have any questions regarding my answer,
please don't hesitate to request a clarification. Otherwise I await
your rating and final comments.
Best wishes!
elmarto |
,
0 Comments
)