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Assignments: Elasticity

As the Midwest regional manager for American Airlines, you have recently undertaken a survey of economy-class load factors (the percentage of economy-class seats that are filled with paying customers) on the Chicago-Columbus, Ohio route that you service. The survey was conducted over 5 successive months. The survey results appear in the table below. Assume that all other factors have remained constant over the 5-month period:

Per Capita
American's United's Monthly American's United's
Mo Price Price Income Load Factor (Q) Load Factor
1 \$110 \$112 \$1,900 65 60
2 110 110 1,900 62 63
3 110 110 2,100 70 66
4 109 110 1,900 70 61
5 108 110 1,900 72 59

Based on the data you have collected, how responsive is your company's load factor on the Chicago-Columbus route to your own price, income levels, and United's price? That is, select appropriate months and compute elasticity values to complete the following table.
Elasticity (arc) Value

(1)own-price elasticity of demand for American's economy class seats

Using months 1 & 5 and the mid-point method, my value = 5.57

(2) income elasticity of demand for American's economy class seats

Using months 2 and 3 and the mid-point method, my value = 1.2

(3) cross-price elasticity of demand for American's economy class seats with respect to United's price on the same route

Using months 1 & 2 and the mid-point method, my value = 2.61

Hint: In each case, choose a pair of months in which all else is equal except quantities and the variable you are examining (for example, between months one and two, the American price, and income remained constant and only United's price changed. We can attribute the change in demand for American load factor to change in United's price level. Knowing these changes, we can calculate the cross price elasticity.)

Are economy class tickets a normal or inferior good in the Chicago-Columbus market? Explain.

It is a normal good. When income increases, the demand for the good increases.

How close a competitor/substitute does United appear to be in the Chicago-Columbus market? Explain.

I think United is a very close competitor/substitite for American's flights in this route.

Based on the survey you have undertaken, to increase your profits, should you raise your price, lower it, leave it unchanged, or is it impossible to tell without more information? (Hint: consider what will happen to TR and TC if you change your price.)

I think American could lower its price to increase profits.

If you had conducted your survey over a period of 5 successive years rather than over 5 successive months, would the own-price elasticity of demand for your product be larger or smaller than your estimate here? Explain.

I think this would be difficult to determine. The longer the time that elapses, the less reasonable it is to assume that all the other variables stayed equal.

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#### Solution Preview

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.

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 ...

\$2.49