Problem Set 2

Worth 50 points

June 24, 2009

Due: June 29, 2009

You must explain how you arrived at your answer.

- Your restaurant chain periodically re-evaluates its pricing decisions.
Since you know that the marginal revenues depend on the elasticities, you
decide to undertake a short-term experiment to generate estimates. For a
month, you raise prices in the Dallas stores by 10% but leave the prices in
the Fort Worth stores unchanged. You calculate that the average Dallas store
decreased sales by 20% but that Fort Worth stores increased sales by 5%.
- What is the diff-in-diff estimate of the price elasticity?
- Is there reason to suspect that this estimate is biased upward or downward?
- Suppose instead that you were estimating an advertising elasticity by decreasing advertising expenditures in Dallas but not Fort Worth (and leaving prices alone). Would suspect the the same bias in this estimate?

- The difference in Fort Worth was +5%. This is an estimate of the general trend in sales that are likely to be common to both Fort Worth and Dallas. Thus, the difference in Dallas or -20% includes both the effect from the price change as well as the general trend. Thus, the diff-in-diff estimate is -20% - (+5%) or -25%. Since a 10% price change caused this the diff-in-diff elasticity estimate is -25%/10% or -2.5.
- It is possible that some of your Dallas patrons became aware of the price difference between the Dallas and Fort Worth stores. Some of them might go over to Fort Worth to purchase their meals. If so, this will tend to both inflate the 5% change observed in Fort Worth and the -20% change in Dallas. In this case, the true demand, if you implemented the price change at all stores, would be a bit less elastic than -2.5. Your estimate might be too elastic.
- This will cause an increase in sales in Dallas. In this case, you worry about the opposite "infection." That is, some Dallas customers who are exposed to less advertising will reduce their purchases when they visit Fort Worth. Similarly, some Fort Worth customers who are regularly in Dallas will be exposed to less advertising and hence purchase fewer units in Fort Worth. If so, some of the decrease in Fort Worth will be due to the decrease in advertising in Dallas. In this case, you are susceptible to underestimating the advertising elasticity.

- The Burrito Barn is considering a price reduction on the Firegut
Burrito, which currently sells for the price of $5.00. Guillermo, the
proprietor of Burrito Barn, knows the price elasticity for the Firegut is
roughly equal to -2.3 over the range being considered for the price
change. The Firegut has been selling at the brisk pace of 500 burritos per
week. To increase market share, Guillermo would like to increase sales to
750 per week. What price should Guillermo set?

Use the formula: price elasticity = (q_{1}-q_{2})/(q_{1}+q_{2})] / [(p_{1}-p_{2})/(p_{1}+p_{2})]

e = -2.3; q_{1}=500; q_{2}=750; p_{1}=5; solve for p_{2}

-2.3 = (500-750)/(500+750) / (5-p_{2})/(5+p_{2})

-2.3 = -250/1250 / (5-p_{2}) / (5+p_{2})

-2.3 = -0.2 / (5-p_{2}) / (5+p_{2})

-2.3 = -0.2(5+p_{2})/(5-p_{2})

-2.3(5-p_{2}) = -0.2(5+p_{2})

-11.5 + 2.3p_{2}= -1- 0.2p_{2}

2.3p_{2}= 10.5 - 0.2p_{2}

2.5p_{2}= 10.5

p_{2}= 4.20

- As a budding entrepreneur, you have purchased a small
commuter airline. You have one plane with 8 seats, and you have engaged in
extensive market study to categorize your customers’ willingness to pay into
8 groups of similar size as follows: ($500, $450, $400, $350, $300, $250,
$200, $150). All of your costs are fixed except fuel and in-flight snacks,
which cost $225 total per ticket sold. What price should you charge and how
many tickets would you sell?

Price Quantity Total Rev MR MC Profit 500 1 500 500 225 275 450 2 900 400 225 450 400 3 1200 300 225 525 350 4 1400 200 225 500 300 5 1500 100 225 375 250 6 1500 0 225 150 200 7 1400 -100 225 -175 150 8 1200 -200 225 -600

P* = 400 and Q* = 3

- Many residents of Laredo, TX enjoy going across the
river into Nuevo Laredo, MX for good, inexpensive restaurant meals. However,
the crackdown on drug trafficking in Mexico has made border cities decidedly
less safe.
- How has this affected the market for restaurant meals in both cities?
- How has this affected the profits of restaurateurs in both cities?

- The violence in Nuevo Laredo, MX makes dining there less attractive. The willingness-to-pay for any meal decreases implying that the demand curve shifts to the down (to the left). The equilibrium price and quantity there falls. Since meals in Laredo are a close substitute, we expect demand to shift up (out) for Laredo, TX. The equilibrium prices and quantities on the Texas side increase.
- With lower prices and fewer customers, restaurateurs in Nuevo Laredo will earn lower profits. Some will likely earn negative profits. This will lead to resources flowing out of the restaurant business there. The opposite happens in Texas where the increase in prices lead to increases in profits and investment resources flow into this use. The restaurant business is characterized by low barriers to entry and exit. This means that the changes in profits are likely to be short lived and a new equilibrium will assert itself in which prices revert back to their original levels (though with fewer restaurants on the Mexico side and more on the Texas side).

- You sell industrial generators that are differentiated
from your competitors' products. As a consequence, your demand elasticity is
-3 and your optimal price is $1,200 which generates a nice stream of
profits. Recently though, your competitors have developed products that are
more similar to yours and your elasticity has increased to -4. How much
should you adjust your price?

We know that optimally, you set (P-MC)/P = 1/|elasticity|. Originally, since your optimal price is $1,200, this meant that ($1,200 - MC)/$1,200 = 1/3 or MC = $800. But with a more elastic demand, your optimal price is (P-MC)/P = 1/|elasticity|, = (P-800)/P = 1/4 or P* = $1,066.67.