Thursday, August 20, 2009

Trash Talk

I recently moved from Philadelphia, where trash and recycling pick-up are included in property taxes, to a smaller town where my taxes cover recycling but not trash pick-up. The waste management companies where I currently live offer several pricing options for garbage collection:

1. Pay-by-weight at the dump: The catch is that there’s a minimum $15 fee, so you need to generate lots of garbage to make this worthwhile.

2. Pay-by-the-can pick up: You pay a nominal charge, usually about $3-$3.50, per 33-gallon trash can. Under this option, your fee fluctuates directly with the amount of garbage you produce.

3. Flat rate: You pay a flat monthly fee of say $10, and this includes only 1 trash can pick-up per week. If you have more than one can, you pay an additional fee, but if you don’t have any trash, you will not receive any credit for future collections. This service makes sense if you reliably generate 1 can per week.

I decided to go with option two: pay-by-the-can pick up. Each Tuesday morning, I put out my 33-gallon trash can (if it’s full), and the lowest cost trash company I could find ($3.00 per can) comes to collect. The window in my home office overlooks the road, so I typically hear any cars and trucks that drive by. To my surprise, I heard five different waste management trucks drive by my house in one day! My immediate reaction was: How can this be efficient? Surely there are economies of scale to trash pick up?

Consider the following simple example. Suppose there are four houses located along Country Road. The road is a one way street, so the only way to drive by any of the houses is to drive east along Country Road, passing by all four houses with any trip. If a trash collection company is hired to pick up trash for House 1, what are the additional costs associated with picking up trash at any of the other three houses?

One could argue that the additional costs are negligible. In other words, the cost of picking up trash at the first house is high because you have to have a trash collection truck, a worker to drive it, a worker or two to collect the trash, fuel, etc. But once you’re out on Country Road, the marginal cost of collecting trash from the surrounding houses is just the wear and tear on the truck’s brakes, a slight wage expense to your workers, and the cost of taking care of the additional waste (such as bringing it to the local dump).

It’s probably true that the average cost curve for a trash collection company is not strictly downward sloping since once a certain number of houses are served, the company would need to obtain additional trucks and workers. I would still argue that there are economies of scale for trash collection companies once they enter a particular neighborhood. It seems silly to me that in a given week I see at least ten different trash collection trucks drive by my street.

Wouldn’t it be more profitable for all companies if they each monopolized a small region? The additional cost of collecting trash from a neighboring house must be smaller than the additional cost of servicing a house in an entirely different neighborhood. Even without changing prices, revenue would probably remain constant while costs would decline, leading to higher profits for each firm.

Discussion Questions

1. What kind of market structure does trash collection represent? If the city decided to step in and control trash collection for my town, what pricing options might it choose?

2. Do consumers benefit at all from having several waste management companies to choose from with different pricing schemes?

3. If the city allowed waste management companies to “monopolize” particular neighborhoods, how might this affect the market? What are the effects of competition on prices, welfare, and pick-up quality (such as timeliness, effectiveness, etc)?

4. Given the number of trash collection companies in my neighborhood, what does this say about the profitability of this industry? If the town does not have strict anti-trust laws, would it be profitable for one firm to buy out all the others? What problems might arise if only one firm controlled trash collection for my entire town?

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Thursday, August 13, 2009

The Demand for Natural Light

I once participated in a blind taste test involving eight light beers. Faced with eight un-marked cups, I was certain I’d prefer the priciest, and presumably classiest, light beer in the field. Alas, I chose Natural Light. For me, the cheap and down-market “Natty Light” is the choicest light beer on offer. But people who have (or think they have) a more refined palate gladly pay for a more expensive option like Heineken or Bud Light.

With the economic downturn, however, cash-strapped beer drinkers appear to be switching to cheaper beers like Busch, Natural Light, and Keystone. As average incomes declined in the United States, sales of these cheaper options have increased substantially. Meanwhile, sales of ‘premium’ brands like Budweiser and Heineken were reportedly down 18% and 14% respectively from a year ago in July 2008.

Discussion Questions

1. If, other things being equal, a reduction in average income leads to an increase in the demand for Natural Light, what type of good is “Natty Light”? If, during the same period, the demand for Bud Light declines, what type of good is Bud Light?

2. What additional information would be useful if you were trying to use changes in average income and beer sales to determine whether a particular brand of beer was a normal or inferior good?

3. What strategy might a large beer company adopt to protect itself from an economic downturn?

4. Information Resources, Inc. reports that sales of Bud Light were down about 7% from a year ago in July 2008. Let’s assume that the price of Bud Light is fixed, so that the percentage decrease in sales is the same as the percentage decrease in the quantity of Bud Light demanded. Assume that personal income per capita in the United States declined by about 3.4% over the same period. Keeping in mind that factors other than income probably affected Bud Light sales over this period, use these numbers to come up with a rough estimate of the income elasticity for Bud Light. Is the income elasticity of demand for Bud Light elastic or inelastic? Would you characterize Bud Light as a luxury or a necessity?

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Wednesday, August 12, 2009

I'd Like to Bid $1, Bob!

In a previous post, we used The Price Is Right as a starting point for a discussion of probability theory and decision-making analysis. But the opportunities to learn from the show hardly stop there. Another practical game theory application can be observed six times a show – when contestants “bid” in an effort to win a prize and to get on stage from “contestants’ row.”

Each time the game is played, four contestants are shown a prize without being told its price. Each contestant takes their turn announcing a single bid, or guess, as to the value of the prize (rounded to the nearest dollar). All bids are known to all the other players as soon as they are made, and no player may bid the same value as another. After all four bids have been made, the player whose bid is closest to the actual retail price of the prize without going over wins both the prize and the opportunity to come on stage and play a “pricing game” in order to win more valuable prizes. If all four contestants guess a price higher than the price of the prize, all bids are erased and the game is played again. In the case that one of the four players actually guesses the exact value of the prize, they receive an additional cash bonus. For the remaining purposes of this analysis though, we will ignore the cash bonus and simply focus the analysis on a strategy to maximize the chances of winning the prize and going on stage. The game is most easily modeled from the perspective of the fourth player, so we will base our analysis on his perspective.

Suppose the first three players bid b1, b2, and b3; assume these are listed in increasing order because only the value of each of the first three bids matters to the fourth player, not which bid was made by which player. The fourth player will then try to pick a value, b4, that is priced closer to the true price of the prize (call it P) than b1, b2, and b3, without going over. Assuming none of the other three players has bid the exact price, P will fall in one of the following four intervals: (1,b1-1), (b1+1,b2-1), (b2+1,b3-1), (b3+1, ∞).

The optimal strategy for the fourth player is to pick what range they think contains P, then bid the lowest value in that range. It is important to note that any bid higher than this but within the same range does not help him, but it does increase the chance that he goes “over” and loses automatically. Suppose, for example, that the fourth player believes that P= $1,000 and b3=$900 (with b1 and b2 defined to be less than $900). The fourth player should bid exactly $901. With a belief that the price is around $1,000, any bid lower than $900 gives the player who guessed b3 the best chance to win, and any bid higher than $901 gives the same player more chances to win if it turns out the fourth player’s belief about the price is an overestimate. In order to act optimally, the fourth player should always bid either: $1, b1+1, b2+1, or, b3+1. Any other bid makes the fourth player strictly worse off; taking away values for P that make the fourth player win, without providing other values that make him win.

Discussion Questions

1. Given the fourth player’s optimal strategy, how should the third player pick their bid? Keep in mind, when making his choice, the third player knows b1 and b2, as well as the fourth player’s strategy. What method can you use to solve for each player’s optimal strategy in this game?

2. What would you expect to happen if all players wrote down their bids simultaneously and did not know the other players’ guesses when making their own selection?

3. Suppose the cash bonus for bidding the exact value of the prize were very large, so large that players would be willing to risk losing the game for a chance to collect the bonus. How would this change the optimal bidding strategy? How would each player’s risk aversion factor into his decision?

4. Many times on the show, we do not observe this optimal bidding strategy by the fourth player. One possible explanation is that players do not want to appear cutthroat and greedy by bidding a single dollar more than an opponent (thus giving the opponent only one way to win: if his bid is exactly the true price). How would the optimal strategy change if you add reputation costs?