Issues with profit

River flow here is from top down. Upstream firm Downstream firm To the consumer Here we have a story of two firms. One firm makes output that is purchased by another firm as an input. The second firm then sells to the final consumer. The upstream firm’s output is an input to the downstream firm. The downstream firm sells to the consumer. Isn’t this slide special?

In the world of sports the teams playing the game itself is upstream and the televised game is downstream. The authors want us to consider two situations 1) The (home) team and the television company are separate businesses, and 2) The team and the television company are part of the same company. This second case is a situation called a vertically integrated firm. If the two entities are separate the thinking is that the team may sell the game at a monopoly (high) price to the TV company. Thus, the TV company may not want to televise many games. Fans would not see many games (relatively). If the team and the TV company are vertically integrated then maybe the team doesn’t charge a monopoly price to the TV section and thus more games can be shown on TV.

The authors are trying to make the point that if the two groups are in the same firm then what is more important to the firm is overall profit, not the profit of any one part of the company. This may mean there is some cross subsidization going on. The team may not sell to the TV station at a price that is best for the team, but when sold to the TV station the TV station makes even more profit so that the overall corporation does better. In other words the team may have to “take one for the team!” The authors try to show this with some graphs that I will combine. If the 2 are separate we will have both the upstream and downstream firms be monopolies. But if the firms are vertically integrated the upstream firm will act competitively and the downstream firm will act as a monopoly. Let’s check this out, shall we?

Q P D MR MC P mup P cup D Q P Upstream Downstream MR MC d = P mup MC d = P cup P with separate firms P when vertically integrated Qsep QVIQ mup Q cup

If the 2 entities are separate then the downstream firm sells at Pmup (price as a monopoly upstream) and this becomes the marginal cost for the downstream firm. They act accordingly and charge in the downstream market at the higher price shown, with the lower output shown. If there is vertical integration, then the upstream firm sells at a lower price and the downstream firm has lower marginal cost resulting in the lower of the two prices and the higher of the two levels of output. What is not totally obvious is that combined profits are more when the upstream company sells at the competive price.

The next set of ideas I want to show you deal with taxes and depreciation ideas as applied in (and out of) the world of sports. Let’s start with taxes IncomeMarginal tax rate $1 or less.1 or 10 percent > $1, but <= $2.2 or 20 percent More than $2.3 or 30 percent Tax if you have $1 of income = $1 times.1 = 10 cents. Tax if you have $2 of income = ($1 times.1) + (second $1 times.2) = 10 cents + 20 cents = 30 cents. Tax if you have $3 of income = ($1 times.1) + (second $1 times.2) + (third $1 times.3) = 10 cents + 20 cents + 30 cents = 60 cents.

Now if you have income above 2 dollars all the dollars above 2 in the example have a marginal rate at 30%. So if you have $10 of income the $8 above $2 is taxed at the rate of 30% for a total of $8(.3) = $2.40. Now, if you can use the tax system to reduce your income to be like $7 instead of the $10 it really is then you tax above $2 of income is now only $5(.3) = $1.50. So, a mechanism that reduces your income for tax purposes reduces the taxes you owe. In our example the tax went down by 90 cents. Note, the higher the marginal tax rate the more your tax would be reduced in the example. Plus the more you can shield income the less your tax.

In a general business setting businesses have some inputs that can not be fully expensed in one year. An example would be the purchase of a machine that lasts 10 years. The machine will generate output for 10 years and help the firm generate revenue during those 10 years. So, the machine cost should be split up over the 10 years to match the revenues in those years. So, the machine is depreciated over the 10 years. This is the way we say the expense is taken over the 10 years. The straight line depreciation method says count as an expense each year the total up front cost divided by the years of life. If a machine costs $1,000,000 and has a 10 year life the depreciation expense is $100,000 per year. Also note that things like electricity that help the machine run are also expensed fully in the year incurred.

So, for tax purposes, a sports franchise takes the total revenue and subtracts out expenses in the year and only pays tax on the difference. Note, that depreciation is one of those expenses. Here is the kicker for a sports franchise. Labor contracts have yearly salaries that are an expense. Plus, the total value of salaries now and in the future are depreciated as well. The example in the book is that a group purchased the then Milwaukee Braves for $6,168,000. And it said all but $50,000 was embodied in the players. So it was able to use a straight line depreciation for 10 years for $6,118,000/10 = $ Thus, for tax purposes it would take the revenue and subtract off the current year salaries of players and then also take off another $611,800. It was in the 52% tax bracket and would have paid.52 times $611,800 = $318,136 in tax on that part of revenue. The team got to keep that money that would have been paid in tax!