Monday, February 19, 2007

Beavis, Butthead, and the Quantity Theory of Money

Today I covered one of my favorite topics of Econ 102, Principles of Macroeconomics. We have begun discussing monetary policy and the Federal Reserve. This is the point at which I can allow Beavis and Butthead to demonstrate the Quantity Theory of Money.

When I was in college, my grandparents came to visit, and one day at the breakfast table my grandmother wondered aloud, "Why doesn't the government just print more money and give it to everyone? Everyone would be rich." Beavis and Butthead could help her to understand why this can't work.

In the episode of Beavis and Butthead entitled "Candy Sale", our heroes get candy bars from "Mr. Candy" (voiced by David Spade). Mr Candy tells them to sell candy bars for $2 each in order to raise money for the school. Beavis and Butthead are not excited about the prospect of selling candy bars, but they dutifully try to sell one to Mr. Anderson, their neighbor. He is not interested until Butthead offers a price of $1. Beavis matches the offer, and Mr. Anderson buys a candy bar from each of them. They have sold their first candy bars.

Butthead now has $1, and let's suppose he has 19 candy bars left. Beavis also has $1, and 19 candy bars. Here's where the episode gets clever: Butthead asks to borrow $1 from Beavis, and Beavis reluctantly agrees. Now that Butthead has $2, he offers to buy a candy bar from Beavis. Beavis agrees. Butthead eats the candy bar. Now Beavis offers Butthead $2 for a candy bar. Butthead agrees. Beavis eats the candy bar.

They go back and forth, trading the $2 to each other for candy bars. The next day in class they reveal to Mr. Candy that they have sold all their candy bars. He is delighted, but when he learns they have only $2 to show for it, he becomes furious. He threatens to harm the students, so Coach Buzzcut intervenes and beats up Mr. Candy.

What is the lesson to be drawn from this? Beavis and Butthead have demonstrated what economists call the velocity of money. The velocity of money is the number of times a dollar is spent, in order to purchase all the goods and services in an economy. It is a part of the equation of exchange, which is typically written:

MV=PY

M is the money supply. V is velocity. P is the price level, and Y is real GDP. IN the case of Beavis and Butthead, it is:

$2 * 38= $2 * 38

They have $2, which must be spent 38 times to buy all the candy bars in their little endowment economy.

This equation looks simplistic, but it is actually very important in the real world. In reality, the velocity of money is stable (i.e., fairly constant) over time. Let's also assume GDP is fixed. This means that any increase in M, the money supply, must lead to an increase in P, the price level. We call such an increase in the price level inflation. That is, the ultimate cause of inflation is almost always an increase in the money supply, which is controlled by the Federal Reserve. Some countries have had very rapid increases in money supply, such as postwar Germany, and as a result they get very high inflation. The Fed increases money supply slowly, so we get low inflation.

In the case of Beavis and Butthead, we can imagine what would happen if they were given $4 instead of $2. They might adjust to this by having each dollar go back and forth fewer times (i.e., velocity could rise). Alternatively, they might bid up the price of candy bars to $4 each. What will not happen, however, is an increase in candy bars--the extra money cannot summon more candy bars into existence, just as an increase in money supply in the U.S. cannot (in the long run, anyway) lead to a permanent increase in GDP.

To answer my grandmother's question, the reason the government doesn't just print enough money to make us all rich is that we would run out and spend the money, driving up the prices of goods and services, leaving us no better off. We'd have more money, but the things we buy will be more expensive, so we'd just be running in place.

Tuesday, February 06, 2007

Bad Economics: Businesses Simply Pocket a Tax Cut

Let's take an economically ignorant statement that I just read and analyze it:

"If a company makes more money per unit sold as a result of lower corporate taxes, that doesn't automatically mean that they will drop their prices."

There are several ways to tax a company. We could tax their profits, tax their output, or assign a lump-sum tax. With two of these taxes, it will always be the case that a lower tax means lower prices, even if there is no competition in the industry at all. If the industry is competitive, it just means that prices will be lower still. So let's see what happens to a monopolist under these different taxes. We'll use some simple calculus to get our results. You could also do this graphically, although it would be a lot more work for a blog like this.

No Tax:
Suppose that the (inverse) demand function is P=100-10Q. Suppose that the monopolist's total costs are C(Q)=50+10Q. We can write the profit function as Total Revenue minus Total Cost, or:

Profit=PQ-C(Q)=(100-10Q)Q-50-10Q

To maximize this, simply take a derivative with respect to Q and set it equal to zero (extra credit: check the second derivative to verify this is a maximum). You get:

100-20Q-10=0

Solving for Q, we get Q=4.5 as the amount of output that maximizes profits. What is the price? Simply substitute Q back into the demand function. You get P=55. So to summarize, with no tax, we get a price of 55 and a quantity of 4.5.

The Output Tax:
Suppose the government imposes a tax of $10 on each unit of output the firm produces (perhaps because the firm's output produces pollution--a Pigovian Tax).

Profit=PQ-C(Q)-Tax=(100-10Q)Q-50-10Q-10Q

Note the new term on the end. That's the tax. Maximizing this gives us:

100-20Q-10-10=0

This gives us a profit maximizing Q=4. The profit maximizing price is therefore P=60. So look at what we have so far: In response to the tax, the monopolist charges a higher price and produces a lower quantity. Take away the tax, and the monopolist charges a lower price and produces a higher quantity (i.e., we're back in our first example).

The Profit Tax:
Suppose the government puts a tax of 5.2632% on the firm's profits (I've picked this odd number for a reason which will later become apparent). The profit function becomes:

Profit=PQ-C(Q)-Tax=(100-10Q)Q-50-10Q-0.052632*[(100-10Q)Q-50-10Q]

The last term is the profit tax. The government takes ten cents out of every dollar of profit the monopolist makes. What happens? Let's check the first order condition:

100-20Q-10-0.052632*[100-20Q-10]=0

Solve this for Q and you get approximately Q=4, and P=60. Do those numbers sound familiar? They're the same numbers we got with the tax on output in the previous example. A tax on profits and a tax on output can be identical, if the taxes are chosen appropriately. And again, eliminating the tax takes us back to the first case with no tax--with a lower price and higher output.


The Lump-Sum Tax:
Now suppose the government simply slaps a fixed tax of $42.5 on the monopolist.

Profit=PQ-C(Q)-Tax=(100-10Q)Q-50-10Q-42.5

Because the tax is not dependent on output, when we maximize profit it will simply disappear (the derivative of a constant is zero). So we're back to our intial first order condition:

100-20Q-10=0

And we get Q=4.5 and P=55 . We're back to the same price and quantity from the no tax situation.

Profitability:
What happens to the profits of the monopolist under these three taxes? Just plug in the four quantities we calculated:

No tax:
Profit=PQ-C(Q)=(100-10Q)Q-50-10Q=(100-10*4.5)*4.5-50-10*4.5=152.5

Output Tax:
Profit=PQ-C(Q)-Tax=(100-10Q)Q-50-10Q-10Q=(100-10*4)*4-50-10*4-10*4=110

Profit Tax:
Profit=PQ-C(Q)-Tax=(100-10Q)Q-50-10Q-0.052632*[(100-10Q)Q-50-10Q]
=(100-10*4)*4-50-10*4-0.052632*((100-10*4)-50-10*4)=151.58

Lump-Sum Tax:
Profit=PQ-C(Q)-Tax=(100-10Q)Q-50-10Q-42.5=(100-10*4.5)*4.5-50-10*4.5-42.5=110

What lessons can we draw from this?
-Even a monopolist will automatically reduce price and increase output when a tax is eliminated. It doesn't matter what form the tax takes, unless it's a lump-sum tax (which doesn't affect output, although it might affect the decision of a firm to start up or shut down). . And they don't do it because they're nice people. Reducing price and increasing output increases profit.
-Different taxes can yield the same output and price, and different profits. Or we could rearrange all the taxes to give the same profits, but different outputs and prices.

Some other things to note:
-If this were a perfectly competitive industry, profits would be competed down to zero (remember, these are economic profits, not accounting profits). This would result in lower prices and higher output, but it would not change the fundamental result that the removal of a tax on a producer will lower prices. Anyone familiar with Supply and Demand should be able to demonstrate this on a graph.
-If this monopolist is the owner of a nonrenewable resource, the price should rise over time as the resource becomes more scarce. The removal of a tax will still have similar short-run effects, however, even if the (untaxed) price eventually rises back to its former (taxed) level due to scarcity.
-Market adjustment of prices sometimes takes time; we may not observe instant and complete price adjustment in some markets. Firms and consumers are working through a discovery process, finding out new information and incorporating it into their production and consumption plans.

A Missing Market

The school at which I teach seems to lack a good system for distributing used goods. Occasionally someone will send around an email offering an extra file cabinet or desk to whoever will pick it up, and it is invariably snatched up in minutes. There must be other items that could be reallocated if there existence was publicized. I've talked to students who have desks, televisions, and other items that they would like to get rid of. Their only option is to put signs up around campus advertising.

I think there is an opportunity for some enterprising individual to set up a used goods website--a Craigslist sort of site, devoted to this school. My previous university had just such a thing, although that school was much bigger than this one, and could perhaps easily spare people to work on it. This school, so far as I can tell, has no central message board at all. I talked about this with a colleague, and he contacted Craigslist, asking them if they might have some sort of college or university version that they could provide. The reply was that they were understaffed and incredibly busy managing their current system, and they could not branch out into anything else at the moment. Of course, students could use eBay, but that seems silly given that their potential customers are living within walking distance.

Isn't this an opportunity waiting for some clever individual? Surely there must be a simple way to set up a site that could fulfill this purpose. Wouldn't something as simple as a bulletin board system work? Are there any particular systems that someone who is barely competent with html could implement? Suggestions are welcome. If it proved necessary, I could work with students to set up such a site using off-campus resources, and perhaps fund it with Google Ads (or whatever other ad service would work--although I suspect the ads wouldn't generate enough revenue to pay the costs involved; it would be something of a work of charity).

We're the Government--and You're Not

This is hilarious:
http://www.youtube.com/watch?v=pvsADU2OOWM
(Thanks to Art Carden for the link.)

It is a satirical video about why government is good for you. I wish it were longer. There are so many more policies that could be mocked:

-Why it's good for you that there are tariffs and quotas that make you pay twice the world price for sugar, and tariffs that make you pay an extra 25% for imported pickup trucks.

-Why it's good for you that your postal service is provided by a government monopoly.

-Why it's good for you that the government can sieze your land merely because it thinks it can get higher tax revenue our of an alternative use.

-Why it's good for you that the government decides whether or not your relationship gets to count as marriage (but it doesn't need to rule on who can be your friends, or your acquaintances, or your best buddy).

-Why it's good for you that the government subsidizes corn producers, so that they can produce ethanol, which provides poorer fuel economy and horsepower than gasoline, while using roughly the same amount of energy to produce as it provides (it may even provide less energy than is used to produce it).

I could go on and on.

Thursday, February 01, 2007

The Road to Serfdom is Paved with Lite-Brite Cartoon Characters Flipping the Bird.

In case you have not already heard, some performance artists in Boston have caused a commotion because they put up some advertisements that resemble Lite-Brite images of a cartoon character from the Cartoon Network show Aqua Teen Hunger Force. A movie based on the television show will be coming out soon. Here is a video showing the ads (which attach magnetically and depict the character Ignignokt displaying a rude hand gesture) being hung around Boston (they were hung in other cities as well, as it turns out).





The ads were spotted by some concerned citizen, who did not know what they were, and reported to the police as possible dangerous devices planted by terrorists. The police then proceeded to go around the city blowing them up, alerting the press to a terrorist threat, and generally causing widespread panic.


The two performance artists have been arrested and charged. In the following clip they hold a press conference--sort of--and refuse to take the charges seriously. Having been advised by their lawyer not to answer questions about the charges (which is the usual advice given by lawyers in these situations), the artists announce that they will answer questions regarding hair in the 1970s.






Some people--particularly the press in that video--are upset that they are not taking the charges seriously. Others are upset with them (and with Turner Broadcasting Systems, which owns Cartoon Network) for causing this panic. A crazed commenter in Reason's Hit and Run blog says that Turner has essentially shouted "fire" in a crowded theater.


My reaction is "To hell with them." The press, the Boston Police, and the overreacting public should all be embarassed and ashamed. It is they who were causing a panic, not Turner or these artists. The artists are giving these charges exactly the degree of respect and serious consideration that they deserve: none. This is a farce. The problem is that the television press benefits from the ratings that panics bring, and a crisis is the most effective method for governments to promote their most important goal: getting, keeping, and using power. Hopefully the artists will benefit from turning this situation on its head by mocking it.


We cannot afford to live in a society in which everyone is constantly concerned about doing anything that any person could possibly interpret as being suspicious. Should all ad campaigns be submitted to several government agencies for approval from now on? Should they be publicly announced and explained so that everyone knows what is an ad campaign and what is not? What about other activities that could possibly be interpreted as terroristic threats? If I leave my satchel at my table when I get up to get a drink refill at the cafeteria, should the bombsquad be called in?


I find it refreshing that someone has the courage to laugh at the absurdity of the reporters and the government. I suspect that most people, unfortunately, will not get the joke.

UPDATE:
As usual, Reason Magazine has a better take on this story.