Shocking Insight: Incentives Matter

There have been a few posts I’ve read lately involving people scaling down their future work expectations based on planned Obama tax increases.  Starting with this hypothetical example, you can quickly go from Jonah Goldberg’s desire not to be one of the suckers having to foot the deficit spending orgy to working fewer hours, or, like in Cafe Hayek’s comment of the week, not working at all (or working abroad).  Here is a quick and very simple model to show the potentially counter-productive disincentives involved in marginal tax increases.

Suppose we have a world with one marginal tax rate (i.e., a flat income tax) of 0%.  In order to raise revenue to pay for spending, the federal government institutes two marginal tax rates:  0% up to $75,000 and 80% after that point.  We will have individuals making various amounts of money, but the important cases to recognize are those in which the tax change can potentially make a difference, so we can look at three cases:  just shy of $75K, just over $75K, and moderately over $75K (with those who make well more than $75K having the same effects as those moderately over).

I’ll work out the second case, as the mathematical process works the same way for all three instances.  We first should calculate a utility function for the individual.  I decided to go with Y = -26X^2 + 2950X, where X is the number of hours worked per week and Y is the gross yearly income.  The individual makes $29.50 an hour and the weight on marginal disutility has been set in this example to give reasonable numbers of hours per week.  For our individual making $29.50 an hour—with the somewhat unrealistic assumptions of no extra overtime payments, no need to worry about a minimum number of hours to work (to cover personal costs), and a flexible number of hours to work each week—he would work 56.73 hours per week and earn $83,676.75 over the course of a year.  You can get this by taking the derivative of Y with respect to X and setting Y equal to zero (which allows for profit-maximizing) and solving for X.  X will be 56.73, and you can calculate earnings as Wages * Hours worked * Weeks worked.  Wages will be $29.5, hours worked 56.73 (which we solved for), and weeks worked 50 (which is an assumption based on the average American’s time worked).  This value of X means that once an individual works 56.73 hours, the income derived from the next unit of time will be less than the disutility of working that extra moment, so the individual will choose not to do this.

But now suppose that we have that 80% tax.  This changes the utility function a bit, as instead of making $29.50 an hour for any dollar amount over $75,000, the individual is only making $5.90 an hour.  We want to find out what the individual’s incentives look like at the $75,000 mark, so to do that, solve the equation 75000 = $29.5 * X * 50 weeks (where 50 weeks is an estimate of the number of weeks worked a year) and you get 50.85.  Up until 50.85 hours per week, the utility function will look the same, but after that point, it will look like Y(2) = -26X^2 + 590X.  At 50.85 hours per week, it does not make sense for the individual to work any more hours, as there will be a net disutility of work—in fact, if 80% were taxed on all dollars earned, the individual would only work 11.35 hours per week.  So in this case, the individual would stop working at 50.85 hours per week and not pay any income tax.

However, let us assume that people decide that an income tax is necessary for paying for desired government services, so a 10% rate is levied on dollars up to $50K and a 30% marginal rate on anything over $50K.  First, we’ll do the simple case for comparison:  a 10% rate across the board.  In this case, the worker, instead of receiving $29.50 an hour, will get $26.55 an hour, so we have to update our utility function to be Y = -26X^2 + 2655X.  After solving this, you can find that the individual will work 51.06 hours per week and earn $67,779.08 (net), paying $7531 in income taxes.  Note that we can already see an distortionary income effect from the tax:  the individual is working 5 fewer hours per week as opposed to the profit-maximizing case and thereby creates approximately $10,000 less than in the first instance.

Now, let us look at the case with the extra marginal rate in place.  In this case, the new rate kicks in at $45,000 net, which the individual reaches at approximately 33.9 hours per week (estimating 50 weeks worked a year, it would be $45000 = $26.55 * X * 50 weeks).  After that point, the new equation is Y(2) = -26X^2 + 2065X (where the 2065 is $29.50 * .7).  In this case, the individual’s profit maximization process will have him work 39.71 hours total:  33.9 hours a week, which will build up the old rate, and 5.81 hours a week at the higher rate.  The total net income will be ($26.55 * 33.9 * 50 ) + ($20.65 * 5.81 * 50) = $51,001.08.  The government will take $5000 in taxes from the first set and $2570.92 from the second set (because $20.65 * 5.81 * 50 = $5998.83.  $5998.83 / .7 = $8569.75, which is the gross income.  Taxed income is $8569.75 * .3).  Total tax receipts are $7570.92.  In this particular case, the government will get approximately $40 in additional receipts, whereas if the person had not cut down on hours in this second scenario, they would have taken roughly $5062 more.  So even though tax receipts go up, a rather large marginal tax rate increase (tripling it at $50K/year) ends up with a minimal increase in revenue because the individual shifts away to non-taxed activities (leisure).  I should also note that if the marginal tax rate were, say, 35%, the governmental revenue would actually be less for that individual than at the 10% flat rate.

The conclusion here is that saying “taxes change the incentives of workers” really does mean something.  The people who earn the most in any given year also tend to be the people who can afford to cut down on their work.  A couple making $400,000 a year can cut down to $199,000 by working fewer hours if punitive taxes after earning $200K are too high.  Their lifestyle will change in an undesirable fashion (given that they presumably had the opportunity to earn $199K a year while working fewer hours), but many will do it because the alternative options would bring less utility and because it’s not like $199,000 a year’s going to leave you in bread lines.  Other productive individuals may drop out of the workplace entirely and live off of annuities or shift their earnings into non-taxed benefits (or benefits taxed at lower rates).  The net effect will be a drain on the economy, by giving incentives to productive individuals not to produce (not to mention on small businesses which happen not to be corporations and are taxed using income tax rates).

Steven Horwitz On Responses To Natural Disasters

Via The Austrian Economists, which includes some good comments.

Steven Horwitz was interviewed regarding the differences in responses to natural disasters in different organizations.  It’s a very interesting discussion in which he notes that Wal-Mart, with a rather decentralized organization structure and profit-oriented mission, did a great job, and notes cases in which store managers broke into their own property to provide emergency goods to people who needed them, and one store manager whose store was heavily damaged and decided to cart out whatever she could and give it away.  As Horwitz notes, just think about the number of lifetime customers that store got by providing relief while FEMA struggled.

Meanwhile, Horwitz makes the same point that James Q. Wilson made in his book, Bureaucracy.  The bureaucracies which can work are those with specific missions and definable goals, as well as measurable outcomes (including on the individual level).  Horwitz probably would add in a note about decentralization being important for a well-functioning bureaucracy—he does praise the Coast Guard for precisely that—but his discussion sounds quite like what Wilson would point out.

Notes Of Curmudgeonliness

When Will It End?

$410 billion more down the drain, at least until “moderates” in the Senate wither it down to a bare-bones $409 billion and then Congress tacks on another $100 billion in committee. Surprisingly (at least to me), Heath Shuler voted yes on this.  Sadly, part of this bill involves de-funding the Washington DC school choice program.  Isn’t that supposed to be one of the things that Obama’s supposedly pragmatic about?  What’s the likelihood of him actually doing something against this?  Yeah, that’s what I figured…

Various Economic Notes

  • “You’ve all won tax liability!” The Taxpayers Clearinghouse is so absurd that it could only happen in reality.  Throwing the money at Tim Geithner—“You’re going to take it from us anyways”—was inspired.
  • Brazil is challenging the “Buy American” provisions in the “stimulus” bill. In other words, a stupid provision has the potential to go Smoot-Hawley on us.  Good job totally re-creating the 1930s, guys.
  • Arnold Kling argues that we—well, that Congress and the executive—have mis-placed priorities when it comes to “stimulus.”
  • TARP (i.e., Corporate Welfare For Banks, Part 1)  isn’t even sending money to banks—it’s going to holding companies.  And these holding companies aren’t putting the money back into banks to loan, in part because of uncertainty (not at all helped by the “new day, new policy” antics at the Fed and Treasury) and in part because the bundling insurance companies aren’t going to buy new mortgage and loan packages until they know what kind of shape they’re in.  Let them fail—it’s the only way to get good information on who’s solid and who’s not.
  • Democrats remain fiscal hawks about defense spending. It’s just a shame that defense spending (even including operations in Iraq and Afghanistan) is about 15% of the federal budget and entitlement spending already takes up twice as much and is going to expand.  I’ve got a compromise for Barney Frank, who is apparently so interested in “fiscal sanity:”  instead of cutting defense, let’s kill the omnibus spending bill being debated in Congress.  That bill, at $410 billion, would be much more than the cuts that anybody could make at Defense without disbanding the military.  If that’s not enough, there’s about $1 trillion that just passed that we could get cut, not to mention dismantling the plans for TARP 2:  Electric Boogaloo.  And that’s before getting drastic and actually cutting existing programs.
  • Via Samizdata, here is TARP in pictures.  To make it realistic, they need a few more rounds…
  • Here is a potential way of pricing illiquid assets.
  • Bobby Jindal has rejected about $100 million in bailout funds because it would require additional state governmental expenditures after the temporary funds run out.  Tennessee’s Governor, Phil Breseden (a Democrat), is looking at doing the same.
  • Ireland’s governmental debt has blown up and they may default.  One thing Heritage points out that a lot of people have missed is that the US isn’t the only country running major budget deficits, and with all of these governments looking for additional funds, interest rates are going to go up, especially if national credit ratings become tarnished.  The fact that the US is adding trillions of debt (and not even counting long-term debt in Social Security and Medicare) means that the Global Debt Bubble is coming.
  • Over at Political Calculations, there is a discussion of chaos in markets and what this actually means.  It’s not nearly as, well, chaotic as you would first think.
  • Pity those with $800,000 houses that are only worth $675,000 now.  But here’s the problem that I see:  it doesn’t matter what your mortgage value is as long as your employment circumstances haven’t changed.  She presumably had that $800,000 mortgage two years ago, and as long as they get the same income, the fact that the house value dropped doesn’t change income.  It’s the same thing when you lease a car:  you lease at full value, but as soon as you drive the car off the lot, the value drops.  This doesn’t mean that you’ve really increased your probability of not paying off that lease, though, as your ability to pay is independent of the value of that asset (except in the case that you need to re-sell the asset to pay off the lease, and in this case, you shouldn’t have gotten the lease to begin with).
  • Poor AIG, they need yet another bailout. Let them fail already.  If they need regular injections of hundreds of billions of dollars, their shareholders and management deserve to lose their money.  You can bet that if they survive, AIG isn’t going to be sending me thousands of dollars if I run into financial troubles, so why am I doing that for them?
  • Miners mine, carpenters hammer, and Europeans regulate.  Because if Basel I was part of the problem and if Basel II is so convoluted that it isn’t even in place yet (after 4 1/2 years), let’s just have politicians throw together some quick regulations—how could that possibly go wrong?

It’s Never As Put Together As It Seems

Political conspiracy theories fail because politicians are clueless.  This is not meant in a pejorative sense (for once); rather, the fact that the left hand doesn’t know what the right hand is doing is a great summation of Hayek’s information problem.  For Hayek, decentralized decision-making via certain institutions (such as markets) allows individuals to make the best use of their own personal stocks of information.  Politics, however, is about command from the top, but the people at the top don’t have all of that specialized information.  They don’t even necessarily have the same summaries, and they certainly don’t have a full grasp of political causality.

Sebelius At HHS?

Kathleen Sebelius may be Obama’s choice for Secretary of Health and Human Services.

After putting the state of Kansas into fiscal trouble (in part by screwing up their Medicaid system) and trying to get their legislature to violate the state constitution, I guess it’s time for her to move up.  The only thing stopping her from getting an Obama cabinet consideration might be if she accidentally paid taxes at some point in her past.