# Even in Principle, Figuring Out a Fair Tax System is Hard

How does one set up a system such that everyone pays their fair share of taxes?  Let us suppose that a “fair” tax is one where everyone gives up the same share of utility to pay for public goods.  One could formulate this such that

U(X(L)-L-t)/U(X(L)-L) = K

The idea is that the fraction of utility one keeps after taxes is the same for everyone.  X is consumption; the amount one gets to consume is a function of effort, L.  To make things easy, we will assume people consumer their incomes, so that income and consumption are the same. Assume that utility function has the shape U’ > 0 and U” < 0.  K is dependent on how much society wishes to spend on public goods.

Just this simple formulation presents three problems.  First, the fair rate of progressivity will be a function of the magnitude of U”.  For instance, if we assume log utility, U’ = 1/(X-L) = U” = -1/(X-L)^2.  This means U” gets very small very rapidly, which also means that the need to increase marginal tax rates in income to maintain the above definition of fairness gets quite small.  We do know that taking money away from people at or below subsistence levels of income will lead to substantial diminution of utility, but beyond that point it is hard to say how sharply progressive taxes need to be in order to be fair.

Second, the correspondence between consumption and effort is not one-to-one.  If the correlation between consumption and effort is less than one–and I will go out on a limb and say that it certainly is–taxing income actually only approximates taxing utility.  The lower the correlation, the worse the approximation.

Finally, defining effort is a problem.  As Matthew Yglesias notes, NYU professors make a lot less money than Wall Street bankers, but their life might well be better.  Perhaps I am wrong, but it seems to me that the -L in a steel worker, coal miner, or line worker is a lot bigger than mine, and so looking at income alone is adequate for approximating utility.

So what to do?  Here is why, despite my liberal leanings, I find a flat tax with a large exemption and a large earned income tax credit appealing.  The rate would have to be sufficient to raise revenue, and would apply  equally to all type of income.  Deductions would be limited.  Such a set up would assure that Warren Buffett would pay no less a share of his income than anyone else.  Bob Hall proposed a similar plan 15 years ago.  I would dress it up with the earned income tax credit.

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About Richard K. Green

Affiliation: University of Southern California

Richard K. Green, Ph.D., is the Director of the USC Lusk Center for Real Estate. He holds the Lusk Chair in Real Estate and is Professor in the School of Policy, Planning, and Development and the Marshall School of Business at the University of Southern California.

Prior to joining the USC faculty, Dr. Green spent four years as the Oliver T. Carr, Jr., Chair of Real Estate Finance at The George Washington University School of Business. He was Director of the Center for Washington Area Studies and the Center for Real Estate and Urban Studies at that institution. Dr. Green also taught real estate finance and economics courses for 12 years at the University of Wisconsin-Madison, where he was Wangard Faculty Scholar and Chair of Real Estate and Urban Land Economics. He also has been principal economist and director of financial strategy and policy analysis at Freddie Mac.

His research addresses housing markets, housing policy, tax policy, transportation, mortgage finance and urban growth. He is a member of two academic journal editorial boards, and a reviewer for several others.

His work is published in a number of journals including the American Economic Review, Journal of Economic Perspectives, Journal of Real Estate Finance and Economics, Journal of Urban Economics, Land Economics, Regional Science and Urban Economics, Real Estate Economics, Housing Policy Debate, Journal of Housing Economics, and Urban Studies.

His book with Stephen Malpezzi, A Primer on U.S. Housing Markets and Housing Policy, is used at universities throughout the country. His work has been cited or he has been quoted in the New York Times, The Wall Street Journal, The Washington Post, the Christian Science Monitor, the Los Angeles Times, Newsweek and the Economist, as well as other outlets.

Dr. Green earned his Ph.D. and M.S. in economics from the University of Wisconsin-Madison. He earned his A.B. in economics from Harvard University.

#### 1 Comment on Even in Principle, Figuring Out a Fair Tax System is Hard

1. Keith Whitcomb

How does one set up a system such that everyone pays their fair share of taxes? It is simple, it is called the Fair Tax. It eliminates 95% of the tax code and replaces it with a national retail sales tax.

Forget about how much society wishes to spend on public goods. The government is spending is completely out of control at \$6.85 million per minute. It is unsustainable and spending is the other side of the coin and a completely different converssation.

According to our laws anytime you want to fiddle with the tax code it must be “staticlly scored revenue neutral” and the people behind the Fair Tax paid 22 million dollars to figure that a 23% rate will bring in the same amount of money that the government collects.

Let’s focus first on just the Dynamic scoring that cannot be counted be counted in that equation.

1. Our country has chased 14 trillion dollars worth of buisness and investment. How much would come back if our corporate tax rate went from the 2nd highest in the world to ZERO? All the money that returns is an example of dynamic scoring and cannnot be counted under the required “staticlly scored revenue neutral” law. How many jobs would be created if only a protion of that returned? Too bad, can’t count it

2. What is the hidden economy? Drugs, Gambling, Prostitution, under the table jobs, and unreported income. The hidden economy is estimated to be somewhere between 1.5 and 3 trillion dollars every year and is untaxed. Under the Fair Tax anytime any of that money visits a cash register we have tax revenue. Another great example of Dynamic scoring and cannot be counted.

3. We have between 12 and 20 million people in this country under questionable immigration status. Guess what? With a national retail sales tax, everyone who visit our country legally or otherwise are taxpayers when they buy a new good or service under the Fair Tax.

Our current system is broken and the Fair Tax would put money in the hands of consumers and prime the pump to grow the economy. TARP funding to the tune of 7.8 trillion dollars failed to grow the economy. Government defecit spending to the tune of 4 trillion dollars failed to grow the economy.

The Fair Tax would allow every worker across the country keep 100% of their paycheck. That is 80 billion dollars every month in the hands of people with a job AKA a consumer. For every dollar confiscated from an employees check before they get to sign the back a matching amount is “contributed” to the government by their employer. Under the Fair Tax the only time the government collects a tax is by the final consumer at the cash register. So employers across the country would have an additional 80 billion dollars every month in their hands so they don’t have to lay off more workers. They might actually have some capital to grow their business.

If you think the IRS is legitimite. Follow this link and learn why the government cannot even ask you to fill out a 1040 form.
http://www.givemeliberty.org/rtp2/updates/update2006-06-09.htm

Our system is broken. Remember the 16th ammendment was an 18 page document to create a 6 1/2% FLAT TAX at a time when it was a commonly understood fact that wages were not considered income. Since then have gone back and fiddled with the tax code 20,000 times and it is now well over 68,000 pages. How is the flat tax working for you so far?

We have 537 elected officials in Washington D.C. and we have well over 13,000 lobbyists to keep them well bribed. We have some of the best politicians that money can buy. If you want real reform don’t look for leadership from our politicians.

Dare to be fair support the Fair Tax.

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