The Optimal Distribution of Income
We don’t need fancy equations to analyze the optimal distribution of income. We simply divide income into earned income from wages and unearned income from economic land rent.
March 31, 2018
Fred Foldvary, Ph.D.

The inequality of wealth has become a big political issue. The distribution of income was a major topic of classical economics, and there has been an upsurge of interest in inequality by economists, religious leaders, and protesters. We can begin our inquiry of inequality with an article by Ray C. Fair, ""The Optimal Distribution of Income," published in the Quarterly Journal of Economics, November 1971.

Karl Marx wrote that income should be distributed according to needs, and indeed that is how income is typically distributed within families. "Needs" are goods without which one suffers illness and death. Parents are usually able to judge the needs of their children, and family members can communicate their needs, but for the greater society, the distribution of desires is unknown, and even if charity or governments provide medicine, food, and shelter for those in need, that does not address the general distribution of income for consumption beyond basic needs.

When they examine income, economists usually use a lifetime distribution, since income is lower on retirement, but that is not a problem if the individual has savings or a pension. There is some choice in a worker’s wages, since a person may choose how much leisure to indulge in, versus time spent in labor that is assumed to have disutility, i.e. most people would prefer more leisure if they did not need the income. Workers also have a choice of how much and what type of education they will obtain. Fair calculates that a 4-year college education requires 7680 hours, and even if tuition is free, a cost of education is the wage given up.

Workers of course have no choice about their innate abilities, with how much talent, strength, and intelligence they were born with. Fair assumes that innate ability is normally distributed, i.e. a bell-shaped curve called "Gaussian." In the model by Fair, government can choose the minimum guaranteed income and the tax rate on income, as individuals maximize their utility or well-being based on after-tax income. Fair calculates that a worker has a maximum of 300,000 lifetime working hours, assuming 8 hours of sleep and labor from age 18 to 70. At $20 per hour after taxes and half of one’s waking time engaging in leisure, a worker could earn a total of $3 million, not counting interest income from saved wages.

Since persons with greater ability also tend to obtain more education and to work more hours, Fair states that "With respect to maximizing social welfare, the best policy the government could follow would be to assign lump sum grants or taxes to individuals." A fixed amount of tax would avoid the disincentive to work that is caused by taxes on wages or on spending from wages. The disincentive of today’s taxes results in more leisure relative to labor and production, less investment in education, and also a greater reliance on student loans versus working part-time. If individuals freely choose more leisure, that is good, but the current system pushes productive people out of the labor pool, who would rather be employed.

With no taxes, or only lump-sum taxes, and no income other than wages, an equal distribution of utility would require a redistribution of income from those with higher innate ability to those with less, to equalize the wages due to talent, since the rest of the income inequality would be based on the worker’s choice of leisure and education. Fair concludes that the optimal inequality would be substantially less than that which actually exists.

Fair admits that his model does not include income from financial wealth, i.e. interest, rent, and gains in asset values. His model is based on the assumption that every person begins with zero wealth, which implies a complete inheritance tax. His model also assumes no income from savings. It is typical of academic studies of inequality that inherited land values are omitted, even though such unearned income is at the heart of the inequality problem.

However, Fair’s model can be rescued from irrelevance by noting that the model implies that land rent income is completely taxed or equalized. Fair’s lump-sum tax is equivalent to a continuous tax on all the land rent, since a tax on a plot of land is a fixed cost to the taxpayer.

We don’t need fancy equations to analyze the optimal distribution of income. We simply divide income into earned income from wages (including income from savings that originates in wages) and unearned income from economic land rent, the potential rent when land is put to its most productive use, which includes the benefit of leaving some land wild.

Since talent is connected to education and labor, optimal productivity is obtained with no taxes on earned income, as that allows individuals to maximize utility based on their preference for leisure versus goods. Ethical optimality is achieved by an equal distribution of unearned income, either in cash or in wanted goods, since the ethics of natural moral law presumes human equality. The equalization of unearned income implies also the prevention of, or compensation paid for, environmental damage.

Optimal income implies that there be no inheritance tax. There is no inherited land value if all the economic land rent is distributed equally. Moreover, if a worker chooses to give some of his wage to children and other heirs, the maximization of his utility implies that this choice not be impeded. Inherited wealth from wages may add to inequality but it also generates optimal production, as the decision to work and invest depends also on whether parents can benefit their children and charities.

In conclusion, the optimal distribution of income requires the equalization of the benefits from land, and the absence of any tax or arbitrary restriction on labor. Whatever distribution results from that is inherently both equitable and efficient.

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Fred Foldvary, Ph.D.

FRED E. FOLDVARY, Ph.D., (May 11, 1946 — June 5, 2021) was an economist who wrote weekly editorials for since 1997. Foldvary’s commentaries are well respected for their currency, sound logic, wit, and consistent devotion to human freedom. He received his B.A. in economics from the University of California at Berkeley, and his M.A. and Ph.D. in economics from George Mason University. He taught economics at Virginia Tech, John F. Kennedy University, Santa Clara University, and San Jose State University.

Foldvary is the author of The Soul of LibertyPublic Goods and Private Communities, and Dictionary of Free Market Economics. He edited and contributed to Beyond Neoclassical Economics and, with Dan Klein, The Half-Life of Policy Rationales. Foldvary’s areas of research included public finance, governance, ethical philosophy, and land economics.

Foldvary is notably known for going on record in the American Journal of Economics and Sociology in 1997 to predict the exact timing of the 2008 economic depression—eleven years before the event occurred. He was able to do so due to his extensive knowledge of the real-estate cycle.