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Peter Crabb: Elasticity a useful concept for taxes

Peter R. Crabb
Peter R. Crabb

We forgot to have a party. Or maybe I just wasn’t invited.

One hundred years ago this month, the United States income tax came into being. On Oct. 3, 1913, President Woodrow Wilson signed into law the federal income tax after the 16th Amendment to the Constitution had been ratified by the states.

Our state income tax came about in 1931. The Idaho State Tax Commission was established to administer a new tax “intended to offset property taxes levied for state purposes.”

Both laws have certainly grown larger over time, but determining the effect on the economy depends on how the labor market is viewed.

To study the benefits and costs of taxes such as income or sales taxes, economists use the basic model of supply and demand. In this model a tax on any good or service reduces the welfare, or well-being, of the buyers and sellers in the market. The quantity sold and produced in the market is therefore lower than it would be otherwise, but the government raises revenue on the remaining quantity with the hope that such funds are used for the benefit of everyone.

The federal income tax, the Social Security tax and other payroll taxes are taxes on labor earnings. In the economic model, the income tax is a tax on the supply of labor. That is, we are taxed based on what we are willing to supply in terms of our labor services.

Any labor tax places what economists call “a tax wedge” between the wage the firm pays and the wage that workers receive. Absent the tax, what the firm pays would be exactly what the worker receives.

Using supply and demand analysis, we find that welfare or well-being in the labor market declines the more we raise taxes on working. The decline in well-being on both the buyers’ side (employers) and the producers’ side (workers or wage earners) is called the deadweight loss of the tax.

Taxes have deadweight losses because they reduce consumption and production. As behavior changes after tax implementation, the overall size of the market shrinks below its optimal output level.

How much below depends on another economic concept known as elasticity. The price elasticity of demand or supply is an economic measure of the responsiveness of the quantity in the market to a change in its price. It’s clear that taxes raise prices — the cost of buying and selling. The quantity demanded and quantity supplied respond accordingly.

Larger elasticities imply larger deadweight losses. The overall effect on society of an income tax, or any other tax for that matter, depends on whether or not demand and supply in the particular market are elastic.

In the labor market, the size of the deadweight loss depends on the elasticity of labor supply and demand, and there is disagreement about the magnitude of the elasticity of supply. Some economists argue that income and payroll taxes have only a small distorting effect on the economy because the labor supply is seen as fairly inelastic.

Others argue that all labor taxes lead to large deadweight losses because labor supply is responsive, or more elastic. Under this argument, more people would be working and earning a wage if we didn’t tax income.

The argument over labor supply elasticity says nothing about the burden of paying income taxes. The administrative burden of a tax (filing forms, sending payments, record keeping, etc.) is another measure of how well a tax is working. Many economists support sales taxes over income taxes because the latter is too cumbersome and costly to administer.

So perhaps I didn’t miss the party. No one is celebrating the 100th anniversary of the income tax.