Optimal tax

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Optimal tax theory is the study of how best to design a tax to avoid distortion and inefficiency. Other things being equal, if a tax-payer must choose between two mutually exclusive economic projects (say investments) that face the same pre-tax risk and returns, the one with the lower tax or with a tax break would be chosen by the rational actor. With that insight, economists argue that generally taxes distort behavior. For example, since only economic actors who engage in market activity of "entering the labor market" get an income tax liability on their wages, people who are able to consume leisure or engage in household production outside the market by say providing housewife services in lieu of hiring a maid are more lightly taxed. With the "Married filing jointly" tax unit in American income tax law, the second earner's income is placed on top of the first wage earner's taxable income and thus gets the highest marginal rate. This type of tax creates a large distortion disfavoring women from the labor force during years when the couple have great child care needs.

The incidence of sales taxes on commodities also leads to distortion if say food prepared in restaurants are taxed but supermarket bought food prepared at home are not taxed at purchase. If the taxpayer needs to buy food at fast food restaurants because he/she is not wealthy enough to purchase extra leisure time (by working less) he/she pays the tax although a more prosperous person who say enjoys playing at being a home chef is less lightly taxed. This differential taxation of commodities may cause inefficiency (by discouraging work in the market in favor of work in the household).

For optimal commodity sales taxes, Frank P. Ramsey developed a theory. (‘A Contribution to the Theory of Taxation’, The Economic Journal, 37, no. 145, (March 1927), 47-61). The intersection on downward sloping demand curve and upward sloping supply curves implies that there is producer surplus and consumer surplus. Any sales tax reduces output and imposes a dead weight loss (DWL). If we assume nonvarying demand and supply elasticities, then a single uniform rate of tax on all commodities would seem to minimize the sum area of all such DWL triangles. Ramsey proposed that we assume suppliers were all perfectly elastic in their responses to price changes from tax and then concluded that taxes on goods with more inelastic consumer demand response would have smaller DWL distortions. Thus, we would tax MILK more heavily than PAPAYA JUICE if consumers were more inelastic in their demand for cow’s milk. The DWL triangles are now called Harberger triangles (after Arnold Harberger).