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).