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The Internet Economy
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SECTION 4:11 THE EFFECT OF A SALES TAX ON PURELY COMPETITIVE EQUILIBRIUM A sales tax differs from a specific tax in that the former collects a fixed percentage of the product price instead of a fixed amount per unit of product. Assume the same initial demand and supply functions as in the previous section. qd = 100 - 2p qs = 3p - 50 but now a sales tax of 5 percent is imposed on the supplier. This means that when the seller receives a price of po - 0.05po. The new supply function is therefore derived by replacing p with p - 0.05p. We then have qs = 3(p - 0.05p) - 50 =3p - 0.15p - 50 =2.85p - 50 The equilibrium market price is found by equating demand and supply functions, which yields 100 - 2p = 2.85p - 50 150 = 4.85p p = $30.93 The 5 percent sales tax thus raises equilibrium price from $30 to $30.93. The supplier, however, must pay the tax on this amount, which is (0.05)(30.93) = $1.55. He thus remains with $30.93 - 1.55 = $29.38, as opposed to the $30 he would keep without the imposition of the sales tax. The supplier therefore pays $0.62 of the tax, while the consumer pays $0.93 of the tax in the form of a higher price. The effects of a sales tax are thus similiar to those for a specific tax. In either case, quantity sold is reduced as a result of the tax. Both taxes are shifted in part to the customer. ILLUSTRATION: Consider the general linear demand and supply function qd = b - ap qs = cp - d where b, d> 0 and a, c > 0 A sales tax of amount h is imposed on the supplier. We then have qd = b - ap qs = c(p - hp) - d = cp - chp - d = (c - ch)p - d Equilibrium is then determined by setting qd = qs , which yields b - ap = (c - ch)p - d b +d = (c + a - ch)p p = b + d / c+ a - ch Comparing this to the equilibrium price without any taxes of p = b + d / c + a we see that equilibrium price increases due to the sales tax. Assume now that a 5 percent sales tax is imposed on the consumer instead of the supplier. The initial demand and supply functions are as: qd = 100 - 2p qs = 3p - 50 As a result of the sales tax, there is a change in the demand function, because at a price of po the product would really cost the consumer po + 0.05po. The new demand function is therefore derived by replacing p with p + 0.05p. This yields qd = 100 - 2( p + 0.05p) = 100 - 2p - 0.10p The equilibrium market price is then found by equating demand and supply functions: 100 - 2p - 0.10p = 3p - 50
5p + 0.10p = 150 5.10p = 150 p = 150 / 5.1 p = $29.41 In addition to the market price of $29.41, the consumer must pay a tax of (0.05)(29.41) = $1.47. The total cost of the product to the consumer is therefore $29.41 + $1.47 = $30.88. Without the imposition of any tax, the equilibrium market price would be $30. Therefore the consumer pays $0.88 of the tax, while the supplier pays the other $0.59 in the form of receiving a lower price. The government thus collects $0.08 less in taxes per unit in this case than when the tax is imposed on the supplier ($1.47 compared to $1.55). The consumer pays $0.05 less ($30.88 compared to $30.93), while the supplier pays $0.03 less ($0.59 compared to $0.62) when the tax is imposed upon the customer. The reason for this result is that when levied on the seller, the tax is a percentage of the full selling price, including the additional amount that the consumer is paying because of the tax. On the other hand, when levied on the customer, the tax is a percentage of the price before taxes. Thus, in the illustration above, the tax when levied on the seller was 5 percent of $30.93, but when levied on the customer it was 5 percent of $29.41. = |