Now consider the effect of introducing a tax on this casino game. The most common form of tax applied to casino games defines the tax base as the adjusted gross receipts (AGR) of the game. Tax revenue T generated by the tax determined by the product of the nominal marginal tax rate t and the tax base AGR: T = tAGR. Recognizing that the tax base AGR is the product of the handle and the takeout rate, AGR = wH, we can write the tax revenue as, T = twH. This expression reveals that the effective marginal tax rate applied to the handle is tw, the product of the nominal tax rate t and the takeout rate w. The higher the takeout rate the larger the effective tax rate.
The supply curve shifts upward in a non-parallel manner. The reason for the nonparallel shift is due to the form of the tax. The tax revenue T is obtained by multiplying the marginal tax rate t times the AGR: T = tAGR. Because the AGR is the product of the handle and the takeout rate, AGR = wH, we can rewrite the tax as T = twH. This expression indicates that the marginal tax rate applied to the handle H is ∂T ∂H = tw. Julie Smith (1999) and Jim Johnson (1985) identify three potential measures of the effective tax rate, depending on the definition of the tax base that is used in the computation. A tax is applied to the casino’s AGR, but we can analyze the market effects in terms of the handle H. The tax shifts the supply curve upward as indicated and results in a higher equilibrium takeout rate w1 and lower equilibrium handle H1.
A tax of tw on handle H1 raises the price paid by gamblers from w0 to w1 and lowers the price received by the casino from the original takeout rate w0 to the new rate w1(1 − t). Revenue generated by the tax is tw1H1. Of that amount, the gamblers bear a tax burden of (w1 − w0)H1 while the casino bears the remaining burden of [(w0 −w1(1−t)]H1. The incidence of the tax can be analyzed in terms of the changes in takeout rate w and handle H.
The tax shifts the supply curve upward as illustrated, resulting in a higher equilibrium price for the casino game w1 and a smaller equilibrium quantity H1. The tax raises the price paid by gamblers from w0 to w1 and lowers the price that the casino receives from w0 to (1 − t)w1. The tax generates revenue of tw1H1, of which the gambler bears the burden (w1 − w0)H1 and the casino bears the burden 22 casinos [(w0 − w1)(1 − t)]H1.
As is typical of tax incidence analysis, the tax has a statutory incidence falling entirely on the casino, but market forces result in economic incidence that differs from that. As usual, the economic agent with the less elastic behavior bears the greater share of the economic incidence of the tax. A regulatory environment that limits the supply of casino games causes the elasticity of supply to be relatively inelastic in relation to the elasticity of demand, thereby causing the incidence of the casino game tax to fall primarily on the casino.
In fact, if the government jurisdiction has legal limits on the number of casinos, slot machines, or table games, then as those limits are reached the supply curve turns vertical. In the extreme with a vertical supply curve, the incidence of the tax falls entirely on the casino. With the proliferation of gaming opportunities in recent years, however, the supply curve is becoming increasingly elastic.