THE DEMAND FOR VANITY (PLATES): ELASTICITIES, NET REVENUE MAXIMIZATION, AND DEADWEIGHT LOSS

ERIK D. CRAFT (*) I. INTRODUCTION Each state is a monopolist in the production of personalized license plates, otherwise known as vanity license plates. (1) State policymakers, therefore, must answer the same questions when setting the price of personalized plates as they do when determining income tax rates, excise tax rates, lottery payout rates, and other user fees. How will revenue change as the price (tax rate) is increased? At what price (tax rate) will revenue be maximized? What is the ratio of the marginal excess burden (deadweight loss) to marginal net revenue at a given price (tax rate)? Any state charging a price that exceeds the monopoly price not only causes a socially suboptimal level of consumption but forgoes revenue as well. In the absence of distributional concerns, the marginal dollar of net revenue raised should have the same deadweight or efficiency cost across all revenue sources. The socially efficient price for a personalized license plate is likely below the net revenue-maximizing price, because social surplus is usu ally maximized when products are priced at marginal cost. This article offers answers to the preceding questions and others using a new data set gathered by the Virginia Department of Motor Vehicles on the prevalence of and fees for personalized passenger license plates in 1997. The article also will argue that special background license plates are a complement to vanity license plates and will extend previous conclusions regarding the optimal pricing of vanity license plates. II. PAST RESEARCH Alper et al. (1987) used 1983 data to present the first published estimates of the elasticity of demand for personalized license plates. Their key price variable was the five-year average annualized cost of owning personalized plates, which they used along with other variables to explain the percentage of license plates that were personalized. Elasticity estimates from their analysis ranged from -0.17 for Alaska to -2.64 for Ohio. If the marginal cost of vanity license plates is close to zero, then the net revenue-maximizing elasticity should be near one. Finding only 12 of 44 states with elasticities in the range between 0.75 and 1.24 in absolute value, the authors concluded that "vanity plated are substantially too cheap in some states and substantially too expensive in other" (p. 108). Harrington and Krynski (1989) extended the set of independent variables used by Alper et al. (1987) to explain the purchase of personalized plates. They also corroborate Alper et al. in showing that many states charge price s too high to maximize net revenues. In addition, Harrington and Krynski (1989) analyzed the decision to purchase personalized plates by including both the initial fee and renewal fee in their regressions. They estimated upper-bound estimates of the initial net revenue-maximizing price and concluded that many states were setting the initial fees too high. Previous research proposed that personalized license plates were normal goods. Researchers also assumed that the demand would be higher in states in which both front and back license plates were required, because personalized plates will have greater visibility. A potential bandwagon effect suggested that the longer personalized plates had been available in a state, the greater the demand. The greater the number of potential combinations, as determined by the number of spaces and extra characters available, the higher should be the demand. Though not justified explicitly, the percentage of the population aged 25-44 years was also included in the set of independent variables. One hypothesis is that such persons are more likely to seek to create an identity or attract a mate. Craft and Schmidt (1999) find evidence that relative increases in this demographic group raise the average level of vehicular capital, holding other factors constant. (2) Harrington and Krynski (1989) added the average registration fee and a dummy variable for earmarked funds. …