Demand price elasticity for vanity tags

In many regions, local governments offer customized automobile license plates, also called "vanity tags." In these programs, a driver can choose to pay an additional fee over and above the basic annual fee charged to register a vehicle and, in return, the driver is allowed to choose the letter and number combination for their automobile license plate.

North Carolina (NC) provides a specific ex of how these programs work. By law, every motor vehicle must be registered with the state and issued a license plate by the Department of Motor Vehicles (DMV). There is a basic annual charge to register/renew a vehicle. The number/letter combination on these plates is issued more or less at random by the DMV. For an added fee, however, a vehicle owner can choose the number/letter combination of their plates; for ex, by paying the added fee an individual can enjoy driving a car with license plates exhibiting highly coveted letter combinations such as "EcoProf."

In recent years, NC experimented with the pricing structure of the vanity tag program. Initially, call it year 1, the price of a vanity tag was 30$ and 80 thousand vanity tags were sold. Then, in year 2, the price was increased to 40$ and 41 thousand vanity tags were purchased.

Your consulting firm has been hired to analyze the results and make recommendations. In answering the problems that follow, you are allowed to make one assumption: the price and quantity observations in year 1 and year 2 correspond to points on the (linear) demand curve for vanity tags.

a. Assess the demand price elasticity for vanity tags. (Use year 1 as the base.)

b. Assess the revenue implications of the year 1 to year 2 price change.

c. Do you recommend further price increases or do you propose price decreases?

d. Offer some price discrimination strategies. [Hint: think of the basic annual fee and also what is observable to the seller.]