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demand price elasticity for vanity tags

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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 example 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 example, 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 questions 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.]

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Solution Preview

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

Price elasticity of demand is measured as the percentage change in quantity demanded that occurs in response to a percentage change in price. The formula used to calculate the coefficient of price elasticity of demand is
Ed = % change in Q / % change in P
= [(Q2 - Q1) / Q1] / [(P2 - P1) / P1]

in this case, percentage change in quantity is
% dQ = (41-80)/80 = -0.4875
and percentage change in price ...

Solution Summary

This posting gives some price discrimination strategies.