Q2 Refer to the document in the appendix (Illustration 6.1) (a) How did the author arrive at an elasticity coefficient of (-0.86) (5 points)? (b) Are the Texas consumers sensitive or insensitive to the price of vanity plates? Why (5 Points)? (c) Solve for the number of vanity plates?to the nearest whole number?after the price was reduced to $40 (10 Points). (d) Should the Texas Division of Motor Vehicles have reduced the price? Why (5 Points) ? (e) Using the theory of absolute value for elasticity coefficients, estimate the revenue that could have been derived if the Division of Motor Vehicles had increased the price to $80 instead (10 Points). (f) Compared to the $420,000 loss of revenue, what would have been the mitigating gain (5 Points)? (g) Briefly discuss the Wesleyan doctrine of vanity and how it relates to the Texas market for vanity plates (5 Points).

ILLUSTRATION 6.1 Texas Calculates Price Elasticity were produced. So the move from $25 to $75 was the right move. In addition to its regular license plates, the state of Texas, as do other states, sells personalized or "van- Moreover, let's suppose that the price elasticity be- tween $75 and $40 is approximately equal to the value ity" license plates. To raise additional revenue, the calculated for the movement from $25 to $75 (-0.86). state will sell a vehicle owner a license plate saying We can use this estimate to calculate what happens to whatever the owner wants as long as it uses six letters revenue if the state drops the price to $40. We must (or numbers), no one else has the same license as the first find what the new quantity demanded will be at one requested, and it isn't obscene. For this service, $40. Using the arc elasticity formula and the price the state charges a higher price than the price for stan- dard licenses. Many people are willing to pay the elasticity of -0.86, higher price rather than display a license of the stan- AQ Average P dard form such as 387 BRC. E = X Average Q For example, an ophthalmologist announces his practice with the license MYOPIA. Others tell their 60,000 - Q (75 + 40)/2 75 - 40 X -0.86 personalities with COZY-1 and ALL MAN. A rabid (60,000 + Q)/2 Star Trek fan has BM ME UP. In 1986, Texas increased the price for such plates where Q is the new quantity demanded. Solving this from $25 to $75. The Houston Post (October 19, 1986) equation for Q, the estimated sales are 102,000 (rounded) reported that before the price increase about 150,000 at a price of $40. With this quantity demanded and price, cars in Texas had personalized licenses. After the in- total revenue would be $4,080,000, representing a de- crease in price, only 60,000 people ordered the vanity crease of $420,000 from the revenue at $75 a plate. If the plates. As it turned out, demand was rather inelastic state's objective is to raise revenue by selling vanity over this range. As you can calculate, the price elastic- plates, it should increase rather than decrease price. ity is -0.86. Thus revenue rose after the price increase, This application actually makes two points. First, from $3,750,000 to $4,500,000. even decision makers in organizations that are not run But the Houston Post article quoted the assistant for profit, such as government agencies, should be director of the Texas Division of Motor Vehicles as able to use economic analysis. Second, managers saying, "Since the demand dropped" the state didn't whose firms are in business to make a profit should make money from the higher fees, so the price for make an effort to know (or at least have a good ap- next year's personalized plates will be $40." If the proximation for) the elasticity of demand for the prod- objective of the state is to make money from these li- ucts they sell. Only with this information will they censes and if the numbers in the article are correct, know what price to charge. this is the wrong thing to do. It's hard to see how the state lost money by increasing the price from $25 "It was, of course, quantity demanded that decreased, not to $75-the revenue increased and the cost of demand. Source: Based on Barbara Boughton, "A License for Vanity," producing plates must have decreased since fewer Houston Post, Oct. 19, 1986, pp. 1G, 10G