Question

Harry and Garry are twin brothers, and they each own appliance stores. Harry lives in Charleston, South Carolina and Garry lives in Gainesville, Florida. Even though they live far apart, they talk often, and trade hints and grievances about the appliance retail business. Lately, they have been discussing the fact that in a tough economy consumers often hold off on the upgrade of an appliance as long as possible, deciding that they will wait to "trade up" when economy turns around or the appliance breaks, whichever comes first. The brothers are discussing the wisdom of instituting short-term rebates in order to make their appliances more attractive to consumers, and to increase their rather dismal recent sales figures. Unbeknownst to each other, both Harry and Garry decide to institute a retail-level rebate on a specific high-end stove. The prices of the stove are $800 and $1,000 in Harry’s and Garry’s store, respectively. Both Harry and Garry’s rebate offers will be advertised in the Sunday paper, and will last one week. Neither Harry nor Garry has done the research necessary to discover the Just Noticeable Difference (which, for the target market and that product category in that economic climate, is 15%). Harry offers consumers a $100 rebate on the $800 stove. Garry offers consumers a $180 rebate on the $1,000 stove. Harry sells 20 stoves during the rebate period, which is about the same number that he sold the week just prior to the rebate offer. Garry sells 30 stoves during the rebate period, which is an increase of about 10 more than he sold the week just prior to the rebate offer.

Required:
a. Did the fact that he didn’t know the accurate Just Noticeable Difference cost Harry any Money
b. Did the fact that he didn’t know the accurate Just Noticeable Difference cost Garry any Money

Answer 1

a. Noticeable difference is 15%

Step-by-step explanation:

Just noticeable difference is 15% which is calculated as :

Original price of the stove $1,000 *15% = $150

The rebate amount should be $150 or more in order to be effective.

The demand equation for the stove is

P = a - bQ

For Harry

P = $700 and Q = 20

b = change in price / Change in quantity

a = P + bQ

a = 900 + 100 * 20

a = 2,900

This is the point where demand will be zero.

For Garry

P = $820 and Q = 30

b = change in price / Change in quantity

a = P + bQ

a = 820 + 82 * 10

a = 1,640

This is the point where demand will be zero.