ABC Sports, a store that sells various types of sports clothing and other sports
ID: 2356464 • Letter: A
Question
ABC Sports, a store that sells various types of sports clothing and other sports items, is planning to introduce a new design of Arizona Diamondbacks' baseball caps. A consultant has estimated the demand curve to be Q = 2,000 - 100P where Q is cap sales and P is price. a. How many caps could ABC sell at $6 each? b. How much would the price have to be to sell 1,800 caps? c. Suppose ABC were to use the caps as a promotion. How many caps could ABC give away free? 2. Mr. Smith has the following demand equation for a certain product: Q = 30 - 2P. a. At a price of $7, what is the point elasticity? b. Between prices of $5 and $6, what is the arc elasticity? c. If the market is made up of 100 individuals with demand curves identical to Mr. Smith's, what will be the point and arc elasticity for the conditions specified in parts a and b?Explanation / Answer
Q= 2000 -100P a. p=6$ Q = 2000 - 100*6 = 1400 cap sales b. Q = 1800 100P = 2000 -Q = 2000 - 1800 = 200 P = 2$ cap has to sold at 2 $ each 2. Q = 30 - 2P a. dQ/dP = -2 Point elasticity at 7$ = dQ/dP * P/Q = -2*7/16 = -7/8 b. between 5$ and 6$ i.e mid P = 5.5 $ Q(5$) = 20 , Q(6$) = 18 i.e mid Q = 19 Arc elasticity = dQ/dP * mid P/ mid Q = 2 * 19/5.5 = 6.909090