ABC Sports, a store that sells various types of sports clothing and other sports
ID: 2505582 • 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
a. How many caps could ABC sell at $6 each?
Solution: Computation of the No of caps could sold
Equation is
Q = 2,000-100P
Where as
P = $6
Q = 2,000-100P
Q = 2,000-100*6
Q = 1400 Caps
Hence the 1400 caps should be sold
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How much would the price have to be to sell 1,800 caps?
Computation of the Price of the cap
Equation is
Q = 2,000-100P
Where as
Q = 1800
1800 = 2,000-100P
1800 = 2,000-100P
P = 200/100
P=2
Hence the Price is $2
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c. Suppose ABC were to use the caps as a promotion. How many caps could ABC give away free?
Solution: Computation of the Price of the cap
Equation is
Q = 2,000-100P
Where as
P = 0 coz for free there would no price of cap
Q = 2,000-100*0
Q = 2,000-0
Q = 2000