ABC Sports, a store that sells various types of sports clothing and other sports

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= 2,000-100 P 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? d. What price would no caps be sold? e. Calculate the point price elasticity of demand at a price of $6.

Explanation / Answer

1- at price of 6 , Q = 2000-600 = 1400

2- at Q = 1800, P = 2000-1800/100 = 2

3- now if caps have to be used as promotion than the max caps given is where the total revenue is zero,

so (20-0.01Q)(Q) = TR

SO THIS IS ZERO WHERE Q = 2000 so 2000 caps can be given as promotion

4- now if Q = 0

then p = 20, so at price of 20 no caps are sold.

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