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

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? ( 5 marks)

b) How much would the price have to be to sell 1,800 caps? ( 5 marks)

c) Suppose ABC were to use the caps as a promotion. How many caps could ABC give away free? ( 5 marks)

d) At what price would no caps be sold? ( 5 marks)

e) Calculate the point price elasticity of demand at a price of $6. ( 5 marks)

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Homework Answers

Answer #1

a) How many caps could ABC sell at $6 each?

answer:

1400

explanation:

Q = 2,000 - 100P

Q=2000-100(6)

Q=2000-600

Q=1400.

How much would the price have to be to sell 1,800 caps?

answer

$2.

Explanation:

Q = 2,000 - 100P

1800=2000-100P

100P=2000-1800

100P=200

P=2.

Suppose ABC were to use the caps as a promotion. How many caps could ABC give away free?

2000 quantity.

explanation:

if firms give free price will be zero

Q = 2,000 - 100P

Q=2000-100(0)

Q=2000

d) At what price would no caps be sold?

$20.

explanation:

Q=0

Q = 2,000 - 100P

0=2000-100P

100P=2000

P=2000/100

P=20.

e) Calculate the point price elasticity of demand at a price of $6

if we take price 6 and 2. quantity is 1400 and 1800

price elasticity of demand =[ change i n quantity/ change in price]*[price/quantity]

=[400/4]*[6/1400]

=0.428.

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