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Calculating Demand

1. The following function describes the demand condition for a company that makes caps featuring names of college and professional teams in a variety of sports.
Q = 2,000 - 100P
where Q is cap sales and P is price.
a. How many caps could be sold at #13 each?
b. What should the price be in order for the company to sell 1,000 caps?
c. At what price would cap sales equal zero?
d. Show on graph.

2. The Teenager Company makes and sells skateboards at an average price of $70 each. During the past year, they sold 4,000 of these skateboards. The company believes that the price elasticity for this product is about -2.5.
a. If it decreases the price to $63, what should be the quantity sold?
b. Will revenue increase? Why?
c. Show on graph.

Solution Preview

1. Q = 2,000 - 100P

a) Q = 2,000 - 100(13)
Q = 2,000 - 1300
Q = 700
700 caps could be sold at a price of $13 each cap.

b) 1000 = 2,000 - 100P
100P = 2,000 - 1000
100P = 1,000
P = 10
To sell 1,000 caps, the price would have to be $10 each cap.

c) 0 = 2,000 - 100P
100P = 2,000
P = 20
If the price were $20 each cap, then no sales would be generated.

d) Please see graph attached on the excel ...

Solution Summary

The solution shows how to derive the demand equation, using price elasticity and the inverse slope. Additionally, these formulas can be rearranged to calculate other points of interest. This question also looks at the effect of changing quantity or price on the resulting price or quantity from the demand equation given or derived. Two excel graphs also support both questions.