2. Suppose you are managing a bookstore. When the price of the latest Dan Brown

Question

2. Suppose you are managing a bookstore. When the price of the latest Dan Brown novel is $20 you can sell 100 copies a month. The estimated elasticity of demand for Dan Brown novels is |-0.5|.

a) Is demand for Dan Brown novels elastic or inelastic?

b) Suppose you want to sell 120 copies next month. By what percent should you change the price to sell 120 copies?

c) Suppose instead you decide to increase to the price to $28. What percent change in Dan Brown novel sales do you expect from this price change?

d) If you wanted to maximize your revenues, should you charge $20, $28, or the price from (b)?

Explanation / Answer

The elasticity of demand for Dan Brown Novels is inelastic and less than 1. This means that 1% change in price of Dan Brown novels will lead to 0.5 percent change in the quantity demanded of Dan Brown Novels.

Ed = % Change in Qty Demanded/% Change in Price

or P1 and P2 are original price and new price respectively similarly for Q1 and Q2 for original and new quantity demanded

= (Q1-Q2)/Q1/(P1-P2)/P1

= (Q1-Q2)/(P1-P2)*(P1/Q1)

-0.5 =(100-120)/(20-P2)*(20/100)

20/0.5 = 100-5P2

40 = 100-5P2

5P2 = 60

P2 = 12 The price should fall by $8

P changes from 20 to 28

% Change in price = (28/20-1)*100 = 40%

Ed = % Change in Qty dd/% Change in Price

0.5 = % Change in Qty dd/40

% Change in Qty dd = 40*0.5 = 20%

0.20*100 = 20 so the demand fior novels will now fall to 80 units

The price charged should be 28 as it raises the revenue.

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