You have been hired as a marketing consultant to Big Book Publishing, Inc., and

Question

You have been hired as a marketing consultant to Big Book Publishing, Inc., and you have been approached to determine the best selling price for the hit calculus text by Whiner and Istanbul entitled Fun with Derivatives. You decide to make life easy and assume that the demand equation for Fun with Derivatives has the linear form q = mp + b, where p is the price per book, q is the demand in annual sales, and m and b are certain constants you must determine.

(a) Your market studies reveal the following sales figures: when the price is set at $55.00 per book, the sales amount to 10,000 per year; when the price is set at $79.00 per book, the sales drop to 1000 per year. Use these data to calculate the demand equation.

b) Now estimate the unit price that maximizes annual revenue.

C)Predict what Big Book Publishing, Inc.'s annual revenue will be at that price.

Explanation / Answer

a)
q = mp + b
10000 = m*55 + b ...eqn 1
1000 = m*79 + b ...eqn 2

subtract eqn 1 from eqn 2
1000 - 10000 = (79-55)*m
m= -375

put this in eqn 1
10000 = (-375)*55 + b
b= 30625

so,
q = mp + b
q = -375p + 30625

b)
revenue,
R = q*p
= (-375p + 30625)*p
= -375*p^2 + 30625p

dR/dp = -750*p + 30625
put dR/dp = 0
-750*p + 30625 = 0
p = $40.83

when p<40.83 dR/dp is positive
when p<>40.83 dR/dp is negative
so, p = 40.83 maximises Revenue R
Answer: $40.83

c)
R = -375*p^2 + 30625p
=-375*(40.83)^2 + 30625*(40.83)
= $625260
Answer: $625260

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