The weekly sales of Honolulu Red Oranges is given by q = 1116 − 18p.

Question

The weekly sales of Honolulu Red Oranges is given by q = 1116 − 18p.

 Calculate the price elasticity of demand when the price is $31 per orange (yes, $31 per orange†).

 ___

Interpret your answer.

The demand is going  ? up down by  % per 1% increase in price at that price level.

Also, calculate the price that gives a maximum weekly revenue.

$ ___

Find this maximum revenue.

$____

Answer 1

PRICE ELASTICITY OF DEMAND

(% CHANGE IN QUANTITY DEMANDED) / (1% CHANGE IN PRICE)

or (dQ / Q) / (dP /P) as framed in calculus.

A 1% change in price (dP/P) = 0.01

At p = 31, the 1% change is (.01)(31) = 0.31 = dP/P

p goes from 31.00 to 31.31.

Demand is q = 1116 - 18p

At p = 31, q = 1116 - 18(31) = 558

At p = 31.31, a 1% price increase,

q = 1116 - 18(31.31) = 552.42

This is a change of dq = 552.42 - 558 = -5.58

The mean q between these two prices was about 555,

so the change in q divided by that mean q is -5.58/555= -0.010 or 1.01%

(keeping the second decimal place to make it easier to follow what is next)

The price change was set at 1%, so the elasticity is - 0.0101/0.01 = 1.01

and the 1.01% percentage decrease change in demand matches the 1% percentage price change.

The weekly revenue from this model is

R = (q)(p) = (1116 - 18p)(p)

You can graph R vs. p to find an approximate maximum.

You can tabulate R vs. p in the vicinity of p = 31 to find an approximate maximum.

When you study calculus, you will get the maximum R by setting

the slope of the R vs p function to

dR/dp = 0

1116-36 p = 0

p = 1116/36 = 31

and that may even be how the price was set.