Question

The weekly sales of Honolulu Red Oranges is given by

q = 860 − 20p.
where q is the number of oranges sold at the price p dollars per orange. Find E(p)
E(p) =


Calculate the price elasticity of demand when the price is $38 per orange (yes, $38 per orange†). HINT [See Example 1.]


Interpret your answer.
The demand is going by % per 1% increase in price at that price level.

Use the elasticity to calculate the price that gives a maximum weekly revenue.
dollars per orange

Find this maximum revenue.
dollars of revenue

Answer 1

Answer: See Explanation

Explanation:

The price elasticity of demand will be calculated as:

q = 860 − 20p.

dq/do = -20

p = 38

Elasticity E(p) = (p/q) × dq/dp

= [38 /(860 - 20p)] × (20)

=38 × 20/(860 - 760)

= 7.6

Therefore, the price elasticity of demand when the price is $38 per orange is 7.6

Revenue = price × quantity

= p × q

= p × (860 − 20p)

= 860p - 20p²

Differentiating with respect to p

= 860 - 40p

40p = 860

p = 860/40

p = 21.50

Maximum Revenue = 860p - 20p²

= 860(21.50) - 20(21.50)²

= 18490 - 9245

= 9245