Question

Lickety Split sells ice cream cones in a variety of flavours. The following are data for a recent week:

Revenue (1,000 cones at $1.75 each)					$1,750
Cost of ingredients			$640
Rent			500
Store attendant			600		1,740
	Pretax income				$10

The manager estimates that if she were to increase the price of cones from $1.75 to $1.93 each, weekly volume would be cut to 850 cones due to competition from other nearby ice cream shops.

Estimate the profit-maximizing price per cone.

(Round entry to 2 decimal places e.g. 15.25. Round percentage change to 2 decimal places, e.g. 25.25% and elasticity to 3 decimal places, e.g. 1.525 for your calculations.)

Price per cone

$

Answer 1

Per cent change in price = ($1.93 – $1.75)/$1.75 = +10%

Per cent change in demand = (1000 – 850)/1000 = –15%

The elasticity is = ln(1 + per cent change in quantity sold)/ln(1 + per cent change in price)

= ln(1 – 0.15)/ln(1 + 0.1)

= –0.16252/0.09531

= –1.705

Variable cost = $640/1000

Profit-maximising price = [–1.705/(–1.705+1)]*$0.64 = $1.55