Question

. After seeing the result (from question 2), Cal decided to lower his price once again to $2.729 per gallon. Once again, volume sold increases and settles at 4,800 gallons per day. He is worried that any further price cut will cause the discount station across the street to also lower its price. What is the price elasticity of demand? Can the demand be characterized as price elastic, price inelastic, or neither? By how much did revenues increase or decrease as a result of the change in price? By how much did profits increase or decline

Answer 1

Price Elasticity of demand

Initial price=2.739 per gallon
Volume= 4400 gallons per day.

New price=2.729
Volume=4800 gallons

Price elasticity of demand is given by= %change in demand/%change in price

In our case, %change in demand= 4800-4400/4400=400/4400=1/11=9.1%

%change in price= 2.729-2.739/2.739=-.365%

Hence, price elasticity of demand= -9.1/.365=-24.93

Characteristic of demand-

The demand is highly elastic. A demand is elastic when increase in the demand is higher (lower) when the price lowers (increases) by a given amount. Which means an elasticity higher than 1 shows elastic demand. In our case its almost 25 (which means demand rises by 25% if the price drops by 1%) and hence, highly elastic demand.

Change in Revenue-

Revenue= Price*demand

Earlier revenue= 2.739*4400=$12051.6
New revenue=2.729*4800=$13099.2

Increase in revenue=13099.2-12051.6=$1047.6

Change in Profit-

Variable cost is given as $2.649 per gallon. Fixed cost is $250.

Total cost for 4400 gallon= 2.649*4400+250=11905.6

Total cost for 4800 gallon= 2.649*4800+250=12965.2

Profit at 4400 gallon=Revenue-Cost=12051.6-11905.6=$146

Profit at 4800 gallon=13099.2-12965.2=$134

The profits decreased by $12.