Question

Cal Overhaut operates an ExxonMobil gas station franchise in Fitzhugh, MD. The price of gasoline is volatile and varies greatly from day to day. The price per gallon varies based on the seasonal blend of gasoline, which is determined by clean-air requirements, and Cal's pricing choices are limited to the profit margin for his price Base price of unleaded regular delivered in New York harbor (Sept 2018) Added cost to Cal: Maryland state gasoline tax Federal gasoline tax Delivery Advertising to ExxonMobil Additives $0.335 $0.184 $0.090 $0.030 $0.030 He recently raised the price of gas by 1 cent per gallon, and his profit declined. Cal would like you to measure his business gains or losses based on the price of $2.851 per gallon. Total additions Cal competes with a local brand on the opposite corner that typically sells gas for 4 to 5 cents per gallon less than his station. They are currently selling gasoline for $2.851 per gallon. Recently, regular gasoline for delivery in New York harbor sold for $2.729 per gallon. Total cost per gallon 2.729 Answer question 1 below. To the right are additional charges that Cal must pay on each gallon of gasoline 1. Cal sold 3,600 gallons per day at a price of $2.841 per gallon. He raised the price 1 cent to $2.851 per gallon, and revenues and profits dropped. His station sold 3,200 gallons per day at $2.851 per gallon. What is the price elasticity of demand? Can the elasticity be characterized as elastic, inelastic, or neither? What does this mean and why does it matter? Will revenues increase or decrease as a result of the price cut? By how much? Cal tells you that his fixed costs are

Answer 1

(1)

Using midpoint method,

Elasticity of demand = (Change in quantity / Average quantity) / (Change in price / Average price)

= [(3,200 - 3,600) / (3,200 + 3,600)] / [(0.01 / (2.841 + 2.851)]

= (-400 / 6,800) / (0.01 / 5.692)

= -33.48

Since absolute value of elasticity is higher than 1, demand is elastic. It means that if price increases (decreases) by 1%, quantity demanded will decrease (increase) by 33.48%. This information is important for pricing purposes so that managers can decide whether to increase or decrease price in a certain market.

With elastic demand, an increase (decrease) in price will lead to a decrease (increase) in revenue and a decrease (increase) in profit, ceteris paribus.

Revenue (R) = P x Q

After price increases by 1 cent,

% Increase in price = (0.01 / 2.841) x 100 = 0.35%

% Decrease in quantity = [(3,600 - 3,200) / 3,600] x 100 = (400 / 3,600) x 100 = 11.11%

New revenue (R1) = (1.0035 x P) x (0.89 x Q) = 0.892 x (P x Q) = 0.892 x R

Change in revenue = (R1 - R) / R = (0.892R - R) / R = (0.892 - 1) / 1 = -0.108 = -10.8% (Decrease)