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 060 Added cost to Cal: 0.335 0.184 0.090 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 Maryland state gasoline tax Federal easoline tax 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. Advertising to ExxonMobil Additives Total additions 0.669 To the right are additional charges that Cal must pay on each gallon of gasoline: Total cost per gallon 729 Answer question 1 below 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 $50 per day. By how much did profits decline? (Profits are revenues minus all costs.)

Answer 1

1. PED = percentage change in quantity demanded/percentage change in price

= (400/3600)/(0.01/2.841)

= 31.567

The elasticity of demand is greater than one indicating the good to be price elastic. When there is small change in price, the change in quantity demanded is proportionately larger. Therefore, for a small increase in price will reduce the quantity demanded as well as the revenues and vice versa. Thus, the price maker should be careful while raising the price for elastic goods as this may reduce their profit by reducing the demand for such goods.

Cal raises the price from $2.841 to $2.851. This has reduced the demand from 3600 gallons to 3200 gallons. At price $2.841, the total revenue was $10,227.6. The variable cost was $2.729 per gallon and $9824.4 for 3600 gallons. The fixed cost is given as $50 per day. Thus, the total cost was $9874.4. The profits were TR - TC = $10227.6-$9874.4 = $353.2.

At price $2.851, the total revenue is $9123.2. The variable cost was $2.729 per gallon and $8732.8 for 3200 gallons. The fixed cost is given as $50 per day. Thus, the total cost was $8782.8. The profits were TR - TC = $9123.2 - $8782.8 = $340.4.

The revenues has decreased by $1104.4.

The change in profits = - $12.8

That is the profits has reduced by $12.8.

2.  PED = percentage change in quantity demanded/percentage change in price

= (400/3600)/(0.01/2.841)

= 31.567

The elasticity of demand is greater than one indicating the good to be price elastic. When there is small change in price, the change in quantity demanded is proportionately larger. Therefore, for a small decrease in price will increase  the quantity demanded as well as the revenues and vice versa.

Cal is reducing the price from $2.841 to $2.831. This has increased the demand from 3600 gallons to 4000 gallons. At price $2.841, the total revenue was $10,227.6. The variable cost was $2.729 per gallon and $9824.4 for 3600 gallons. The fixed cost is given as $50 per day. Thus, the total cost was $9874.4. The profits were TR - TC = $10227.6-$9874.4 = $353.2.

At price $2.831, the total revenue is $11324. The variable cost was $2.729 per gallon and $10916 for 4000 gallons. The fixed cost is given as $50 per day. Thus, the total cost was $10966. The profits were TR - TC = $358.

The revenues has increased by $1096.4

The change in profits = $4.8

3.  PED = percentage change in quantity demanded/percentage change in price

= (400/4000)/(0.01/2.831)

= 28.31

The elasticity of demand is greater than one indicating the good to be price elastic. As said before when there is small change in price, the change in quantity demanded is proportionately larger. Therefore, for a small decrease in price will increase  the quantity demanded as well as the revenues and vice versa.

Cal is reducing the price further from $2.831 to $2.821. This has increased the demand from 4000 gallons to 4400 gallons.

At price $2.831, the total revenue was $11324. The variable cost was $2.729 per gallon and $10916 for 4000 gallons. The fixed cost is given as $50 per day. Thus, the total cost was $10966. The profits were TR - TC = $358.

At price $2.821, the total revenue will be $12412.4. The variable cost was $2.729 per gallon and $12007.6 for 4400 gallons. The fixed cost is given as $50 per day. Thus, the total cost was $12057.6. The profits were TR - TC = $354.8.

The revenues has increased by $1088.4

The change in profits = - $3.2

There will be a fall in profit with further reduction in price. Therefore, Cal should stick to $2.831 where he is earning increased revenues as well as profits.

4.

5. The profit maximizing price is $2.831.

6.

7. In the above table, the maximum revenue is earned at a price $2.830975 where 4001 gallons are sold. At this point MR = MC (when the mc is rounded to 2 decimal points).