Cal Overhaut operates an ExxonMobil gas station franchise in Fitzhugh, MD. The price of gasoline is volatile and varies significantly from day to day. The price per gallon varies based on the seasonal blend of gasoline, which is determined by clean-air requirements. Cal's pricing options are based on the desired profit margin.

Conventional Gasoline Regular Spot Prices can be found at https://www.eia.gov/dnav/pet/hist/EER_EPMRU_PF4_Y35NY_DPGD.htm.

Cal recently raised the price of regular gas by 1 cent per gallon from $2.749 to $2.759, and his profit declined. Cal would like you to explain why that happened.

Cal competes with another gas station across the street that typically sells regular gas for 2 to 3 cents per gallon less than his station. They are currently selling gasoline for $2.729 per gallon. Recently, regular gasoline for delivery in New York harbor sold for $2.008 per gallon.

Cal tells you that his gas station has fixed operating costs of about $250 per day.

To the right are the components that determine the cost of a gallon of regular gasoline to Cal's business.

Answer the seven questions below. You are required to use Excel for all calculations.

1. Last week, Cal sold an average of 4,000 gallons per day at an average price of $2.749 per gallon. This week, he raised the average price by 1 cent to $2.759 per gallon, and both revenues and profits dropped. His station is now selling an average of 3,600 gallons per day.Fixed costs of operating the gas station are $250 per day.

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? (Profits are revenue minus all costs.)

2. After seeing your analysis, Cal decides to lower the price of gas to $2.739 per gallon. After this change, the volume sold increased to 4,400 gallons per day. He asks you to measure his business gains or losses as a result of this price change. Fixed costs are $250 per day.

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? (Profits are revenue minus all costs.)

3. 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? (Profits are revenue minus all costs.)

4. Cal's son is studying in the MBA program at UMUC. He tells his father that profit maximization occurs when the marginal cost (MC) = marginal revenue (MR). Cal understands that his marginal cost is the same as his variable cost or $2.649 per gallon. Technically, marginal cost is the added cost from selling one more gallon.

Cal asks you for a chart to show how profits vary with sales volume, assuming that he sells an additional 400 gallons for each 1 cent decrease in price.Also, he wants to know how much he can lower his price without losing money.

Given that you know the price and quantity of gallons sold so far, and that Cal's cost per gallon is $2.649 per gallon and his fixed cost is $250 per day, complete the table to the right.

5. Once you calculate total profit, what is the profit-maximizing price?

6. Next calculate marginal revenue, knowing that it is the difference between the revenue at the price shown and the revenue at 1/400 of a cent less. Calculate 1/400 of a cent as well as the new price.

Calculate the marginal cost of selling one more gallon at each price.Prove that MC = $2.649

Prove to Cal that MR = MC at the maximum profit.

Complete the table to the right.

7. Does MC = MR at the maximum profit point?