Most car rental companies offer their customers two alternative fueling options. Renters can fill up the...

Most car rental companies offer their customers two alternative fueling options. Renters can fill up the tank themselves at the going price (currently $4.00 per gallon) and return the car with a full tank (the “Do It Yourself”, or DIY option), or they can pay in advance for a full tank at a below-market rate (say $3.50 per gallon), with no credit for unused fuel (the “Fuel Service”, or FS option). Consider Mike, a customer who rents a compact car with a 16-gallon tank. For a “typical” car trip, Mike has the following demand for gasoline:

Q= 18 – 2P,

where P is the price per gallon (in dollars) and Q represents gallons of gas.

1. (10 points) Draw and label Mike’s demand curve. For the following, explain your answers and illustrate on the graph:

a. How many gallons of gas would he purchase under the “Do It Yourself” option? b. How much would he spend? c. What is his average price per gallon of gas? d. What would be his consumer surplus

Expert Solution

The following diagram exhibits Mike's demand curve with quantity demanded of gasoline on X-axis at the respective price that Mike is willing to pay on Y-axis. Given his demand function as Q = 18 - 2P, different points have been formulated and joined to form the required demand curve.

a. Under the DIY (or Do-It-Yourself) scheme, since the price rallies at $4 per gallon, putting it into the demand function to find out quantity, we get:

Q = 18 - 2P

Q = 18 - 2*4

Q = 18 - 8

Q = 10

Hence, he would require 10 gallons of gasoline for his usual trip.

b. For DIY option, he would be spending a total of $ (10*4) = $40.

c. Therefore, the average price per gallon would be the same as the market price which is $4 under the DIY option as for each gallon he requires $4 of price to be paid.

d. The above diagram illustrates the quantity purchased is 10 at the market price of $4. It also depicts consumer surplus which is nothing but the difference between the price consumers are willing to pay and price they actually pay. It is obtained graphically as the difference between demand curve and market price.

Rahul Sunny answered 9 months ago

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