We’re bringing back price theory with our series on Price Theory problems with Professor Bryan Cutsinger. You can see all of Cutsinger’s problems and solutions by subscribing to his EconLog RSS feed.
Share your proposed solutions in the Comments. Professor Cutsinger will be present in the comments for the next couple of weeks, and we’ll post his proposed solution shortly thereafter. May the graphs be ever in your favor, and long live price theory!
Question: Suppose the market price of gasoline is $5.00 per gallon. Politicians, responding to their constituents who believe that such a price is outrageous, impose a price control of $2.00 per gallon. At this price, you want to buy 9 gallons of gasoline per week but gas stations are now only willing to sell you 5 gallons per week. There is a shortage.
Assume that to buy gas, you must wait in line. Doing so gives you the right to purchase gasoline at the controlled price of $2.00 per gallon. Assume also that you would be willing to pay up to $6 per gallon. Finally, assume that your wage is $10 per hour.
How long will you wait in line to buy gasoline? What will be your total expenditure on gasoline each week? What price will you pay per gallon? Did the price control reduce the price of gasoline?
READER COMMENTS
John Hall
Apr 24 2025 at 2:29pm
Assume that if you wait in the line, then you will fill up as much as you can since it is a shortage. That implies the number of gallons purchased would be 5 gallons. Based on the willingness to pay, you wouldn’t be willing to wait more than 2 hours (5*2+10h=6*5, solve for h).
If you are able to get the gas, then you would spend $10. That wouldn’t include the opportunity cost of waiting (which would be $10+$10h, depending on how long you wait)
You will pay $2 per gallon, not including the opportunity cost. Including the opportunity cost, it would be $2+$2*h.
The price control reduces the dollar cost of gasoline. Whether it reduces the overall cost of gasoline depends on how long you wait in line. You also may not be able to get gasoline at all.
Bryan Cutsinger
May 2 2025 at 6:04pm
Nice! Definitely on the right track here!
David Seltzer
Apr 24 2025 at 3:30pm
Bryan: My total market cost is explicit cost + implicit opportunity cost.
Buy 9*$5 is $45 plus 15 minutes to fill up is .25($10) Opportunity cost. Total cost = $47.5
To be no worse off: 5*$2 is $10 plus opportunity cost of waiting in line = $47.5
The opportunity cost: -$10 – $10* x hours =-$47.5 = -$37.5/$10 = 3.75 hours in line.
Willing to pay $6. OC = 1.83 hours in line at $10 per hour.
The implicit opportunity cost depends on how long one chooses to wait in line.
Bryan Cutsinger
May 2 2025 at 6:05pm
Nice…on the right track here!
robc
Apr 24 2025 at 3:53pm
I would buy 9 gallons a week, probably at $6 per gallon, from my local black market gas dealer.
robc
Apr 24 2025 at 3:56pm
My wait time would be zero.
Bryan Cutsinger
May 2 2025 at 6:06pm
I love this answer! I’ll discuss it in my solution.
Knut P. Heen
Apr 25 2025 at 7:27am
I would hire someone at $5 per hour to fill gas and let him figure out whether it is worth waiting or not.
Bryan Cutsinger
May 2 2025 at 6:07pm
Why stop at paying the person $5 an hour?
Grand Rapids Mike
Apr 26 2025 at 10:36am
As a black market dealer, would start by contracting with local kids in the neighborhood to buy what they can at $2.00 and offer them a $2.00 profit. From which I would sell for price starting at $6.00
Bryan Cutsinger
May 2 2025 at 6:08pm
I like this answer! I’ll address it in more detail in my solution.