The Case of the Minimum Wage Gas Station Attendant, a Problem in Economic Analysis

Vladimir is a legal immigrant working his second job on the lonely night shift at BORDER CITSTOP GAS, a station with three self-service pumps and one full-sevice pump. The station is located in Indiana, 200 yards from the Illinois border, and all of its effective competition comes from several nearby stations in Illinois.

Vladimir's shift is twelve hours long, from 8 PM to 8 AM, six days a week. He is paid the Indiana legal minimum wage, assumed to be $6 per hour for this problem, pre-tax, and no considerations of overtime are to be invoked. For simplicity, assume that the $6 per hour rate is also the total employment cost of Vladimir to the station owner.

The rounded pump prices are $3 a gallon for self-service regular, and $3.24 per gallon for full-service regular. For simplicity, premium grades of gasoline are to be ignored in this problem.

On the first of August, the Indiana legal minimum wage will increase by one third to $8 per hour.

What are the most likely expected consequences of this increase?

 

POST COMMENT ANALYSIS :

The key point is that the wages paid to Vladimir are not dependent on sales quantities or revenues, i.e. are not marginal or variable costs, and thus are not involved in the setting of profit-maximizing (or loss-minimizing) prices. Only if there were a non-slack, non-recoverable opportunity cost to the owner for Vladimir's time would there be an effect on prices. For example, if Vladimir spends the time not used  for servicing either self or full service customers knitting station momentos for owner sale, then their revenues forgone would be a marginal cost that could change the prices. More likely, Vladimir catches up on his sleep between customers.

So the simplest answer is that the prices will not  change and the station will be shut down overnight, as the extra (relative) fixed cost of $24 a day may destroy any profitability of remaining open, with Vladimir getting laid off. Note that some of the business lost during the night may reappear during the day.

This problem has a unusual characteristic in that the profit maximizing price for full-service alone increases when self service come into the picture. If the full service price is raised enough to reduce the quantity sold by one gallon, the full revenue loss only occurs if none of the demand is shifted into  self service.

 

 

 

 

 

 

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They keep paying him 6 bucks

They keep paying him 6 bucks an hour since he's working illegally already. They've already been falsifying his time sheet and claiming he was working 40 hours a week at 72 * 6 / 40 = 10.80 an hour, so they don't even have to change the way they're falsifying things.

I am sure that there are

I am sure that there are many possibilities, but here are the three basic ones as I see it:

1) They keep prices the same and just accept a lower profit margin.
2) They keep prices the same, cut Vlad's benefits (if any) or cut hours of operation and keep the same profit margin.
3) They raise prices, keep the same margin and lose sales to competition accross the border.

My guess is that they would do #2.

obvious answer

The obvious answer is they either fire Vlad and turn the full service into a self serve, or they raise the price of the full service to astronomically high levels. It would have to be a higher raise then what Vlad is getting, since some drivers would opt for the self-serve instead of paying the price increase, thereby driving the price increase even higher.

All, Until proven otherwise,

All,

Until proven otherwise, assume that economic law and correctly understood self interest remove any voluntary choices from the owner, and that they have done so in the past to bring about the current environment.

Regards, Don

I did

I assumed that, since Vlad was working illegally anyway, the fact that he was paid the legal minimum wage was a coincidence.

But if you want to assume that the minimum wage law will be enforced even though other employment laws aren't, I think the point you're trying to make is, there's no point in changing the price per gallon of full service gas. The cost per gallon doesn't change since Vlad is paid by the hour, so the profit maximizing price won't change, at least not as a direct result of the minimum wage change.

It seems likely that Vlad will be let go, or at least have his hours cut back. How much demand for full service gas is there in the middle of the night anyway?

not enough info

We don't know how much self- or full-serve gas is being sold, we don't know what Vlad's mix of duties is (guard, cashier, attendant, mini-mart restocker, etc.), we don't know the finances of the station, the availability of alternate workers, etc. So the answer is : we have no idea know what will happen.

I'd expect it to be along the lines of:

1) Nothing. The $2/hour comes out of the producer surplus (station profits), and causes future price hikes to be very slightly larger (or price drops to be smaller) so it comes out of the consumer surplus as well.

2) Vlad is asked to do more around the station. If he can't or won't, he's let go, in favor of an $8/hour worker who will.

3) Station hours are cut back, so Vlad (and the owner, and the customers) no longer benefit from those hours that are now marginally unprofitable.

These effects could take years to manifest, so it's going to be hard to notice that they are caused by the change in minimum wage.

Unequal Costs under PC

Unequal Costs under PC

The problem is set up so that the station is initially in long run competitive equilibrium. Therefore the price/gallon is equal to the stations minimum average cost.

An increase in the minimum wage will shift the stations average cost curve upward. But the other stations are across the border so their cost curves are unchanged. This means the demand curve, and hence the price, will stay the same. The station owner cannot raise prices else he will lose all his business.

The effect of the increase in the minimum wage will be to destroy the profitability of this station. The owner will shut down the station, or at least close the station at 8pm and open it up again at 8am.

Analysis added to bottom of post itself

Reread post.

Regards, Don