Does a store suffering increased theft generally cause higher prices?

Price is set by the competition

In general, the prices are set by the supply and demand for the whole market. If a merchant sells the same goods for a higher price than competitors without a corresponding advantage (location, better service, convenience) then people won't buy these goods and the merchant will earn less profit as the decrease in volume will outweigh the higher margin.

In highly competitive markets, the prices get very aligned between all the vendors and it essentially means that your costs don't matter when setting the price, what matters is the costs that everyone else has. If your costs are lower or higher than the competitors, then the optimal price is still almost the same, so instead of adjusting the prices you get more or less profit than they do.

So in a competitive environment increased theft (which is just one type of increased costs) that affects just a particular store (as opposed to changes that cause increase in theft for everyone) would not cause an increase in prices there, the main immediate effect would be on their profitability. However, if the profitability drops low enough, the expected result is that the theft-prone store will stop selling these items or go out of business at all; and that would result in decreased competition which would allow everyone else to raise their prices a bit.

Your reasoning seems to be this:

1. Under the old conditions, a widget seller calculates that the profit-maximizing price of a widget is $1.
2. Conditions now change (e.g. because of increased theft).
3. Under these new conditions, she should not change her selling price, because of her earlier calculation that $1 maximizes profits.

But the above reasoning is wrong. When conditions change, there's no reason to assume that the profit-maximizing price remains the same.

(Or more specifically, you have not provided any valid reason for why this profit-maximizing price should remain the same. The only reason you've provided is that this is what the seller calculated before conditions changed. But this is not a valid reason.)

I see your point. However, theft in effect increases the cost of purchase, which changes everything.

The easiest way to get to the bottom of the answer is thinking of a simple scenario but in extremes.

A shop sells one item only, has no thefts, purchases the items for 10 each, and sells them for 15 (making 5), and sells 10 per hour (making 50 profit per hour).

(15 sale price - (10 cost)) * (10 sales) = 50 profit

The shop also knows that (through a previous trial), that if they sell it for 16, that they will only sell 8 per hour (making just 48 per hour). So selling at $15 is optimal.

(16 sale price - (10 cost)) * (8 sales) = 48 profit

The neighborhood goes down hill and thefts start. At 15 sale price, for every theft, the shop needs to sell two more items to make up for that theft (10/5) and break even.

In an extreme example, if for every 2 sales there is 1 theft, the shop will never make any money.

(15 sale price - (10 cost * (1.5)) * (8 sales) = 0 profit

(1.5 is based on having to buy 3 items per every 2 sold (3/2 = 1.5), effectively pushing the cost price up to $15.)

So, even though selling 16 or above meant less overall profit when there were no thefts, now selling at 16 would give 8 profit per hour.

(16 sale price - (10 cost * (1.5)) * (8 sales) = 8 profit

In this example, this means that without theft, 15 is the optimal price, but with theft, 15 is no longer the optimal sale price.

At a 5% theft rate (rather than the 50% above), it is better to keep selling at 15 (plug in the numbers to see). At a 10% theft rate, selling at 15 or 16 give the same profit. Anything above 10% means increasing your price is now more profitable.

It all depends on the situation really, mainly the current profit margin, how much increasing the cost decreases sales, etc.

But the above should prove that theft does indeed push the optimal price higher, and does pass the cost on to the customer.

A high level of theft increases the cost of a product and therefore changes the profit-volume relation.

In price setting the cost of a product is normally analyzed along several levels of cost fixed and variable. Theft increases both cost types (increased fixed costs for theft prevention measures and variable costs due to high shrinkage level).

As with all cost increases how a business decides to relay that increase to its customers depends on the market environment.

How competitive is the market, how elastic is the demand? Nevertheless theft is simply part of the cost of a product and if the cost changes you have to at least analyze whether price should too.

The principle of Supply vs. Demand states that prices increase when supply falls or demand increases. Theft reduces the supply of sellable items, so it implies that the price should increase to reflect this.

However, there can be feedback effects that prevent this from continuing unchecked. Suppose the reason for the theft is that the price is too high for many people to afford, but they still need the item (e.g. basic necessities such as food and water). Increasing the price will simply exacerbate this problem, causing more theft. Competition should theoretically address this: if vendor A charges too much, vendor B can charge less and people will buy from B rather than steal from A. But if the vendor has a monopoly, they need to set price that allows them to make a reasonable profit while not encouraging theft.

Vendors do generally expect some theft and incorporate that into their pricing models, but if theft increases significantly they may need to adjust their prices. It would also be nice if reduced theft resulted in lower prices, but it's likely that companies will simply view this as a happy windfall and use it to increase their profits. Also, it may be possible that this is just a temporary drop; if they reduce prices and then theft returns to its original level, they would have to increase prices again, and customers would view this negatively.

What you're describing is retail shrink.

It is taken into consideration when setting prices. A business will typically have consultants come in, measure their shrink to be X percent, and prices will be adjusted accordingly.

Back when I worked in retail, there was a big printout in the break room informing everyone on shrink. The 5 kinds of shrink outlined on that particular flyer were Shoplifting, Employee Theft, Damaged in Store, Damaged on Arrival, and Spoilage.

Our company goal was to keep shrink under 3% - That's to say, that our recorded inventory vs our actual inventory needed to be fairly close. This was in a grocery store. I also worked logistics for the same company, as a side note- At the distribution level the acceptable level of shrink was .02%. That should give you an idea how much shrink was attributed to the product actually being in a store.

But in answer to your question, When setting prices, shrink increases cost. I'll give a simple example regarding spoilage, but keep in mind that it is ALL shrink, so in the eyes of the Inventory Control Analysts, it's all just lost inventory we must account for.

Suppose a store wants to sell 100lbs of fruit.

A store may purchase 100lbs of fruit, but they know 20lbs may spoil - That's a shrink rate of 20%. If that happens, then the store must purchase 20% more fruit in order to meet their goal. 100 / .80 = 125lbs of fruit. The 25lbs of fruit that spoils will be passed down somewhere, be it the bottom line of the store or the consumer. That's how shrink gets passed along. Our employer liked to tell us the cost ended up in our 401k to motivate us to prevent shrink.

The National Retail Security Survey (2019) writes more in depth about the different levels of thievery a retail environment can experience, and in fact shows that thievery costs even more than just the missing product. Security cameras and other theft prevention devices are all justified through recovering the cost of loss.

Any company replacing cashiers with self checkouts has determined that the increase in theft they will experience (due to self checkout) is less than the cost of a cashier.

prices should have already been set to maximize the trade off between profit-per-sale and volume sold

But profit-per-sale depends on costs, which depends on the theft numbers, so if theft increases, the equation changes.