## Sunday, November 18, 2012

### Taxes Are Not Simply Passed On To The Consumer

A recurring argument in political discussions regarding taxes is that taxes on corporations, products, or resources are not really affecting the corporations, as they are simply passed on to the consumer. This argument is, in the extreme form, simply false and is based on a common misconception of how prices are formed.

# Origin of Prices

A rather common idea on how prices are created is that producers sum up the cost of everything that’s needed for a product, maybe add a little margin for profit, and sell it for that. So, if the state puts some taxes on it, it’s simply going to raise the price by that amount, and then that’s it. This argument is false because this common idea of where prices come from is overly simplistic.

Actually, the level of prices is a bit more complex. A product’s cost consists of two major groups, the per-item and the per-time costs. The cost for materials, for example, is pretty much fixed per item, even though certain large quantities can get you discounts. But in general, this amount is fixed per item. Next, you have cost like rent, wages, etc., all of which are per time, no matter how many items you produce. This means that the total cost per item goes down the more items you produce. It’s a function of items per time.

Let’s look at a concrete example.

You’re building chairs. The wood comes up as 10 EUR per chair. The rent for your factory and your two workers comes up as 400 EUR per week. With two workers and this factory, you can produce up to 100 chairs a week. If you produce 100 chairs, your cost per chair will be 14 EUR:

(400 ÷ 100) + 10 = 14

Now, there might not be enough demand in the area you are producing in to sell 100 chairs each week. Maybe there’s only demand for 10 chairs a week. But if you only get to sell 10 chairs a week, your cost per item changes:

(400 ÷ 10) + 10 = 50

Next, the amount of chairs you sell is also directly related to the sell price. The higher the price, the fewer people will want to buy it. This results in the profit calculation.

At any given price, your profit per time is the price times the amount of sold items at this price minus the cost times the amount of sold items at this price. The goal of a business is to find the price that maximizes profit per time.

Let’s go back to our chair company. Let’s say if we sell chairs for 100 EUR, we get a single buyer per week. 90 EUR means three buyers, 80 EUR results in nine buyers, 70 EUR in 16 buyers, 60 EUR in 25 buyers, 50 EUR in 36 buyers, 40 EUR in 49 buyers, 30 EUR in 64 buyers, 20 EUR in 81 buyers, and 10 EUR in 100 buyers.

This results in the following profit calculation:

PriceChairs SoldItem CostProfit per Week
100.001410.00-310.00
90.004110.00-80.00
80.00954.44230.00
70.001635.00560.00
60.002526.00850.00
50.003621.111040.00
40.004918.161070.00
30.006416.25880.00
20.008114.94410.00
10.0010014.00-400.00

Now, as you can see, under these assumptions, we should sell our chairs for 40 EUR each. That results in the largest profit per time for us. If we sell the chairs for 90 EUR or more, or 10 EUR or less, we even make a loss.

So, this is how prices come to pass. Please note that this is a huge simplification. Actual businesses have to deal with a lot of other problems there. Not the last one being that it is simply impossible to know beforehand how many items you would sell at a given price, an estimate of which being the main point of market research. Also, price changes have different effects than introduction prices, meaning changing prices afterwards will usually result in different conditions than if you had set the price that way right the first time.

All of this does not affect the main point I am trying to make here. Namely, that the basic way of how prices come to pass is an optimization of profit, not a simple profit margin on top of unit cost. Because this has important effects when taxes, or tax increases, come into play.

# Effect of Taxes

Taxes directly change the cost of an item, not the price. The price is then calculated just like we did above, by optimizing profit. But as those taxes do not affect how many items at a given price are sold, it is rarely sensible to simply add the extra cost to the price. That will reduce the number of items sold, increasing cost per item, reducing profit.

Let’s look at how this would affect our example. The state is cruel and decides to charge a 50 % tax on chairs. (I’m using large numbers because we only have 10 EUR steps in our table, lest we get rounding problems.) With the common idea, this would mean that chairs would now be sold for 80 EUR, so the company retains the 40 EUR input from before. But that would mean they only sell nine chairs—and actually incur a 130 EUR loss!

PriceChairs SoldItem CostProfit per Week
100.00 1460.00-360.00
90.00 4155.00-260.00
80.00 994.44-130.00
70.001670.00 0.00
60.002556.00100.00
50.003646.11140.00
40.004938.1690.00
30.006431.25-80.00
20.008124.94-400.00
10.0010019.00-900.00

With the new profit calculation, the chair company is best off selling chairs for 50 EUR a piece, resulting in a total weekly profit of 140 EUR. Customers are paying 10 EUR more per chair of the 36 ones sold, so shoulder 360 EUR of the tax, while the company’s profit is reduced by 930 EUR.

This should make it clear that the effect of a tax is to distribute the extra cost between the customer and those who would benefit from the profit.

That is to say, taxes will (likely) mean that prices go up, but they also mean that the businesses themselves will need to pay part of the extra cost. Claiming that prices will be simply transferred to the customer is wrong.

# Other Effects

I mentioned above that price changes are tricky. Every change in price makes consumers re-think the situation, possibly deciding that they do not need the product anymore, or having resentments towards the corporation for the price increase. This means that corporations are reluctant to change prices, even though in an ideal situation the higher price would cause higher profits. Tax increases now give corporations an excellent excuse and culprit for price changes.

My theory is that this is likely one of the reasons for why corporations tend to be so keen on pointing out tax changes. It gives them a reason to change prices, and deflect the customer anger onto the state. Usually, the price change has very little to do with the tax itself.

Finally, one last effect of taxes shouldn’t be discounted, as it’s unrelated to who pays for it. If resource consumption is taxed, the tax might make other resources more attractive that were prohibitively costly before. This can be an extremely important tool for environmental policies.

# Summary

Tax increases will usually lead to higher prices, but the tax cost is not simply passed on to the customer. Rather, the cost is paid for from both corporate profits and the customers.

On the other hand, tax increases can serve as a handy scapegoat for price changes that have been intended for a while anyhow, trying to deflect customer upset at the state and not at the corporation.