The effects of theft or destruction of goods on a monopoly

Firms are always complaining about theft and how there are enormous economic impacts associated with it. From the recent Stop Online Piracy Act (SOPA) and the Protect IP Act (PIPA), it is clear that the politicians have been paying a lot of attention to the issue. For an economist, there’s a lot of questions to be had here. Below is a basic profit maximization model modified to accommodate destruction or theft of goods.

Before I begin my analysis, I must make clear that the model assumes that α, the percentage of goods received by the firm, is a completely independent variable, meaning it is not affected by other variables. One could account for the obvious notion that price and the willingness of people to steal (and conversely the amount of goods paid for) by having α be a function of price. However, that adds a fair amount of math, and so we’ll leave that out. Furthermore, the demand function is linear.

If we look at where MC is low, the effects of destruction and theft on quantity produced is minimal. It makes intuitive sense. If it’s cheap to produce a good, then who cares if half of what you make gets destroyed; just make more! So at a MC of 2, even when the firm only receives half of what it makes, the quantity produced is barely affected with a change of only 1.

Now when MC gets high, the firm produces a fair amount less. But when the firm receives only half of what it makes along with a high MC, there is another massive reduction in quantity produced. From this relationship, it seems that if government desires to benefit society, they should focus on removing theft, piracy, or destruction of goods on firms with high MC than firms with low MC.

Another interesting note we should examine is how profits have changed for the firm. Remember how the firm with low MC produced nearly the same amount despite receiving payment for only half of its goods? Its profits have fallen by about 50%. As we can see, firms have a huge incentive to complain about theft. In the case of firms with low MCs, theft hurts them more than it hurts society.

Software firms fit the model very well. For the most part, software tends to be monopolistic and in many cases, full blown monopoly. Their MC is also very low. If we take the above model to be true, then it’s no wonder that a lot of the lobbying has been about online piracy. Software firms have a lot to lose in profits.