Ace Rimmer wrote:Edit: Hehe, xander, again the grocery store analagy is a poor one. Doesn't the grocery store have insurance for broken pickle jars? Now, you'll say, "they're paying for the insurance", but I'll say, no, you are, as is their employees, and Americans don't have that type of insurance anyway. ad infinitum?
You are being to literal. In the analogy, the goal of the store is maximize profit. Profit is revenue minus costs. Revenue can be increased by charging more per item, or by making more sales. Costs are things like maintenance, wages, breakage, insurance, &c. The goal is to minimize net costs while maximizing net profits.
In a welfare system, the goal is to maximize the efficiency with which benefits are disbursed to people in need. Efficiency can be seen as the ratio of funds that go to people in need and the total available funds (i.e. funds disbursed to people in need plus employee wages plus enforcement plus fraud &c). In this case, the goal is then to minimize the non-disbursement terms in the denominator.
The analogy is imperfect, as are all analogies. However, the logic of the statements that I have made is sound. Fraud is one variable, among many. For simplicity, suppose that fraud and enforcement are the only variables. As a further simplifying assumption, let's assume that fraud is a function of enforcement (i.e. more enforcement means less fraud). Thus we can write W(x) = x + F(x), where x represents the amount of money spent on enforcement, f(x) represents the amount of money lost to fraud if x is spent on enforcement, and W(x) represents the total waste or inefficiency. Moreover, let's say that x ranges from 0 to 1, with 0 representing no money spent on enforcement and 1 representing 100% of all funds spent on enforcement. Clearly, W(1) = 1. That is, if we spend all of our money on enforcement, then we have wasted all of our money. On the other hand, we might assume that W(0) = 1-epsilon, where epsilon is so small as to make no difference. That is, if we spend no money at all on enforcement, then all of the money is lost to fraud.
With the final assumption that the overall waste function is more or less continuous, we may apply Rolle's Theorem (a basic result from calculus) to conclude that there is some x0 between 0 and 1 which minimizes W. That is, W(x0) is as small as we can make it. Note, however, that F(x0) need not be zero. That is, even at the optimum solution, there will almost certainly still be some fraud.
The assumption that I am making is that 0.3% lost to fraud is pretty close to the optimum. This seems a safe assumption as 0.3% is a very small amount of the total, and most enforcement regimes face exponentially dimishing returns.
xander
studying was so much more fun
