Consider the evidence

Philadelphia Inquirer opinion editorial "Consider the evidence" (December 21st, 2009) ignores an interesting possibility concerning the delay in police departmental testing of rape kits. The article is perturbed that there is a shortage in processed rape kits.

The backlog of untested kits includes about 12,500 in Los Angeles, 10,000 in Detroit, 6,000 in San Diego, and 4,000 in Houston. (Philadelphia police, to their credit, say their lab tests every kit).

And

Money shouldn't be a roadblock to solving these crimes. Congress passed a law in 2004 to provide grants to states for rape kit testing. But the law allows police departments to use the money for other DNA testing, not just rape kits. Human Rights Watch reported last March that the Los Angeles Police Department's backlog of untested rape kits occurred despite LAPD's receiving $8 million in grants for testing during the previous four years.

There is no explicit price mechanism to clear the market for processed kits, so instead it is cleared by the implicit price mechanism of time-to-process (perhaps mixed with a nebulous definition of priority). Furthermore, supply is constant. If we increase supply, we expect waiting time to decrease in the short run. However, in the long run, prosecutors and police change their standard methods of operation, and increase their use of more sophisticated methods. This, in turn, raises the waiting time. If long run elasticity is very high, we expect supply shifts to only ever shift waiting time a little. Such a case is depicted graphically below (click to enlarge).  Additionally, our expectations on the evolution of "price" and quantity over time are depicted below (click to enlarge).  

It is foolish to focus only on waiting time or backlog--instead, optimizing behavior would be to first minimize the sentence-adjusted cost of bringing in a suspect (which may include many rape kits or few rape kits), and then choose the amount of money one wants to spend, setting the sentence-adjusted marginal benefit to our (minimized) marginal cost.