The Many Uses of Elasticity: An Example from Law Enforcement Policy

In this chapter, we have studied several types of elasticities, starting with the price elasticity of demand. Elasticity is a general concept that economists use to measure the effect of a change in one variable on another variable. An example of a more general use of elasticity, beyond the uses we discussed in this chapter, appears in a new academic paper written by Anne Sofie Tegner Anker of the University of Copenhagen, Jennifer L. Doleac of Texas A&M University, and Rasmus LandersØ of Aarshus University. 

The authors are interested in studying the effects of crime deterrence. They note that rational offenders will be deterred by government policies that increase the probability that an offender will be arrested. Even offenders who don’t respond rationally to an increase in the probability of being arrested will still commit fewer crimes because they are more likely to be arrested. Governments have different policies available to reduce crime. Given that government resources are scarce, efficient allocation of resources requires policymakers to choose policies that provide the most deterrence per dollar of cost.

The authors note “we currently know very little about precisely how much deterrence we achieve for any given increase in the likelihood that an offender is apprehended.” They attempt to increase knowledge on this point by analyzing the effects of a policy change in Denmark in 2005 that made it much more likely that an offender would have his or her DNA entered into a DNA database: “The goal of DNA registration is to deter offenders and increase the likelihood of detection of future crimes by enabling matches of known offenders with DNA from crime scene evidence.”

The authors find that the expansion of Denmark’s DNA database had a substantial effect on recidivism—an offender committing additional crimes—and on the probability that an offender who did commit additional crimes would be caught. They estimate that “a 1 percent higher detection probability reduces crime by more than 2 percent.” In other words, the elasticity of crime with respect to the detection probability is −2.

Just as the price elasticity of demand gives a business manager a useful way to summarize the responsiveness of the quantity demanded of the firm’s product to a change in its price, the elasticity the authors estimated gives a policymaker a useful way to summarize the responsiveness of crime to a policy that increases the probability of catching offenders.  

Source: Anne Sofie Tegner Anker, Jennifer L. Doleac, and Rasmus LandersØ, “The Effects of DNA Databases on the Deterrence and Detection of Offenders,” American Economic Journal: Applied Economics, Vol. 13, No. 4, October 2021, pp. 194-225.