There are some interesting and under-reported papers on this topic, here is one of them, by Jordan D. Matsudaira and Emily Greene Owens, here is the abstract:
In 2006, approximately 49% of violent crimes were not reported to police. Being the victim of sexual assault is expensive; each incident imposes an external cost of over $100k on the victim. However, recent estimates of the total social cost are an order of magnitude larger suggesting that from a social welfare standpoint rape is likely to be underreported if the victim’s demand for reporting is price elastic. In spite of the centrality of victim reporting in the functioning of the criminal justice system, to date there is very little systematic evidence on what governments can do to encourage victims to report crimes. We estimate the sensitivity of victims to the cost of reporting in an Alaskan city between 1993 and 2006, during which time a chief of police publicly supported a policy of charging victims of sexual assault for medical procedures required to collect evidence against their attackers. Using a triple differences approach that compares trends in reported sexual assaults to other index crimes over time and across Alaskan cities, we estimate that this shift in cost of approximately $1,200 from the city government to victims reduced the number of reported rapes by between 50 and 80%. This large response highlights the importance of public policies which reduce the private cost of reporting crime.
The full paper is here. Here is a paper by Paul Zimmerman and Bruce Benson on the economics of alcohol and rape, the published version is here. Here is W. David Allen on the under-reporting of rape. Here is a paper on rape as an economic crime. This Scott Cunningham paper covers the connection between prostitution and rape. This study shows that porn does not seem to lead to rape. That said, if you enter “economics rape” into scholar.google.com, many of the top entries are about the crop. My Google searches for “political economy of rape” do not turn up much useful, although that ought to be a very important topic.