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We consider the use of Quantifier Elimination (QE) technology for automated reasoning in economics. QE dates back to Tarski's work in the 1940s with software to perform it dating to the 1970s. There is a great body of work considering its application in science and engineering but we show here how it can also find application in the social sciences. We explain how many suggested theorems in economics could either be proven, or even have their hypotheses shown to be inconsistent, automatically; and describe the application of this in both economics education and research. We describe a bank of QE examples gathered from economics literature and note the structure of these are, on average, quite different to those occurring in the computer algebra literature. This leads us to suggest a new incremental QE approach based on result memorization of commonly occurring generic QE results.

Price theory says that the most important effects of policy and technological change are often found beyond their first point of contact. This appears opposed to econometric methods that rule out spillovers of one person's treatment on another's outcomes. This paper uses the industry model from price theory to represent the statistical concepts of treatments and controls. When treated and control observations are in the same market, the controls are indirectly affected by the treatment. Moreover, even the effect of the treatment on the treated reveals only part of the consequence for the treated of treating the entire market, which is often the parameter of interest. Marshall's Laws of Derived Demand provide a guide for empirical work: precise price-theoretic interpretations of the direct and spillover effects of a treatment, the quantitative relationships between them, and how they correspond to the scale and substitution effects emphasized in price theory. [ABSTRACT FROM AUTHOR]

The health costs of in-person schooling during the pandemic, if any, fall primarily on the families of students, largely due to the fact that students significantly outnumber teachers. Data from North Carolina, Wisconsin, Australia, England, and Israel covering almost 80 million person-days in school help assess the magnitude of the fatality risks of in-person schooling (with mitigation protocols), accounting for the age and living arrangements of students and teachers. The risks of in-person schooling to teachers are comparable to the risks of commuting by automobile. Valued at a VSL of $10 million, the average daily fatality cost ranges from $0.01 for an unvaccinated young teacher living alone to as much as $29 for an elderly and unvaccinated teacher living with an elderly and unvaccinated spouse. COVID-19 risk avoidance may also be more amenable to Bayesian updating and selective protection than automobile fatalities are. The results suggest that economic behaviors can sometimes invert epidemiological patterns when it comes to the spread of infectious diseases in human populations. [Financial support for this research was provided by the University of Chicago's Initiative on Enabling Choice and Competition in Healthcare.]