The first two terms in brackets on the right

The first two terms in brackets on the right-hand side of this expression capture the direct impact of α on the difference Δ. Since q is by construction the argmax of V under integration, the envelope theorem implies that there is no indirect impact: . If q were the argmax of V under separation, then by the same token one would have and the whole expression would reduce to E[V(q, α)−V(q, α)]. This is strictly negative since q0. However, the common agency distortion makes and, as shown in the appendix, it follows that the derivative becomes strictly positive, and bounded away from zero, if α is large enough. It follows that Δ is positive for large projects even if it is negative for small ones.
Conclusion
Introduction The literature reviewed shows that there is a close relationship between health status and socioeconomic variables, especially education and income. This relationship has been found in different countries and various measures of health have confirmed these findings. In explaining this relationship, Grossman (2000) argues that healthy people have advantage in obtaining additional years of schooling and knowledge quality. Hence, individuals in poor health miss more days of school and they learn less during the school year. Some studies have shown empirical evidence of this relationship by addressing the effect of low birth weight on adult outcomes in twins (Black et al., 2007; Oreopoulos et al., 2008), individual shocks in utero (Almond, 2006; Almond et al., 2009) and early childhood nutrition problems (Maluccio et al., 2009; Khanam, 2014). Other important aspect is that better health is associated with higher labor productivity and time available to work, which are essential factors in the labor market and, therefore, income. Healthier people tend to have higher labor productivity due to their greater physical Microcystin-LR and mental clearness, besides having a greater investment in human capital, the main driver of productivity (Bloom and Canning, 2000). Furthermore, Smith (1999) showed that poor health is associated with lower income and fewer accumulated assets because people with poor health have increased medical expenses and limitations on working, so healthier people can work for more hours in a week and more weeks in a year. Bloom and Canning (2000, p. 1209) conclude that “poor health is more than just a consequence of low income; it is also one of its fundamental causes”. The literature has several studies of the relationship between health status with education and income, however, estimates of return to education that include health status, like this one, are limited. Although higher education is commonly related with higher wages, the returns to education may differ for different groups. The literature usually breaks down the returns by gender (Psacharopoulos and Patrinos, 2004; Mendolicchio and Rhein, 2014; Daoud, 2005), race (Mwabu and Schultz, 1996) and location (Suliano and Siqueira, 2012). There are few studies that have investigated returns to education across health groups. It is well known that the average schooling, average hourly wage, labor productivity and availability for work differ between health and unhealthy individuals. Likewise, the rate of returns might also differ by health status, as found for individuals with disabilities and poor health (Lamichhane and Sawada, 2013; Lamichhane and Watanabe, 2015; Hollenbeck and Kimmel, 2001). In specific for developing countries, to our knowledge, there is no study that analyzes the difference of return to education in terms of individuals’ health (good and poor health). In this paper, we investigate whether the returns to education change in the context of poor health and the year of schooling for which the difference intensifies. Specifically, we examine the influences of health status on the rate of return to education. The remainder of this paper is organized as follows: Section 2 provides a brief summary of studies in relation the rate of return and nonlinearity regarding the schooling; Section 3 explains our empirical strategies and describes the data set from Brazil; in Section 4, the empirical findings are reported. Finally, Section 5 presents the paper\'s conclusions.