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Problem 1: Covid-19 Vaccination Campaign [6 Points] You were just hired by the CDC to lead the Covid-19 vaccination campaign. The private payoff from getting vaccinated is it = c, where c is cost parameter that incorporates the risk of complications associated with vaccination (vaccines per se are free of charge). The private payoff associated with not getting vaccinated is 71' = bR0(VC V), where: b is a cost parameter that incorporates the health risks associated with catching Covid-19; R0 is the basic reproduction number (i.e. how transmissible the disease is); VC is the critical level of immunity, or vaccination, the population needs to reach to eventually eradi- cate Covid-19 (i.e. the herd immunity threshold); V is the fraction of the population that is currently immune / vaccinated. Together, \"ROG/C V)\" represents the probability of catching Covid-19. For simplicity, assume that the immunity one develops to Covid-19 is permanent, and that catching the disease provides you with the same immunity that the vaccine does, so that V includes both vaccinated and infected individuals. 1.A. [0.5 point] Let 3 denote the fraction of the population that is susceptible. Find R, the effective repro- duction number and nd VG, the herd immunity threshold. How does VC change as new variants that have higher a Re become the new dominant strain? Show your work and explain in words. 1.3. Private incentives of vaccination. i) [0.5 point] Find V*, the equilibrium level of vaccination that private individuals would choose on their own. Show your work and explain in words. ii) [0.25 point] How does V* change if people falsely believe that complication costs (2 are much higher than what they actually are? Show your work and explain in words why a good estimate of the c is impor- tant. iii} [0.25 point] For this subquestion only, suppose that a newly approved vaccine makes it such that c = D. How does V' change and how does it compare to V\"? Show your work and explain in words what this means and what it implies if c > 1]. LC. Social incentives of vaccination. i} [1 point] Suppose that the total population is of size N. Find V\