Suppose individuals react to the threat of getting infected by COVID by reducing their social activity. Denote person i's level of social activity as at- E [0.1]. Further denote the average activity level in the society as a. A person's resilience to the virus is given by 19,-. The disutility an infection causes for person i is 1/95. Finally, the infectiousness of the current variant is given by p. A person chooses her activity level in order to maximize her enjoyment from social activity net of expected health consequences of an infection. The probability pt- of contracting the virus depends on activity level. average activity level in the society and on the infectiousness of the variant. Hence, the objective function of person i is Ways) == Ha.) \"9\" For simplicity use the following functional forms: Pi (at: a) = 903351: f(ai) = as 1. Find the optimal activity of person 3' as a function of E; if the society is so large that i's impact on the average activity is negligible and provide an intuition for the impact of ft on the optimal social activity of 1'. Now assume that the population consists of two groups of equal size, the vulnerable and the non-vulnerable with 6., and 6,1, respectively. 2. Calculate the equilibrium activity :15, a; and indirect utility for members of both groups. (Note that E: = (as + anl/ 2)