1 Grossman Model (35 points) Consider a simple model of a person making decisions about their health over 2 periods during the worldwide novel coronavirus pandemic. For convenience, you can represent each period as one year; call the first period Year 0 (pre- pandemic) and the second period Year 1 (post-pandemic). Suppose they start with an initial stock of health capital Ho = 1. In both periods they happen to only care about leisure, Zt, and so their utility function takes the form Ut = Zt. They have a discount factor of 6 = 0.9. The only health risk they face is that of contracting the novel coronavirus. We model this by stating that their health evolves according to the following equation: H1 = Ho(1 -70) + Io health depreciation, 70, is determined by the local area infection rate, and is between 0 and 1, 70 E [0, 1]. It, health investments, are countermeasures that can help the person avoid contracting the disease. We will assume for the moment that countermeasures to avoid contracting the disease - purchasing masks, getting grocery delivery, etc. - are goods that are purchased (i.e., It is only a function of Me, not a function of TH ), and have a price normalized to Pt = $1. Their production function for health investment It is given by the following equation: It = Mt $19, 500 (1) Leisure is obtained by playing video games that they already own, and so their production function for leisure is dependent only on time spent, i.e., Zt = T. (2) The relationship between healthy hours in a year, ht, and health, Ht, is determined according to the function ht = 8, 760 * Ht, where 0