1. (25 points) Suppose citisen welfare is given by th where h is public healthiness and y is income per capita. a) (2 points) How many first order partial derivatives does the function u have? What are they? b) (2 points) Choose one of these and explain what it describes, in terms of public healthiness and income per capita. During the COVID19 pandemic, policy makers set lockdown regulations, balancing infection risk against economic outcomes. Let L} be the number of hours per day citisens must stay at home. Suppose public health and income per capita are both completely deter- mined by q according to the functions h= y= c) (6 points) What is the likely effect of lockdown strictness on citisen welfare? Justify your answer mathematically. d) (1 points) Given your 1c) answer, why might have lockdown policy been so contentious? e) (2 points) How would you determine the welfare-maximising num- ber of lockdown hours? Suppose lockdown hours are set at the optimum level, which is q* = 8. f) (3 points) What is the optimum level of public healthiness h*, income per capita y*, and citisen welfare u *? g) (2 points) Describe in words what the level curve u(h, y) = u* represents, in terms of public healthiness and income per capita. h) (2 points) Let y = ((h) be this level curve. What's the likely sign of l' (h)? Explain with economic intuition. i) (5 points) Suppose f' (8) = 1 and g'(8) = 1. Calculate ('(h*), justify- ing your answer mathematically