Please fully answer both questions and show full work.

1. ( 25 points) Suppose citisen welfare is given by u(h,y) 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 COVID-19 pandemic, policy makers set lockdown regulations, balancing infection risk against economic outcomes. Let q be the number of hours per day citisens must stay at home. Suppose public health and income per capita are both completely determined by q according to the functions h=f(q)y=g(q) 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 number 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 (h) ? Explain with economic intuition. i) (5 points) Suppose f(8)=1 and g(8)=1. Calculate (h), justifying your answer mathematically. 2. (15 points) An island economy grows coconuts and provides medical services. For each coconut harvested, coconut farmers need to eat half a co conut and receive 45 minutes of medical attention. For every four hours of medical service provided, doctors on the island need to eat a coconut and receive half an hour of medical attention. The island economy ultimately exports 100 coconuts, but imports 50 hours of medical services (by Zooming with doctors based in Canada). a) (d points) Represent this economy as a system of equations. b) (5 points) How many coconuts total are grown on the island? How many hours of medical service are provided by doctors on the island? Justify your answer mathematically. c) ( 2 points) How many total coconuts are consumed on the island? Justify your answer mathematically. d) (2 points) How many total hours of medical attention do the islanders receive? Justify your answer mathematically