Free response question

IEO past paper: 2021 International Economics Olympiad, open questions

Last year, IEO contestants were asked to solve a problem about an optimal lockdown. Unfortunately, in 2021 this topic is no less relevant. So suppose society is facing a severe viral pandemic and contemplates introducing a lockdown. How strong should the lockdown be? The answer to this question apparently depends on the preferences of the society between the lives/health of people and GDP. Or does it really? Let $d \in [0, 1]$ be the level (strength) of a lockdown ($d = 0$ is no lockdown while $d = 1$ is complete lockdown) and $v$ be some measure of the total amount of virus in circulation. The relation between the two is given by $v = 2(1 - d)$. Aggregate demand in the economy is given by the function $Y = 10 - 2d - P$ while aggregate supply is governed by the equation $Y = 2 + P - d - \alpha v$ where $\alpha \geq 0$ is a parameter; $Y$ is real GDP and $P$ is price level, as usual. Finally, let $H$ be the aggregate health of people; it depends on the amount of virus in circulation as follows: $H = 3 - v/2$. Define the Pandemic Possibility Frontier (PPF, for short) as the set of all pairs $(Y, H)$ that can be achieved by a policy-maker by choosing various levels of lockdown $d \in [0, 1]$.