Free response question

IEO past paper: 2022 International Economics Olympiad, open questions

Question 5. "Going Green" There are two groups of consumers of solar panels in country S: 150,000 households who consider purchasing them because they care about the environment and 200,000 households who consider purchasing them because it is trendy (this is sometimes called the bandwagon effect). The demanded quantities of the solar panels are given by: $$Q_{c(are)} = 150{,}000 - 5p, \qquad Q_{b(andwagon)} = 40{,}000 - 5p + 500\sqrt{N},$$ where $p$ is the price of a solar panel (in USD) and $N$ is the total quantity of solar panel users (in equilibrium, $N = Q_c + Q_b$). For simplicity, assume that $Q_c$, $Q_b$, and $N$ can be non-integer. The supply of the solar panels is perfectly elastic, $p = 25{,}000$. The market adjusts to the equilibrium in the following way. First, customers who care about the environment decide whether they will have solar panels. At every step after that, customers from the 'trendy' group observe the quantity of solar panels around and decide whether they will have solar panels based on this observation. This goes on until everyone is happy with their choice.