The society considers three levels of Covid-19 regulation. There are no regulation (level 0), some regulation (level 1), and strict regulation (level 2). Suppose the society consists of 57%,18%, and 25% Type 0,1 and 2 voters, respectively. Their happiness from the regulation can be described by the following function: Ui(x)=−(i−x)² +1, where i=0,1,2 represents the voters' type and x=0,1,2 represents the level of regulation. Suppose the society use a majority voting rule to choose the level of regulation. (a) Is each voter's preference single-peaked? Explain your answer with a graph in which the horizontal axis is the level of regulation and the vertical axis is the level of happiness. (b) Does the median voter theorem apply in this case? Why? If your answer is yes, what level of regulation does it predict?