The city of Waterloo is thinking of devoting funds to build a new ice rink for the community. The issue is that people have very different views on the ice rink as a public good. While all residents have some benefit from the rink, some people derive greater benefits than other. z denotes the size of the ice rink in terms of the number of seats around the rink. There is the cost of z that must be paid, which is z/2. Broadly speaking, Type 1 people have the following utility function; U1 = b1 + 20z - (z/2)2 And Type 2 people have the following utility function; U1 = b2 + 40z - (z/2)2 'b' represents number of units of private goods consumed by individuals. There are 20 Type 1 individuals in the economy and 30 Type 2 people. The Marginal Rate of Transformation (MRT) is MRT = - (340 + 40z). (a) Which group has a higher utility from more units of the public good z? why? (b) Calculate the MRS for each group if MRSi = - (Ui/ z)/(Ui/ bi), where i = 1,2. (c) Now calculate the optimal size of the ice rink in terms of the number of seats.