Consider an economy in which one unit of labour yields one unit of output. Paul, the representative consumer, has one unit of time at his disposal. Paul values consumption and leisure; His preferences are such that, at the margin, Paul is ready to give up C/l units of the consumption good for an extra unit of leisure. The goal of the government is to set spending so that they represent 40% of national income. Government spending is nanced with a lumpsum tax. Prot maximization implies that w : l and that 7r : U regardless of the value taken by N. a) Find the maximum consumption level which can be achieved in this economy given any amount of leisure and any given value of G. b) Explain why a benevolent planner should choose any bundle with C* = l*. Use this fact and the production possibility frontier found in a) to determine the planner's solution. How much should the government be spending to achieve its goal? c) Explain why Paul will choose any bundle with 0* : 1*. Use this fact, Paul's budget constraint, and the government's budget constraint (with G = 0.25) to determine the market solution. Explain why the equilibria in c) and in d) coincide. (1) Suppose that T : 0.4Y rather than being a fixed amount. Find the market solution in this case. e) Illustrate on a graph the solutions found in c) and in d). Explain why the market solution in d) does not coincide with that in c)