(20 points) Consider an economy where the representative consumer has a utility function 11. (0,13) over consumption 0 and leisure L. Assume preferences satisfy the standard properties we saw in class. The consumer has an endowment of H units of time, faces a wage rate 10 and receives prots H from the representative rm. The govemment subsidizes consumption paying the representative consumer an amount proportional to their consumption expenditures, 3 - C, where 3 is a pro- portional subsidy rate, with 3 E (D, 1). The government expenditures incurred with this subsidy policy are nanced by a tax levied on the representative rm. In this exercise we will take the impact of that tax into consideration. (a) (4 points) Write the consumer's budget constraint, derive the relative price of leisure in terms of consumption. (b) (4 points) Set up the consumer's problem and derive the optimality conditions, a set of equations that will allow you to nd the optimal labor supply N\Assume for the remaining parts of this exercise that the utility function is given by 15((3', L) : logC + @109; L over consumption 0 and leisure L, where T > 0. (c) (4 points) Use this utility function to nd optimal labor supply N*, optimal consumption, 0*, and optimal leisure, L\