2. (14 points) Consider an economy where the representative consumer has a utility function a(C,L) 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 in and receives prots H from the representative rm. The government subsidizes consumption paying the representative consumer an amount proportional to their consmnption expenditures, 3 . C, where s is a pro- portional subsidy rate, with s E (I), 1). The government expenditures incurred with this subsidy policy are nanced by a tax levied on the representative rm. In this exercise we will not take the impact of that tax into consideration. (a) (3 points) Write the consumer's budget constraint (b) (4 points) Derive the relative price of leisure in terms of consumption. {(3) (3 points) Set up the consumer's problem (d) (4 points) derive the optimality conditions, a set of equations that implicitly allow you to nd the optimal labor supply A", optimal consumption, C\