Consider an economy where the representative consumer has a utility function u (C; L)over consumption C and leisure L. Assume preferences satisfy the standard properties we saw in class. The consumer has an endowment of H units of time thatthey allocate to leisure or labor. The consumer also receives dividends, D, from therepresentative firm. The representative consumer provides labor, Ns, at wage ratew, and receives dividends D, from the representative firm.The representative firm has a production technology given by Y = AF (K; N) whereK is the fixed capital input and N is labor input.Please answer abcde please!

Consider an economy where the representative consumer has a utility function u (C, L) over consumption C and leisure L. Assume preferences satisfy the standard prop- erties we saw in class. The consumer has an endowment of H units of time that they allocate to leisure or labor. The consumer also receives dividends, D, from the representative firm. The representative consumer provides labor, N., at wage rate w, and receives dividends D, from the representative firm. The representative firm has a production technology given by Y = AF (K, N) where K is the fixed capital input and / is labor input. (A) Set up the consumer's problem. (B) The general formula for the optimality condition of the consumer's problem is (Relative price of leisure in terms of consumption) MUC = MUL where MUC and MUL are the marginal utility of consumption and the marginal utility of leisure respectively. Use this expression to write a set of equations that implicitly allow you to find the optimal labor supply N', optimal consumption, C', and optimal leisure, Zo, as a function of (w, D). Assume for the remaining parts of this exercise that the utility function is given by over consumption O and leisure A, |where op - 0. with the marginal utilities given by: (4) "c(CL) - - 2 (8 -210 (5) (c) (4 points) Use this specification for the utility function to find optimal labor supply /', optimal consumption, C', and optimal leisure, 4', as a function of (w, D) from the optimality conditions you derived in 2a. (D)) Use the above optimality conditions to assess how the optimal supply of labor, " responds to a change in dividends. (E)) ) How does optimal consumption respond to a change in dividends? What is going on? Consumption changes as much as dividends. All changes in dividends are absorbed by consumption with no response from leisure or labor supply. This utility function is such that there is no income effect on leisure or labor supply