C File | C:/Users/AMALITECH%20PC%2056/Downloads/assign1.pdf + Co Page view | A Read aloud Mela A Highlight Erase 1. Omar's preferences over consumption (C) and hours of leisure (L) are represented by the utility function: U = In(C) +al, where a is a parameter measuring her taste for leisure. Omar earns money by working. His weekly constraint is given by C + WL = 168w, where w is Omar's hourly wage rate . (a) Find Omar's optimal consumption and hours of leisure in terms of w. [Note: You may assume that there is an interior solution.] (b) Use the envelope theorem to find an expression for OU* /da. (c) Use your answer from part (a) to find an expression for U* in terms of w and a and verify your answer in part (b) by differentiating the resulting maximum value function with respect to a. 2. A firm's profits, 7, depend on the quantity of capital, K and labour, L, that it hires, according to the following expression