題組內容

2. Consider a worker whose utility depends on consumption and leisure. The worker's income comes from labor income and non-labor income. The worker's utility maximization problem is given by: $$\underset{C,N}{Max} \quad U = \ln C + \beta \ln(H - N)$$ $$s.t. \quad C = wN + v$$ where C denotes consumption, N denotes hours of labor supplied, H is the total time endowment, w is the real wage, v > 0 is non-labor income, and $\beta > 0$ measures the relative importance of leisure in utility. The worker takes w, v, H, and $\beta$ as given. Complete the following tasks:

(b) Solve for the worker's optimal consumption \( C^* \) and optimal labor supply \( N^* \). (5%)