Please answer the following questions:

Consider the utility function U(c, () = \\(c+1)( . Let the wage rate, non-labor income, maximum time available, and price of the consumption good c be denoted by w, I, T, and p. respectively. Let the optimal consumption and leisure be denoted by c' and (" , respectively. (a) Find c and (" . What is the condition that guarantees (" 0. Calculate the reservation wage w . Prove that w > w. What is the economic interpretation of this result