Assume that individuals have the same utility function over consumption and labor given by: U(c,1) = (10) In(c) + 0 ln(501) where c represents consumption and constrained to be between 0 and 1. also be denoted by log(x)). represents hours of labor and is a given parameter, Here, In(x) denotes the natural logarithm of x (this can Assume also that the only income that individuals have is from labor income and that the hourly wage rate is given by w. (a) Write the budget constraint faced by the individual in a situation without taxes and transfers. [5 points] (b) Set up the maximization problem of this individual and solve for the optimal choices of labor and consumption. [10 points] (c) Now, suppose that there is a linear tax 7 on labor income. Solve for the new optimal choice of labor and consumption. [10 points]