Consider an individual whose utility function takes the form: ln(c)+2ln(100l), where c is weekly consumption in dollars (we normalize the price of consumption to 1), and l is weekly hours worked (of a maximum of 100 available hours per week). Individuals have a wage equal to 62 (dollars an hour), and additional non-wage income equal to $230.

(a) Write down the maximization problem that you need to solve.

(b) Compute the optimal combination of hours worked, leisure and consumption.

(c) Suppose now that the government imposes a tax of 25% on labor income and a tax of 15% on consumption. Write down the maximization problem and compute how the policy aects the behavior of this individual.

(d) Compute the revenues that the government collects. Suppose now that the government collects directly the tax revenues independently of the individual choices (a lump sum tax). Write down the maximization problem and compute how behavior changes. Is the individual's welfare higher or lower?