Consider the consumption-labor model of chapter 2 where a representative consumer has the following utility function over consumption and labor:

u(c, n) = ln c + A ln l,

where c and l represent consumption and leisure hours. Here, A is a positive parameter outside the control of the agent. Also suppose that the real budget of the consumer is:

c = (1 - t) x w x (1 - l),

where t is the labor tax rate, and w is the real hourly wage rate (W/P ). Finally, labor and leisure hours are normalized to one:

1 = l + n,

(a) Set up the Lagrangian and compute the representative consumer's rst-order conditions with respect to consumption and leisure.

(b) Based on both the rst order conditions, solve for the optimal choices of consumption and leisure.

(c) Plot the theoretical labor supply curve against the wage rate.

(d) Macroeconomist and Nobel Laureate Edward Prescott's empirical work indicates that the reason Europeans leisure more than Americans is that wages are taxed more heavily in Europe. That is, Europeans face lower net wages and thus choose to work less. Based on your analysis above, is Prescott correct? If not, what would you need to change in the above analysis to match Prescott's work? Explain.