Question

Low Wages, High Wages, and Taxes. There are two categories of people: those that receive high nominal wages and those that receive low nominal wages. Denote these two nominal wages as WH (high wages) and WL (low wages), respectively, and WH > WL .

The utility function for each person, regardless of the nominal wage he/she receives, is identical: u (c,l) =lnc +lnl , in which, exactly as in Chapter 2, c stands for consumption and l stands for leisure. Furthermore, after defining n as labor, keep in mind that n + l = 1 (which is also identical to the framework considered in Chapter 2).

The labor income tax rate for individuals that earn high wages is t^H (the Greek lowercase letter “tau”), and the labor income tax rate for individuals that earn low wages is t^L. To complete the notation, P is the nominal price for each unit of c (which, once again, is identical to the notation in Chapter 2).

The rest of this question focuses on the tax rates t^L and  t^H . For the sake of clarity, suppose that WH , WL , and P are all unaffected regardless of the particular policy setting of the two tax rates.

g. If t^H = t^L, could it be the case that low-wage individuals’ optimal choices for both c and l are identical to the high-wage individuals’ optimal choices for c and l? More precisely, is it possible that their numerical values both for c* and l* could be the same? If so, briefly explain why using the results you obtained above. If not, briefly explain why not using the results you obtained above. If it’s impossible to determine, describe briefly why not.

Answer 1