Optimal Labor Income Tax Policy: Consider our static (i.e., one period) consumption-leisure framework. In this problem, you will use this framework as a basis for offering guidance regarding optimal labor income tax policy. Recall the basic consumption-leisure optimality condition

ul (c, l)
uc (c, l)
= (1 − τ
n
)w

Suppose that now rms are monopolistically competitive (rather perfectly competitive). It can be shown in this case that when RMS are making their profit-maximizing choice regarding labor hiring, the following condition is true:

MP N = w(1 − monpol)

Here, MP N denotes the marginal product of labor and monpol is a measure of the degree of monopoly power that rms wield. For example, if monpol = 0, then rms wield no monopoly power whatsoever, in which case we are back to our perfectly-competitive framework of rm profit maximization from Chapter 4. If instead monpol > 0, then rms do wield some monopoly power. (Notes: The variable monpol can never be less than zero. You also do not need to be concerned here with how the above expression is derived just take it as given).
Now suppose that:
1. Any monopoly power that rms have cannot be directly eliminated by the government. That is, if monpol > 0, the government cannot do anything about that; all the government can do is to choose a labor income tax rate τn.

2. Instead of sending a tax rate that maximizes its revenue, the only goal that the government has is to choose a labor tax rate to ensure that the perfectly-competitive ecient outcome in labor markets is attained.
Based on all of the above, derive a relationship between the optimal (i.e., in the sense that it attains the goal of the government described in point #2 above) labor income tax rate and the degree of rms' monopoly power. Very carefully explain all your logic and arguments, including any mathematical derivations involved.