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2 An equilibrium La'er curve (optional, not graded) The La'er curve relates the labor tax rate (it-axis) to the labor tax revenue {yaxis}. It was...
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This is a macroeconomics question.

1.2 An equilibrium Laﬂ'er curve (optional, not graded) The Laﬂ'er curve relates the labor tax rate (it-axis) to the labor tax revenue {y—axis}.
It was popularized by Arthur Laﬁ'er (at the time he was an economics professor at the
University of Southern California} when he tried to convince the Republican candidate
Ronald Reagan to decrease direct taxes in the 1981] presidential elmtion. Some years
before, during an afternoon meeting with Nixon/Ford Administration ofﬁcials Dick
Cheney and Donald Rumsfeld, Laffer sketched the curve on a napkinl. In this exercise, we are going to revise the Laﬂfer curve through the lenses of the
one-period model we studied in Lecture 3. In particular, we are going to derive the
Laﬂ'er curve as an equilibrium outcome of the model. For this purpose, consider the
same setting of problem set 1 and modify it as follow. Introduce a government that
needs to ﬁnance an exogenous government expenditure G through labor tax 7. The
Government collects tax income HUN&quot; and runs a balance budget constraint: mNs=G Re-solve all points in problem set 1, starting from re—writing the consumer’s budget
constraint. Stop at point 3.b when asked to solve for N in function of all exogenous
parameters. Now the equilibrium N also depends on 1'. The LaHer curve is given by the government revenue:
Rfr, cc, K, z,*y) E T ‘ w(1’,or, K, z, 7} - NU, cu, K, 41,7) Provide a closed-form formula for R(T,o, K , 2:, '7]. Plug the following parameters for
capital share ct = [L4, K = 65.7 trillions dollars and z = 1. Also consider two
cases T = 1 and ”y = 5, separately. Use a computer2 to graph the following curves:
Rfrl'y = 1), N(T|&quot;}‘ = 1), R(T|'y = 5) and N(T, hr = 5]. How does the prohibitive
range change in function of 7? Comment on your ﬁndings. Consider that the US government income tax over GDP is 24.1 %. Through the lenses
of our model, the corresponding tax rate T* to reach this objective is: Mﬂm =,. a=%e4o%
Y l—cu Is this taxation rate located in the prohibitive range or normal range? In light of this 7*wN =G =ﬂ.241 - Y =;. analysis, would you suggest to cut taxes in order to increase government revenue? 1Check the sketch for deﬁnition of prohibitive range and normal range
5*e.g.: Excel, Matlab, Python, Wolﬁamalpha etc.

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