Optimal behaviors The representative consumer maximizes (2) subject to (3) and (4).
The first order conditions yield:
ct = 1⅛ (1 -τt)wt'
st = + (1 - τt ) wt.
The representative firm must only choose the labor input and maximizes profits subject
to (1). Marginal productivities are thus equal to factors prices:
Rt = αAktα-1 ,
wt = (1 - α)Aktα .
The savings function is therefore:
st = ι+β(1 - τt)(1 - α)Akt. (6)
Savings increases with the wage and decreases with the income tax.
2.2 The dictatorial regime
At the initial date, t = 0, the dictatorial regime is already in place starting with initial
conditions reflecting its history. The objective is to study dictatorship from date t = 0
onwards.
important for the analysis is that the public good, whatever it is, requires an authority to deliver it. If
the authority breaks down, there is no spontaneous private substitute for this public good.
12
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