This question was asked in a micro exam last semester and I just dont know the answer, have been thinking about it for weeks. Please help.
In a Robinson Cruse Economy Robinson produces Coconuts (C) and Fish (F) with Labour (L).
The Production functions are:
C(Lc) = Lc^0.5
F(Lf) = Lf^0.5
his utility function is: u= C*F
A politician wants Robinson to introduce a tax on the consumption of coconuts of 300% (The consumer has to pay Cpc and in addition 3pc*C to the government)
Robinson thinks that he will be worse off after the introduction of the tax. The politician tells him that wont be the case, because all the tax money will be paid back to the consumer as „coconut money".
Task: Use the Robinson Crusoe Modell to find out how much C and F Robinson consumes with tax. The coconut money he gets from the government doesnt depend on his consumption.
The optimum without tax is: F=C= 40^0.5
(when the consumer chooses C and F, to maximise CF s.t. pcC+3pcC+pfF= w80+profit+M (M=coconut money), he assumed that the profit and M dont depend on his consumption)