Question 3. [Lump Sum Principle] Suppose we use fixed proportions utility function with their optimal quantity choices as below. utility = U(x, y) = min(x, 2y), I I Px +0.5py 2px + Py ➡) Suppose px = $1,py = $2 and 1(= income) = $10. Calculate the indirect utility in this a) case. c) x* y* = b) ( Now a tax of $1 is levied on good x. Calculate the indirect utility after tax, and the tax collection amount. Show that the lump sum income tax of the same tax collection amount from b) leaves the utility level the same as in b).

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Chapter6: Consumer Choice And Demand
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Question 3. [Lump Sum Principle]
Suppose we use fixed proportions utility function with their optimal quantity choices as below.
utility = U(x, y) = min(x, 2y),
I
I
Px + 0.5py
2px + Py
Suppose px = $1,Ppy = $2 and 1(= income) = $10. Calculate the indirect utility in this
a)
b)
c)
d)
case.
x*
y*
Now a tax of $1 is levied on good x. Calculate the indirect utility after tax, and the tax
collection amount.
Show that the lump sum income tax of the same tax collection amount from b) leaves the
utility level the same as in b).
) Explain why the after-tax utility is the same under both the excise tax and the lump sum
income tax in this utility function case.
Transcribed Image Text:Question 3. [Lump Sum Principle] Suppose we use fixed proportions utility function with their optimal quantity choices as below. utility = U(x, y) = min(x, 2y), I I Px + 0.5py 2px + Py Suppose px = $1,Ppy = $2 and 1(= income) = $10. Calculate the indirect utility in this a) b) c) d) case. x* y* Now a tax of $1 is levied on good x. Calculate the indirect utility after tax, and the tax collection amount. Show that the lump sum income tax of the same tax collection amount from b) leaves the utility level the same as in b). ) Explain why the after-tax utility is the same under both the excise tax and the lump sum income tax in this utility function case.
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