The preferences of a consumer are represented by the utility function
U = X + 2(Y)1/2
a) In the initial situation, the prices of the commodities and the income of the
consumer are
P
X = 5 , PY = 1 and I = 150
Determine the optimal consumption vector (X*
, Y*
) and compute the
maximum utility (U*
) of the consumer.
b) Assume the government implements a commodity tax (t). In this situation,
we have
P
X = 5 + t , PY = 1 and I = 150
and
t = 5
i. Determine the optimal consumption vector, the maximum utility of the
consumer, and (iii) the government revenue from the tax.
ii. Given the new prices induced by the commodity tax, determine the
additional income the consumer would need to reach the same level of
utility (U*) as in the initial situation. How does this additional income
compare to the government revenue from the tax? Explain.
.
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The preferences of a consumer are represented by the utility functio.docx
1. The preferences of a consumer are represented by the utility
function
U = X + 2(Y)1/2
a) In the initial situation, the prices of the commodities and the
income of the
consumer are
P
X = 5 , PY = 1 and I = 150
Determine the optimal consumption vector (X*
, Y*
) and compute the
maximum utility (U*
) of the consumer.
b) Assume the government implements a commodity tax (t). In
this situation,
we have
P
X = 5 + t , PY = 1 and I = 150
and
t = 5
i. Determine the optimal consumption vector, the maximum
utility of the
consumer, and (iii) the government revenue from the tax.
ii. Given the new prices induced by the commodity tax,
determine the
additional income the consumer would need to reach the same
level of
utility (U*) as in the initial situation. How does this additional
income
compare to the government revenue from the tax? Explain.
