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
PX = 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
PX = 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.