Question: There is one (representative) consumer. The utility function of the consumer is u(x1,x2)=(x1)4(x2), p1=2,p2=1, and the consumer's wealth w=25. (a) Find the consumer's optimal consumption

There is one (representative) consumer. The utility function of the consumer

There is one (representative) consumer. The utility function of the consumer is u(x1,x2)=(x1)4(x2), p1=2,p2=1, and the consumer's wealth w=25. (a) Find the consumer's optimal consumption plan. (b) The government subsidizes good 1 with a 50% price subsidy. So the effective price the consumer pays now is p1/2, i.e., the government pays the other 50% of the price for the good 1 that consumer buys. Find the optimal consumption plan under the subsidy. (c) How much does the subsidy cost the government? (d) Suppose, instead, the government subsidizes income (wealth) by an amount that is equal to the cost of the price subsidy (that you determined in (c)). Find the optimal consumption plan under the income subsidy. (e) Demonstrate that the consumer is better off, i.e., obtains a higher utility value, with the income subsidy than with the price subsidy. There is one (representative) consumer. The utility function of the consumer is u(x1,x2)=(x1)4(x2), p1=2,p2=1, and the consumer's wealth w=25. (a) Find the consumer's optimal consumption plan. (b) The government subsidizes good 1 with a 50% price subsidy. So the effective price the consumer pays now is p1/2, i.e., the government pays the other 50% of the price for the good 1 that consumer buys. Find the optimal consumption plan under the subsidy. (c) How much does the subsidy cost the government? (d) Suppose, instead, the government subsidizes income (wealth) by an amount that is equal to the cost of the price subsidy (that you determined in (c)). Find the optimal consumption plan under the income subsidy. (e) Demonstrate that the consumer is better off, i.e., obtains a higher utility value, with the income subsidy than with the price subsidy

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