Hi, please help me with the following question. Thanks in advance! Suppose that

Question

Hi, please help me with the following question. Thanks in advance!

Suppose that preferences for x1 and x2 are represented by right-angle indifference curves:

(x1 on x axis and x2 and y axis, and the equation of the line is x2=2x1)

a. Find the demand functions for the two goods as a function of p1, p2, and I.

b. Suppose that good 1 is taxed with a per-unit tax $t. Illustrate the effect on the consumer's optimum, and show the amount of the tax collected in units of good 2.

c. Instead of a tax on good 1, the government proposes a lump sum tax. Illustrate the budget constraint for the consumer assuming the lump sum tax raises the same revenue as the per unit tax. How does the optimum differ depending on which tax is used? Why?

d. Find the expenditure function for the consumer, and the compensated demand functions when the consumer is given enough income to reach a level of utility U. Take the derivatives of the expenditure function with respect to p1, p2 and verify that these are equal to the compensated demand functions

Explanation / Answer

Given the goal of consumers is to maximize utility given their budget constraints, they seek that combination of goods that allows them to reach the highest indifference curve given their budget constraint. This occurs where the indifference curve is tangent to the budget constraint (combination A). Note that combinations B and C cost the same amount as A; however, A is on a higher indifference curve. Combination D yields that same utility as C and B but doesn

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