C in light of your answers above which of the two tax

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(c) In light of your answers above, which of the two tax policies would you recommend the government? Why? 2. A consumer spends her total income, m , on goods x 1 and x 2 with prices p 1 and p 2 , respectively. The price p 2 decreases and as a result the consumption of x 1 increases. Therefore: (a) x 1 is a normal good (b) x 2 is an inferior good (c) the consumption of x 2 may increase, but the total expenditure on x 2 does not change. Discuss each of the three statements above, indicating whether they are true or false . 1
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3. Consider a variation of the two-period model seen in class with interest rates r b and r ` for borrowing and lending, respectively. In the model discussed in class, we assumed that r b D r ` . Now suppose that r b > r ` > 0 . Also, assume that the consumer’s endowment is m 1 D m 2 D 1 . (a) What is the consumer’s intertemporal budget constraint? Plot the consumer’s bud- get set. (b) Suppose the consumer’s utility is u.c 1 ; c 2 / D .1 ˇ/ log c 1 C ˇ log c 2 ; where ˇ 2 OE0; 1Ł is a preference parameter. (c) What is the marginal rate of intertemporal substitution? Explain why the preference parameter ˇ can be interpreted as a measure of the consumer’s degree of patience. (d) Show that there exist thresholds ˇ and ˇ such that for ˇ < ˇ the consumer will be a borrower, for ˇ > ˇ the consumer will be a lender and for all ˇ in the interval OEˇ ; ˇ Ł the consumer will spend exactly his endowment in each period. (e) Show that ˇ is decreasing in r ` , that is, the lower the interest rate for lending, the more patient the consumer needs be in order to be willing to lend. 2
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