Question

3 Consumption Taxes and Ricardian Equiv- alence (8 points) Suppose a consumer has income y in period 1, y' in period 2, and faces a proportional tax on consumption. That is if consumption is c in period 1 'and c' in period 2, the consumer pays a tax sc on period 1 consumption and s'c' ou period 2 consumption. Thuss and s' represent the rate of sales tax in each period. The government wishes to collect total tax revenue in periods 1 and 2, which has present value of R. Now suppose that the government reduces s and increases s' in such a way that R is unaffected. 1. Write down the lifetime budget constraint of the consumer. (2 points 2. Show that the lifetime wealthof the consumer is the same before and after the tax rate change. (2 points) 3. What effect, if any, does the change in tax rates have on the consumer's choice of current and future consumptions, and on savings? (2 points) 4. Does Ricardian equivalence hold here? Explain why or why not. (2 points)

Answer 1

Solution: (3) consumption taxes and Richardian Equivalence: O lifetime budget constraint of the Consumer: → Budget anstraint in the current period is c+S = y-TC Budget Constraint in future period is c = y'-T'el +(1+r)s. Then 's cl_yltt'c' to Substituting it into ament period bodget constraint we can obtain life time budget Constraint of: ct cly't Tlc - gate 1+ 8 cuenta - YouT' = y.to CV C+ c = 4 -10 + y'-T'd HO TY

There.fore life time budget constraint would bei + 1x=y-Tc + yl_TIJ Ity same before (2) lifetime wealth of the consumes is the and after the tax rate change: Ttot and increase thot - let government reduces then accordingly: on z tetto - To TC + T c 1 ltr ity life time faving is the life is the life time wealth we can get life time wealth by substracting life time consumption from life time income. Thus before change, life time wealth would be: + Td y y + - - 4+TC -y TTT I+Y H78 = Tettle THE

Similarly after change life time wealth would be: tot t'c 1+8 Both are same. , (3) change in tax rates have on consumers, effectis: > life time belget constraint, after change would be: ctedy = y-tc to you thing ct en n = 9-te to the y (te tot goed It is seen that te + the Te te Tlol Then et d - yt fic at the end = y-tc't y! -tid 1+8 1+%

" As the budget constraint remain same, there is no change in consumes & choice of current and forture consumption and so as savings. (4 Ricardian equivalence hold ornot: Yes, Ricardian equivalence holds here Reason: Because the government Revenue of life time fax revenue is same in both cases, it does not affect consumers choic of their ultimate life time tax payment ramains same