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3 Ricardian equivalence Consider a consumer who consumes two \"goods\": consumption in period 1, (:1, and consumption in period 2, (:2, with utility function U051, (22). The consumer has income I in both periods. Let the interest rate be r > 0. 3.1 State the budget constraint for the consumer. Suppose the government needs to raise a xed amount of revenue T in each period. In what follows, we shall discuss two options for raising this required revenue. 3.2 The rst option is to levy a proportional income tax of t in each period, where t is set so that H : T. Here we are thinking this consumer as a representa tive consumer and there is only one consumer in the economy. Write the new budget constraint for this consumer, and nd the rstorder conditions for the consumer's utility maximization. 3.3 The second option for raising the required revenue in each period is that the government considers collecting taxes only in the second period, and borrows money in the rst period to cover its rstperiod expenditure. Suppose the second period tax is T, then T must be such that T] = T +(1+ HT, where 7\" is the interest rate. Write the new budget constraint for the consumer in this case and nd the rstorder conditions for utility maximization for the problem. 3.4 Compare your rst order conditions in 3.2 and in 3.3 and show that they are identical (so that the consumer's utilities are the same for the two options). If you have followed the above, then you have just (re)discovered the socalled Ricardian equivalence (after the English economist David Ricardo): how the government nances its expenditure, via taxation or borrowing, is irrelevant to the individuals in the economy. ln reality, however, we often hear constant warnings about the dangers of bor rowing to nance government expenditures and arguments that the government debt is too high. Some even go on to propose that the government must be required to balance its budgets. These warnings and arguments sugest that people do view how the government nances its expenditures matters. So, what is missing from this simple model? You need not answer this part