Ricardian equivalence please help by writing out I need help with 3.1 3.2 and 3.3

Consider a consumer who consumes two \"goods\": consumption in period 1, c1, and consumption in period 2, 03, with utility function U (c1, (:2). 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 t! = 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 rst-order 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 rst-period expenditure. Suppose the second period tax is 7', then 1" must be such that TI = T + (1 + r)T, where r is the interest rate. Write the new budget constraint for the consumer in this case and nd the rst-order 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)