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Suppose a government has to decide on a budget. Its tax revenue

Suppose a government has to decide on a budget. Its tax revenue in 2012 is Y and its tax revenue in2013 will be kY , where k > 1 is the growth rate of the economy. The government has to decide howmuch to spend this year, x1, and how much to spend next year, x2. Because of the poor economy thisyear, the government will certainly run a deÖcit x1Y> 0. For each dollar of deÖcit, the governmentwill have to pay bond holders 1 + r dollars next year, where r > 0 is the interest rate. Next year,the government can spend its 2013 tax revenue kY , minus what it will owe bond holders to Önancethe 2012 deÖcit. (The government cannot continue to run a deÖcit in 2013). The governmentísobjective function is U(x1; x2) = v(x1) + v(x2), where v refers to the annual social beneÖt generatedby government spending. Assume v is C2, v0(c) > 0 and v00(c)


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