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A consumer's income in the current period is y=60, and income in the future period is y=100. He pays lump-sum taxes of T=20 in the current period and T'=20 in the future period. His utility function is u(c,c' )=logc+βlogc'. For simplicity, β=1 and the real interest rate is r=0.
a. Set up and solve the consumer's problem and find optimal c and c', assuming that the consumer is not credit constrained, i.e. he can borrow or save as much as he wants in the current period: what are the expressions and numerical values for consumption today, savings today and consumption tomorrow?
b. Suppose that government decides to give a tax cut on current taxes so that T decreases to 15
and T' increases to 25. Redo the computation in part (a). Do optimal c and c' change? Explain why or why not with reference to Ricardian Equivalence.
c. Now suppose that consumers are credit constrained so that they can save as much as they want in the current period but are unable to borrow at all (we must satisfy s>=0). Redo parts (a) and (b). Are optimal c and c' different? Explain why or why not with reference to Ricardian Equivalence.
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