3. Consider a two period problem where a consumer has preferences over consumption in the two...

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3. Consider a two period problem where a consumer has preferences over consumption in the two periods given by: log c + Blog c'. She has no initial assets and has income y in the first period y' in the second, pays taxes (net of benefits) T in the first and T' in the second, and can borrow and lend (s) at interest rate r, thus giving the two flow constraints: c+s=y-T, c' = (1 + r)s + y' T'. The government finances spending through taxes and borrowing: G=T+B, G' + (1+r)B = T', where the government borrows at a lower rate than households: G < r. (a) Solve for the agent's optimal consumption choices c and c' and savings s. (b) Now suppose that the government cuts taxes in the current period, so T falls by some amount A, but government spending is unchanged. Thus future taxes must rise to pay back the principal and interest on the deficit this policy creates. How does this affect the consumer's optimal choices? 3. Consider a two period problem where a consumer has preferences over consumption in the two periods given by: log c + Blog c'. She has no initial assets and has income y in the first period y' in the second, pays taxes (net of benefits) T in the first and T' in the second, and can borrow and lend (s) at interest rate r, thus giving the two flow constraints: c+s=y-T, c' = (1 + r)s + y' T'. The government finances spending through taxes and borrowing: G=T+B, G' + (1+r)B = T', where the government borrows at a lower rate than households: G < r. (a) Solve for the agent's optimal consumption choices c and c' and savings s. (b) Now suppose that the government cuts taxes in the current period, so T falls by some amount A, but government spending is unchanged. Thus future taxes must rise to pay back the principal and interest on the deficit this policy creates. How does this affect the consumer's optimal choices?

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a To solve for the agents optimal consumption choices and savings we start by rewriting the flow con... View the full answer