Problem 10.2: Ricardian Equivalence with borrowing constraints. (20 points) Consider an economy in which agents live...

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Problem 10.2: Ricardian Equivalence with borrowing constraints. (20 points) Consider an economy in which agents live for two periods. They are born with $50,000 of wealth in the first period, and receive an income of $30,000 in their first period and $100,000 in their second period. They can freely save and borrow at a nominal interest rate of 5%. The price level is is equal to P₁ = $1 in period 1 and P2 = $1.03 in period 2. Government spending is equal to $50,000 in the first period and $75,000 in the second period. The agent's utility function is: u(c₁, c₂)=√c₁ + -3³-√C₂² C2 4 (a) Suppose that taxes are equal to $60,000 in the first period. Calculate i) how much the government needs to tax in the second period, ii) the agent's consumption in the two periods of its life and iii) the agent's savings/borrowing decision in the first period of its life. (b) Suppose next that taxes are equal to $40,000 in the first period. Calculate i) how much the government needs to tax in the second period, ii) the agent's consumption in the two periods of its life and iii) the agent's savings/borrowing decision in the first period of its life. (c) Suppose next that agents cannot borrow but are allowed to save. Calculate the household's consumption in the two periods of its life under the assumption that i) taxes are equal to $60,000 in the first period and ii) taxes are equal to $40,000 in the first period. (d) Use your answers above to more generally describe the effect of changes in the size of govern- ment expenditure on consumption in the presence and absence of borrowing constraints. Problem 10.2: Ricardian Equivalence with borrowing constraints. (20 points) Consider an economy in which agents live for two periods. They are born with $50,000 of wealth in the first period, and receive an income of $30,000 in their first period and $100,000 in their second period. They can freely save and borrow at a nominal interest rate of 5%. The price level is is equal to P₁ = $1 in period 1 and P2 = $1.03 in period 2. Government spending is equal to $50,000 in the first period and $75,000 in the second period. The agent's utility function is: u(c₁, c₂)=√c₁ + -3³-√C₂² C2 4 (a) Suppose that taxes are equal to $60,000 in the first period. Calculate i) how much the government needs to tax in the second period, ii) the agent's consumption in the two periods of its life and iii) the agent's savings/borrowing decision in the first period of its life. (b) Suppose next that taxes are equal to $40,000 in the first period. Calculate i) how much the government needs to tax in the second period, ii) the agent's consumption in the two periods of its life and iii) the agent's savings/borrowing decision in the first period of its life. (c) Suppose next that agents cannot borrow but are allowed to save. Calculate the household's consumption in the two periods of its life under the assumption that i) taxes are equal to $60,000 in the first period and ii) taxes are equal to $40,000 in the first period. (d) Use your answers above to more generally describe the effect of changes in the size of govern- ment expenditure on consumption in the presence and absence of borrowing constraints.

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a i Government spending in period 1 is 50000 and taxes are 60000 so the government needs to tax 0 in ... View the full answer