Consider the following two period economy. Let the utility function of the agent be u (C,...

 

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Consider the following two period economy. Let the utility function of the agent be u (C₁, C₂) Blog (c₁) + (1-3) log (C₂) The budget constraints of the agent in each period are given by: Period 1 Pic₁ + b₁ = a Period 2 P₂c2 + b₂ = 1-a+(1+r) b₁ where P₁ is the price of the consumption good at time 1, P₂ is the price of the consumption good at time 2, b₁, b2 are the agent's bond holdings, r is the interest rate and a, 1-a are his endowments in periods 1 and 2, respectively. We assume that a < 1. 1. Derive the intertemporal budget constraint. 2. Write the Lagrangean of his problem using the interemporal budget contraint. 3. Solve the problem of the agent. Write the FOC and clearly show the Euler equation. 4. What are his optimal holding of bonds by and b₂? 5. What are the optimal consumption of goods in each period (C₁, C₂) ? 6. Consider a change in the agents endowment. Suppose that a goes down. Show graphically the income and substitution effect. 7. Consider a change in the price of the consumption good at time 2 P2. Suppose that P2 goes up. Show graphically the income and substitution effect. 8. Suppose that the interest rate increases, what is the effect over the savings rate of the agent from this increase? Will he save more or less? You need to derive an expresion for the savings rate (savings/income) 9. Find the value of the interest rate r such that the agent has no holding og bonds. (0 savings) 10. Now suppose that a = 8. What are the optimal savings of the agent and how does it change with 3? Give an economic intuition for this result. Consider the following two period economy. Let the utility function of the agent be u (C₁, C₂) Blog (c₁) + (1-3) log (C₂) The budget constraints of the agent in each period are given by: Period 1 Pic₁ + b₁ = a Period 2 P₂c2 + b₂ = 1-a+(1+r) b₁ where P₁ is the price of the consumption good at time 1, P₂ is the price of the consumption good at time 2, b₁, b2 are the agent's bond holdings, r is the interest rate and a, 1-a are his endowments in periods 1 and 2, respectively. We assume that a < 1. 1. Derive the intertemporal budget constraint. 2. Write the Lagrangean of his problem using the interemporal budget contraint. 3. Solve the problem of the agent. Write the FOC and clearly show the Euler equation. 4. What are his optimal holding of bonds by and b₂? 5. What are the optimal consumption of goods in each period (C₁, C₂) ? 6. Consider a change in the agents endowment. Suppose that a goes down. Show graphically the income and substitution effect. 7. Consider a change in the price of the consumption good at time 2 P2. Suppose that P2 goes up. Show graphically the income and substitution effect. 8. Suppose that the interest rate increases, what is the effect over the savings rate of the agent from this increase? Will he save more or less? You need to derive an expresion for the savings rate (savings/income) 9. Find the value of the interest rate r such that the agent has no holding og bonds. (0 savings) 10. Now suppose that a = 8. What are the optimal savings of the agent and how does it change with 3? Give an economic intuition for this result.