Consider a representative consumer who maximizes his life-time utility: 1 max log C + - log...

  

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Consider a representative consumer who maximizes his life-time utility: 1 max log C₁ + - log C₂, C1,C₂ 1+p where C₁ and C₂ denote consumption in the first and second period respectively, and p> 0 denotes the time preference rate. Suppose that the consumer receives income Y₁ and Y₂ in the first and second period respectively, and the consumers have access to the financial market where they can freely borrow or lend at the interest rate r. (a) Write down the consumer's budget constraint. (b) Solve the optimization problem and write the optimal consumptions (C₁, C₂) and savings (S*) as functions of Y₁, Y2, p and r. (c) How does saving and C₂ change if p increases? Interpret these changes. (d) What % does C₁ change if r increases by 1%? (e) What % does C₂ change if r increases by 1%? Now, we introduce government that collects proportional income taxes with the tax rate 7 and returns the tax revenues to the consumer as a lump-sum transfer Teach period. (f) Solve the consumer's utility maximization problem with the government tax- transfer policy as specified above and write the optimal consumptions (C+, C₂) as functions of Yı, Y2, p, r, 7 and T. (g) What should be in order to satisfy the budget balance over two periods taking T as exogenously given? How much should the government borrow in the first period? (h) What would happen to C₁, C₂ if the government increases T while the government maintaining the budget balance over two periods? Does the Ricardian equivalence theorem hold in this economy? Consider a representative consumer who maximizes his life-time utility: 1 max log C₁ + - log C₂, C1,C₂ 1+p where C₁ and C₂ denote consumption in the first and second period respectively, and p> 0 denotes the time preference rate. Suppose that the consumer receives income Y₁ and Y₂ in the first and second period respectively, and the consumers have access to the financial market where they can freely borrow or lend at the interest rate r. (a) Write down the consumer's budget constraint. (b) Solve the optimization problem and write the optimal consumptions (C₁, C₂) and savings (S*) as functions of Y₁, Y2, p and r. (c) How does saving and C₂ change if p increases? Interpret these changes. (d) What % does C₁ change if r increases by 1%? (e) What % does C₂ change if r increases by 1%? Now, we introduce government that collects proportional income taxes with the tax rate 7 and returns the tax revenues to the consumer as a lump-sum transfer Teach period. (f) Solve the consumer's utility maximization problem with the government tax- transfer policy as specified above and write the optimal consumptions (C+, C₂) as functions of Yı, Y2, p, r, 7 and T. (g) What should be in order to satisfy the budget balance over two periods taking T as exogenously given? How much should the government borrow in the first period? (h) What would happen to C₁, C₂ if the government increases T while the government maintaining the budget balance over two periods? Does the Ricardian equivalence theorem hold in this economy?

Answer rating: 100% (QA)

a The budget constraint is C1 S Y1 C2 Y2 1rS b The Lagrangean is L logC1 11logC2 Y1 C1 S Y2 1... View the full answer