Consider an economy in which consumers live for 2 periods, 1 and 2, and have preferences...

  

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Consider an economy in which consumers live for 2 periods, 1 and 2, and have preferences U(c1, c2)= = 1 1.1 Consumers are born with no initial wealth, and work n₁ = n2 = 1 units of time in each period. They can save or borrow at a nominal interest rate i in period 1. The budget constraint of a consumer in period 1 is Pic₁ Wini - B and in period 2 is P2c2 W2n2+(1 + i)B where P1 and P2 are the price levels in the 2 periods, W₁ and W2 are the nominal wage rates in the 2 periods and B is the amount the consumer saves. There is no government spending, investment or net exports in this economy. 1. Prove that the consumer's life-time budget constraint is 1 1 C1 + C₂ = win1 + աշոշ 1+r 1+r where r, w₁, and w2 are the real interest rate and the real wage rates in the two periods. Derive the relationship between r and the nominal prices and interest rate in the economy. 2. Prove that the consumer's optimal choice of consumption in the 2 periods gives rise to the following optimality condition: 1 1+ 1 = 1.1 √√2 3. Suppose that firms produce output using technology Yt = Atlt in both periods, t = 1,2, where At is productivity and It is the amount of labor firms hire. Calculate the equilibrium real wage rates, wt, in both periods, as a function of productivity, At, and the underlying parameters of the model. 4. Suppose that A₁ = 1 and A2 = 1. What are r, y₁, and y2 equal to? Suppose instead that A₁ = 121 and A2 = 1. What are r, y₁, and y2 equal to now? 5. Explain the economic intuition behind your numerical results in the previous question. In particular, how and why does a decrease in productivity in period 1 affect output and the real interest rate in the economy? 6. Suppose that consumers are more impatient and value period 2 consumption relatively less. In particular, suppose that consumer preferences are now: 1 U (c1, c2)=√√√1 + C2 1.2 Calculate what this change in preferences would do to real wages, real interest rates, and output in the 2 periods. If it helps, assume that A₁ = A2 = 1. 7. Explain the economic intuition behind your numerical results in the previous question. In particular, how and why does a demand shock (an increase in consumer's desire to consume in period 1) affect output and the interest rate in the economy? Consider an economy in which consumers live for 2 periods, 1 and 2, and have preferences U(c1, c2)= = 1 1.1 Consumers are born with no initial wealth, and work n₁ = n2 = 1 units of time in each period. They can save or borrow at a nominal interest rate i in period 1. The budget constraint of a consumer in period 1 is Pic₁ Wini - B and in period 2 is P2c2 W2n2+(1 + i)B where P1 and P2 are the price levels in the 2 periods, W₁ and W2 are the nominal wage rates in the 2 periods and B is the amount the consumer saves. There is no government spending, investment or net exports in this economy. 1. Prove that the consumer's life-time budget constraint is 1 1 C1 + C₂ = win1 + աշոշ 1+r 1+r where r, w₁, and w2 are the real interest rate and the real wage rates in the two periods. Derive the relationship between r and the nominal prices and interest rate in the economy. 2. Prove that the consumer's optimal choice of consumption in the 2 periods gives rise to the following optimality condition: 1 1+ 1 = 1.1 √√2 3. Suppose that firms produce output using technology Yt = Atlt in both periods, t = 1,2, where At is productivity and It is the amount of labor firms hire. Calculate the equilibrium real wage rates, wt, in both periods, as a function of productivity, At, and the underlying parameters of the model. 4. Suppose that A₁ = 1 and A2 = 1. What are r, y₁, and y2 equal to? Suppose instead that A₁ = 121 and A2 = 1. What are r, y₁, and y2 equal to now? 5. Explain the economic intuition behind your numerical results in the previous question. In particular, how and why does a decrease in productivity in period 1 affect output and the real interest rate in the economy? 6. Suppose that consumers are more impatient and value period 2 consumption relatively less. In particular, suppose that consumer preferences are now: 1 U (c1, c2)=√√√1 + C2 1.2 Calculate what this change in preferences would do to real wages, real interest rates, and output in the 2 periods. If it helps, assume that A₁ = A2 = 1. 7. Explain the economic intuition behind your numerical results in the previous question. In particular, how and why does a demand shock (an increase in consumer's desire to consume in period 1) affect output and the interest rate in the economy?

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1 To prove the consumers lifetime budget constraint we start with the assumption that the consumers income in period 1 wage multiplied by labor supply is spent on consumption in period 1 c1 and saved ... View the full answer