Consider a model in which individuals live only two periods. Individuala maximize the following utility function...

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Consider a model in which individuals live only two periods. Individuala maximize the following utility function 3 2 U=In(C₁) +ln(C₂), where C₁ is the consumption in period 1 and C₂ is the consumption in period 2. In each period there are N young individuals and N old individuals. An individual receives an income of $300 in period 1 and no income in period 2. The market interest rate is 5 percent, and the person can borrow or lend money at this rate. (a) Use a diagram of indifference curves and an intertemporal budget constraint to illustrate the individual's optimal consumption in each period, if there is no public pension system. Make sure you label the axes and provide the numerical value of the slope of the budget constraint. [1 mark] (b) Write down the individual's lifetime budget constraint and solve to find C₁, C₂ and S, which is personal savings. [2 marks] (c) Now assume that the government introduces a public pension program. The government takes $50 from each individual in period 1 and gives it directly to individuals in period 2. i. What is the terminology for this public pension program? [1 mark] ii. How much does an individual privately save now? [2 marks] iii. How does an individual's utility with the public pension system compare to an indi- vidual's utility without the public pension system? [1 mark] iv. Explain the intuition behind your findings in iii. [1 mark] Consider a model in which individuals live only two periods. Individuala maximize the following utility function 3 2 U=In(C₁) +ln(C₂), where C₁ is the consumption in period 1 and C₂ is the consumption in period 2. In each period there are N young individuals and N old individuals. An individual receives an income of $300 in period 1 and no income in period 2. The market interest rate is 5 percent, and the person can borrow or lend money at this rate. (a) Use a diagram of indifference curves and an intertemporal budget constraint to illustrate the individual's optimal consumption in each period, if there is no public pension system. Make sure you label the axes and provide the numerical value of the slope of the budget constraint. [1 mark] (b) Write down the individual's lifetime budget constraint and solve to find C₁, C₂ and S, which is personal savings. [2 marks] (c) Now assume that the government introduces a public pension program. The government takes $50 from each individual in period 1 and gives it directly to individuals in period 2. i. What is the terminology for this public pension program? [1 mark] ii. How much does an individual privately save now? [2 marks] iii. How does an individual's utility with the public pension system compare to an indi- vidual's utility without the public pension system? [1 mark] iv. Explain the intuition behind your findings in iii. [1 mark]

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a To illustrate the individuals optimal consumption in each period we can use a diagram with indifference curves and an intertemporal budget constraint Lets start with the axes the horizontal axis rep... View the full answer