Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Yt+1 Ct+1 Ct+2 (1+r) (1+r)² (1+r) Ct + + +...+ Ct+T+1 T+11 (1+r) = Yt + + Yt+2 Yt+T+1 (1+r)² (1+r)ª 2+...+
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- Using this Intertemporal Budget Constraint how can you solve for C2 (consumption in period 2)1. How much is $1 million to be delivered 20 years in the future worth today if the interest rate is 20 percent? 2. As the interest rate rises, does the intertemporal budget constraint become steeper or flatter? 3. Would the assumption that goods are perfect substitutes be valid in a study of intertemporal food purchases?Q 1 5. Refer to the following intertemporal budget constraint of a respective consumer: a. How would this budget constraint change if individual becomes more presented oriented (he discounts future heavily)? b. How would this budget constraint change if individual faces a borrowing constraint in second period?
- Using this functional form in the intertemporal trade-off condition that you previ- ously derived, do some algebra to obtain an equation that specifies how much the individual would save as a function of q, β, y1 and y2.Consider an economy where individuals live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log(C1) + 2 log(C2), where C1 and C2 are period 1 and period 2 consumption levels respectively. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in bank accounts, earning interest rate of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2. a. What is each individual’s lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period? b. Suppose that the government introduces a social security system that will take $10 from each individual in period 1, put it in a bank account, and transfer it back to…An individual earns $100 this and $100 next year. On the diagram below, draw the person's intertemporal budget constraint assuming an interest rate of 5%. (Be sure to label the axes correctly. Put in the appropriate numerical values. Note that subscript 1 denotes this year and subscript 2 denotes next year.)
- Suppose your current income is $90,000 and your future income is $110,000. The interest rate is 10%. a. Suppose your optimal bundle is to live “paycheck by paycheck”, draw the intertemporal budget constraint and optimal bundle in a graph, and mark the optimal bundle and maximum C1, C2.b. What if your MRTP is 1.05, how should you change your consumption? c. What if your MRTP is 1.2, how should you change your consumption?d. If the interest rate decreases to 5%, how should you change your consumption? If the interest rate increase to 15%, how should you change your consumption?Of means-tested programs and IRA’s, which lower the rate of return on saving? a. Both means-tested programs and IRA's. b. Means-tested programs, but not IRA's. c. IRA's but not means-tested programs. d. Neither means-tested program, or IRA's.Suppose a consumer has $1500 in the current time period and $1100 in the future time period.Suppose also that the consumer can borrow and lend freely and, unless otherwise specified, borrowing and lending interest rates are the same. (a) If the interest rate between time periods is 50%, what is the budget constraint between consumption in the present and consumption in the future? (B) If the interest rate at which the consumer can borrow is 75% but the rate at which she can lend is25%, what is the budget constraint? (C) Suppose the interest rate is 50%. If the consumer has to pay a fee of 10% of the loan amount in order to borrow money, what is the budget constraint?
- If Evan's income is reduced to zero after he loses his job, his consumption will be ________ and his saving will be ________. a.greater than zero; less than zero b.greater than zero; greater than zero c.less than zero; greater than zero d.less than zero; less than zeroQ1. Consider the following two-period model of consumption and saving: Utility = C1^0.5 + B*C2^0.5 C1 + C2/(1+r) = Y1 + Y2/(1+r) where Y1 = 4, Y2 = 1, r = 0.17 and B = 0.5. Find a numerical solution for period 1 consumption, C1. (State your answer to 2 decimal places.)“Permanent Income of consumption is just the average of all current and future incomes. Thus, one does not need to do the maximisation of intertemporal utility”. True or False. Discuss according to the model. Note that you need to discuss according to the model?