A consumer is making saving plans for this year and next. She knows her real income after taxes will be $50,000 in both years. Any part of her income saved this year will earn a real interest rate of 10% between this year and next year. Currently, the consumer has no wealth (no money in the bank or other financial assets, and no debts). There is no uncertainty about the future. a) Formally derive the consumer's intertemporal budget constraint. b) Using the given numerical values rewrite and graph the budget line. c) Find the consumer's PVLR.

Cindy takes a summer job and earns an after-tax income of $5,000. Her living expenses during the summer were $1,000. What was Cindy's saving during the summer and the change, if any, in her wealth? >>> If your answer is negative, include a minus sign. If your answer is positive, do not include a plus sign. Cindy's saving during the summer is $

U = c¹/² + Bc¹²/2 tt+1 A) Suppose that the household faces two within period budget constraints of the form: C++ 1 = Y++1 + (1+r)s Combine the two period budget constraints into one intertemporal budget constraint. B) Use the intertemporal budget constraint and this utility function to derive the Euler equation characterizing an optimal consumption plan. C) Use this Euler equation and the intertemporal budget constraint to derive a consumption function expressing cas a function of Y, Y₁+1, and rt.

Suppose you know the following facts about consumer behavior of Amy in 2019. In a year, Amy spends $10000 on basic household items regardless of how much she is earning. For every dollar of disposable income earned, Amy spends 50% on extra purchases. Amy pays taxes in the amount of $1000, and receives no transfers. Use this information to:  Derive Amy’s consumption function in nominal terms. Suppose the price level index in the economy for 2019 is estimated to be P = 2. Rewrite the consumption function in real terms.

Suppose as a hypothetical scenario that you deposit $400 today into a savings account with a variable interest rate and will collect a payment in one year. True or False: If over the course of the year the interest rate falls, this increases the future value of your investment. True False

Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Ct+2 Yt+2 Yt+1 (1+r) (1+r)² (1 + r)² Ct + Ct+1 (1 + r) + 2+...+ Ct+T+1 (1+r)² \ T = Yt + + +...+ Yt+T+1 (1+r)

Consider the problem of an individual that has Y dollars to spend on consuming over two periods. Let c, denote the amount of consumption that the individual would like to purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase c1 units of the consumption good at a price P and can save any unspent wealth. Use sı to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the individual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2. 2 The individual's total happiness is measured by the sum of period utility across time, u(cı) + u(c2). Let u(c)…

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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…

Describe the effects of a decrease in the interest rate on present and next period’s consumption if the individual is a net lender (i.e., has savings) after period 1 and the substitution effect is larger than the income effect. Show your answer graphically