1. Consider a two-period model in which you work and save in the initial period (period 0) and live off savings and the interest from savings in retirement (period 1). Suppose that income in period 0 is $250,000, income in period 1 is $0, and the interest rate is 50%. a. Draw the budget line. b. Draw an indifference curve consistent with a person whose preferences causes them to equalize their consumption in period 0 and period 1. c. Savings are $
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- A person has a 2-period utility consumption function U(c1, c2), with a budget function W = c1+c2/1+ra. Explain with pictures how one should choose c1 and c2 such that MRS(from c1 to c2) equals 1+r.b. Also explain with pictures how when the individual receives income, whileconditions at that time was a crisis.Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up the corporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) + βu(C2) 1. Assume this consumer cannot borrow. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve. 2. Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraints such that for one of them consumer prefers to borrow and for the other - prefers to save. 3. Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin t r a d e s a t P1 > 0 in the first period…A consumer has utility u(x,y) = x^4 y^2 where x is this year’s consumption, and y is next year’s consumption. She makes 600 dollars income this year and 720 dollars income the next year. There is also a bank where she can borrow money at the interest rate r=%50 and lend money (to the bank) at the interest rate r=%20 (of course, she will decide to borrow or lend this year and pay off her debt or receive her savings the next year). a. Should she borrow money from or lend to the bank this year? How much b. If her utility were u(x,y) = xy2 instead, re-solving (a), would she borrow money or lend? How much? c. If her utility were u(x,y) = x^c y^2, what should “c” be so that she ends up neither borrowing nor lending?
- Given the utility function: U = ln c + l + ln c’ + l’ and the budget constraint: w(ℎ−l)+(w′(ℎ−l′))/(1+r)=c+(c′)/(1+r) (see pictures of function and constraint) where c = current consumption, c' = future consumption, l = current leisure, l' = future leisure, and r is the market interest rate.Suppose that the current wage, w = 20 and the future wage w' = 22. a) What is the optimal value of current consumption, c? b) What is the optimal valueof future consumption, c’*?Assume Marco is initially borrowing and investing 100, with a return on investment of 50% and an interest rate on borrowing at 10%. The return on investment falls to 5%. Which statements are correct? Select one or more: A. Marco’s decision to continue to invest will depend on his preference between consumption today and consumption in the future. B. Marco will wish to invest and borrow, but he will be worse off than when the return to investment was 50%. C. If he continues to invest and borrow, the dashed line representing his new frontier will start at 105 on the y axis and be shallower than the solid red line, so he’ll continue to invest and borrow D. In the remaining questions, assume the central bank now cuts interest rates so that the real interest rate falls to zero. Marco will still not wish to invest and borrow. E. If he just invests his money in the bank instead, his frontier will cross the x axis at 100 and be steeper than the frontier if he invests.…Problem 4 - Costless Magical MacGuffinConsider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up thecorporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) +βu(C2)Assume this consumer cannot borrow.1. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utilitycurve.Assume that now the consumer is allowed to save or borrow.2. Write down the new budget constraint. What is the consumption in period 1 and period 2? Displaygraphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraintssuch that for one of them consumer prefers to borrow and for the other - prefers to save.Assume once again that a consumer cannot borrow, but can borrow and immediately sell some ‘MacGuffins’, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffins trade at P1 >…
- In the two-period Fisher model of consumption, suppose that the first period income is $5,000 and the second period income is $5,000 for both Matt and Paola. The interest rate is 10 percent. Matt’s lifetime utility function is C1 + C2 while Paola’s lifetime utility function is C1 + 0.8C2. If there is a borrowing constraint, whose consumption is affected by that?H3. An investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C1= 240 (16,000 − C0)0.5 where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indifference curves, is defined as: U(C0, C1) =C0C1 . What is the NPV of the investment chosen by the investor? Show proper step by step calculationOver a three-year period, an individual exhibits the following consumption behavior: Px Py x y Year 1 3 3 7 4 Year 2 4 2 6 6 Year 3 5 1 7 3 Is this behavior consistent with the axioms of revealed preference?
- Draw and explain a graph for a two-period consumer. Include the budget line, indifference curve, utility maximization, and all labels. a. Draw the effect of an increase in the interest rate. Show graphically and explain the effect on the level of consumption C1 and C2. b. Why would C1 change? Explain c. Why would C2 change? ExplainSuppose that there are only 10 individuals in the economy each with the following utility function over present and future consumption: U (c1, c2) = c1 +C2, where ci is consumption today, and c2 is consumption tomorrow. Consumption tomorrow is less valued because people are impatient and prefer consuming now rather than later. Buying 1 unit of consumption today costs $1 today and buying 1 unit of consumption tomorrow costs $1 tomorrow. All individuals have income of $10 dollars today and no income tomorrow (because they will be retired) but they can save at the market interest rater> 0. How much of his or her income will an individual consume today given that the interest rate is 0.3? O. Less than half of it O. Exactly half of it O. The individual is indifferent between consuming today and saving O. More than half of it O. All of it O. None of it How much of his or her income will an individual consume today given that the interest rate is 0.5? O. Less than half of it…Q1. 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.)