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- A consumer's consumption-utility function for a two period horizon is 0.5 U(Cg,G) =C,G" he consumer's earned income stream is given by mo, m1 and the market rate of interest is r. a) Write the intertemporal budget constraint in present value terms. If the consumer does not consume anything in peripd 0, what is the most she can consume in period 1? b) Draw a graph that shows optimal consumption in each period co* and c1*. What is the slope of her budget line? c) Solve the problem for optimal consumption in each period co* and c;*. d) Suppose mọ is S50 and mị is S110 and r = 0.1. Is the consumer a borrower or a lender? Show this outcome by drawing co*. C1*, mo, mį, and bond-holdings on your graph.Assume an intertemporal budget constraint that shows how consumption can be traded off between two periods, t and t+1. Assume the consumer can save and borrow at the same interest rate of 10%. Assume the consumer collects income of $100 in each period. To gain an extra $10 dollars in period t+1, what must the consumer give up in period t?Help me
- Explain how does adecrease in the current income y affect the consumer’s consumption-saving decision. In particular,explain: 1) How will current consumption c, future consumption c′, and savings s change; 2) Arethere any substitution effect or income effect. Make sure you draw two figures, one for the borrowersand one for the lenders3. A consumer maximises the following two-period utility function 1 V = max 1 ule,) + Fu(c) (1+p)? subject to the following 2-period budget constraint, C2 Ao + 1+r" (1+r)² Y2 1+r*(1+r)²' By choosing consumption at each period, c, and c2. r denotes the real interest rate, p is the time preference rate, Ao is initial wealth and y, and y2 represents incomes in period 1 and period 2 respectively. (a) Use the Lagrangian method to obtain the first order conditions for the utility maximisation problem and obtain the Euler equation. (b) Assume utility function has the form of u(c,) = 5 0.2 and r = 0.3. Obtain the equations/solutions for maximal c, and c2 by substituting the Euler equation back into the two-period budget constraint for the situations of either A, = -50 or Ao = 50. Explain the results. , Y1 = 200, y2 = 300, p = 0.64. Mateo is deciding how many dollars to consume today and how many to consume next week. We earns $1,000 each week and earns a real interest rate of p = 0.01 on any money saved today. He also needs to pay the same interest rate if he borrows money today and repays it next week. If his utility function is U (C₁, C₂) = cc₂, where c₁ is units of consumption today and c₂ is units of consumption next week, how many units will he consume this week?
- Suppose that a person can borrow and lend at an interest rate of 10 percent. But there is a 5% rate of inflation and one has to pay an income tax of 30 % on all interest income. If you borrow money, you can deduct interest as an expense. Where current consumption is on the horizontal axis and future consumption is on the vertical axis: (a) the budget line will have a kink at the point of no saving or lending. (b) the budget line will be a straight line with a slope of about 1: 02. (c) the budget line will be a straight line with a slope of about 1:05. (d) the budget line will be a straight line with a slope of about 1:35.APPLIED ECONOMICS Topic: Intertemporal Choice Levinn’s utility function is expressed as the following: U= C1 C2 0.3 where C1 is his first periodconsumption and C2 is his second period consumption. His income in the first period is$2500 and interest rate is at 10%. If at equilibrium, Levinn is neither a borrower nor a lender,then what is his expected income in the second period? Do not copy from othersExercise 2 (The Saving Schedule). Consider a two-period economy populated by identical households with preferences defined over consumption in period 1, C1, and consumption in period 2, C,, and described by the utility function Assume that households are endowed with Y, kilos of apples in period 1 and with Y, kilos of apples in period 2. Let P, and P, denote the price of apples in periods 1 and 2. Households can save (or borrow) at the nominal interest rate i. Let r denote the real interest rate, so that the gross real interest rate is 1 +r = P, P, (1 + i). Let St denote saving in kilos of apples. 1. State the household's budget constraints in periods 1 and 2. 2. Derive the household's intertemporal budget constraint in terms of C1, C2, Y1, Y,, and r. 3. State the household's utility maximization problem. 4. Find the optimal level of consumption in period 1, C,, in period 2, C2, and the associated level of saving, S,. Express your answer in terms of Y,, Y,, and r. 5. Now assume that…
- Course: Introduction to Microeconomics Topic: Intertemporal Consumption DecisionsA consumer makes decision to consume in this year and next year. This year she has an income of M1 = $ 1.5 million and next year her income will be M2 = $ 2.75 million. Interest rate is 10%. Her intertemporal preferences are represented by function U(c1, c2) = c1*c2, whose intertemporal marginal rate of substitution is IMRS = c2/c1.a) Find and graph Budget Constraintb) Find and graph optimal consumption basket and indicate whether the consumer SAVES or BORROWS in the FIRST YEAR.c) Indicate whether following statement is true or false: "Any increase in interest rate will cause a decrease in consumer's welfare" Justify.d) If next year's income is maintained, how much would this year's income have to be for consumer to neither save nor borrow money at 10% interest rate?e) How much would interest rate have to be for consumer to consume exactly her initial endowment (M1 = $ 1.5 million and M2 = $ 2.75…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)Kenji is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $3.00, and a slice of pizza costs $4.00. Let E be the amount in dollars that Kenji spends on salad and pizza. If Kenji buys S bowls of salad and P slices of pizza, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation Suppose Kenji has $48.00 to spend on salad and pizza; that is, E= $48.00. Complete the following table with the values of S or P that make the equation true. Hint: To complete the first row, determine the number of pizza slices Kenji can purchase with $48.00, when the number of salad bowls he purchases is 0. Pizza Budget Salad (Dollars) (Bowls) (Slices) 48.00 0 48.00 48.00 8 0