3 c pleasePrésent bias may induce individuals to save too little for old age, when they no longerhave labour income. Consider the following model to address this concern formally.Assume that an individual lives for three periods, t 0, 1,2 and has income w inboth periods 0 and 1 but zero income in period 2. In each period t the individualderives utility u4(1L) = In(r;) from consumption I. The individual discounts thefuture. Lifetime utility U, from the perspective of period t = 0, respectively t = 1 is%3Dgiven by:Uo = uo + Bou + B8*uz and U1 = u1 + Bôuz,%3Dwhere 0 < 8 <1 and 0 < B< 1. The individual can borrow and save,at an interest.rate of 0, so that total consumption expenditure must equal the sum of income.(a) Derive the individual's preferred consumption plan (z6, Tỉ, r5) from a period1 = () perspective (i.e. maximising Uo). Explain the roles of parameters B and 6.(b) Derive the individual's preferred consumption pattern (zN, ) from a periodt = 1 perspective (i.e. maximising U1) for a given value of zo. Explain thedifference, if any, between (zN, 1) and (ri, 13).(c) Suppose that > i, but that the individual's preferred consumption r inperiod 0 when anticipating that later consumption will be (z, ) is the sameas ri, i.e. the individual would prefer to save a higher proportion of their period1 income from a period 0 point of view than from a period 1 point of view. If theindividual is aware of their present bias, could a financial product that preventsborrowing, requires an investment k in period 0 and pays back k in period 2increase period 0 utility Uo? Argue verbally or compute

"As stated by the client, the answer to part C is only provided."The utility function is given as…

Présent bias may induce individuals to save too little for old age, when they no longer have labour income. Consider the following model to address this concern formally. Assume that an individual lives for three periods, t= 0, 1, 2 and has income w in both periods 0 and 1 but zero income in period 2. In each period t the individual derives utility (T) = ln(r) from consumption T. The individual discounts the future. Lifetime utility U, from the perspective of period t= 0, respectively t = 1 is given by: Uo= uo + Bou₁ + B8² u₂ and U₁ = ₁ + Bôu₂. where 0 < 8 ≤ 1 and 0 ri, but that the individual's preferred consumption r in period 0 when anticipating that later consumption will be (1, 1) is the same as ro, i.e. the individual would prefer to save a higher proportion of their period 1 income from a period 0 point of view than from a period 1 point of view. If the individual is aware of their present bias, could a financial product that prevents borrowing, requires an investment k in period 0 and pays back k in period 2 increase period 0 utility Uo? Argue verbally or compute.

Présent bias may induce individuals to save too little for old age, when they no longer have labour income. Consider the following model to address this concern formally. Assume that an individual lives for three periods, t= 0, 1, 2 and has income w in both periods 0 and 1 but zero income in period 2. In each period t the individual derives utility (T) = ln(r) from consumption T. The individual discounts the future. Lifetime utility U, from the perspective of period t= 0, respectively t = 1 is given by: Uo= uo + Bou₁ + B8² u₂ and U₁ = ₁ + Bôu₂. where 0 < 8 ≤ 1 and 0 ri, but that the individual's preferred consumption r in period 0 when anticipating that later consumption will be (1, 1) is the same as ro, i.e. the individual would prefer to save a higher proportion of their period 1 income from a period 0 point of view than from a period 1 point of view. If the individual is aware of their present bias, could a financial product that prevents borrowing, requires an investment k in period 0 and pays back k in period 2 increase period 0 utility Uo? Argue verbally or compute.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.1P

See similar textbooks

Similar questions

Exercise 3 An individual lives two periods, 0 and 1. The income is 14,000 in period 0 and 5,000 in period 1. The individual's marginal utility is: K- Co in period 0 and d8(K – C1) in period 1, where C is the consumption in period 0, C1 the consumption in period 1 and d a discount rate. K is a constant (higher than the consumption in each period). Suppose that the person can save or borrow from the bank from period 0 to period 1 with a 25% interest rate. Set the discount rate & to 0.8. a) How much will the individual consume in the two periods? How much will she save? b) A National Insurance scheme (pension system) is established. The individual must pay 4,500 in period 0 and receives the same amount with interests in addition to her income in period 1. What will the consumption and savings be in the two periods if the National Insurance scheme uses the same interest rate as the bank?
During any year, I can consume any amount that doesnot exceed my current wealth. If I consume c dollars duringa year, I earn ca units of happiness. By the beginning of thenext year, the previous year’s ending wealth grows by afactor k.a Formulate a recursion that can be used to maximizetotal utility earned during the next T years. Assume Ioriginally have w0 dollars.b Let ft(w) be the maximum utility earned during years t, t 1, . . . , T, given that I have w dollars at the be-ginning of year t; and ct(w) be the amount that should be consumed during year t to attain ft(w). By workingbackward, show that for appropriately chosen constantsat and bt,ft(w) btwa and ct(w) atwInterpret these results.
If a consumer starts at point A, and then receives an income in current income, this would appear as an outward shift of the budget constraint. is it true or false
What is the logarithmic transform of the utility function U= 52, given the budget constraint - M. Select one: O a. In U = a ln a +Bin 2 +y In os %3D O b. In U = In a + In + In e In U = a ln a -Bln a -yln es Od. InU=n 2? + In e? + In a
Pls help with thsi question Consider an Individual who buys films (F) and books (B) with the following utility function:?(?, ?) = 5? + 2?This individual also has the following incomes (m) and prices (pF and pB):? = $50, ?f= $5, ?b= $10Given the above:1) Draw the utility functions for utility levels of 10 and 20. Draw these with films on the x-axis and books on the y-axis. 2) What is the MRS for these utility functions? Assume that films remain on the x-axis andbooks remain on the y-axis. 3) What is the consumption bundle that delivers the highest level of utility that is alsoaffordable?
1. Use budget constraints to express consumption levels, ct and ct+1. (Hint: Use income conditions given above in the budget constraint. Notice that there are two possible states in the second period.)2. Rewrite the utility maximization problem as choosing the optimal at alone. (Hint: Replace ct and ct+1 in the utility function with your answers from point 1. Use probabilities to derive the expected value in the utility function. Remember that a random variable that takes values x1 in state one with probability p and x2 in state two with probability 1 − p has the expected value E [x] = p.x1 + (1 − p).x2)3. Derive the first order condition and find the optimal value of savings, at. (Hint: The only control (choice) variable is at)4. Does household accumulate precautionary savings to self-insure against the scenario of low income in the second period? Why or why not?
For this question, assume that indifference curves are strictly convex, consumption andleisure are normal goods, and the optimal amounts of consumption, leisure, and labor arealways positive. A wage increase ______. (SE = substitution effect; IE = income effect)(a) increases labor supply via the SE and decreases labor supply via the IE(b) decreases labor supply via the SE and decreases labor supply via the IE(c) increases labor supply via the SE and increases labor supply via the IE(d) decreases labor supply via the SE and increases labor supply via the IE(e) Can’t tell without knowing the utility function
1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental…
Consider an economy with two periods (interpreted as “when young” and “when old” periods)and two consumers, Gillian Davis and Joana Wolinsky. Gillian is a star ballet dancer with a lifetime income given by ωG= (400,0). Joana is an Econ Ph.D. student with incomeωJ= (0,400). Gillian and Joana have identical utility functions given by Ui(x1,x2) = 6 lnx1+ 3 lnx2 for i=G, J a) Plot an Edgeworth box and mark the initial endowment point. b) Write the general definition of Pareto efficient allocation (one sentence) and give the equivalent condition in terms of MRS (give formula). Check if this condition is satisfied for initial endowments. c) Derive the contract curve (write down the appropriate conditions and solve for the curve) and depict it in the Edgeworth box. d) Suppose Gillian and Joana can “trade” consumption in both periods at pricesp1,p2. Find the competitive equilibrium (6 numbers) and depict the equilibrium allocation in the Edgeworth box. e) Using the MRS condition from part b),…
This question is very similar to Question #1 but recasts the problem in terms of a single type of good consumed over time instead of two different types of goods within the same period of time. 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 ci units of the consumption good at a price P and can save any unspent wealth. Use s1 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…
Please teach not just solve
Suppose a household has the following lifetime utility function: U=c1/2 + ẞc¹/2 12tt+1 A) Find expressions for the partial derivatives of lifetime utility, U, with respect to period t and period t + 1 consumption. Is marginal utility of consumption in both periods always positive? B) Find expressions for the second derivatives of lifetime utility with respect to period t and t+1 consumption, i.e., 2U and a 20_Are these second derivatives always negative for ac²²+1 any positive values of period t and t+1 consumption? C) Derive an expression for the indifference curve associated with lifetime utility level Uo (i.e., derive an expression for C++₁ as a function of U₁ and c). What is the slope of the indifference curve? How does the magnitude of the slope vary with the value of c?