Consider the decision problem of a representative household optimally choosing a sequence of consumption (c) and...
Fantastic news! We've located the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the decision problem of a representative household optimally choosing a sequence of consumption (c) and asset holdings (+1) over an infinite horizon, taking as given the real interest rate r (assumed to be constant), the initial wealth ao, and the sequence of labor income [w). The household's preferences are represented by Eo Et=0Bu(at) Take the utility function to be u(c) = ac,  (1/2)c for 0 c, s a (we take a big enough so consumption in this economy never attains that level). The budget constraint for each period tis c+at+1 = (1 + r)a + we. For all questions below assume r = p. where = 1/(1+p), p>0. 1. Take the first order conditions of the problem and obtain the Euler equation.  Combine the budget constraints into an intertemporal, expected present value budget constraint; use the Euler equation together with the present value budget constraint to solve for the optimal decision rule that will determine the level of consumption c (the "permanent income" rule). Let's consider now some alternative processes for the labor income sequence (w). For each case, you can use the above solution, but with the appropriate calculation of the expected present value of incomes. 2. Suppose there is no uncertainty and labor income is a constant flow w, w for all 1 (with a positive initial wealth a.). Saving sav, is defined as total income minus consumption, where total income includes labor income w, and financial income ra: i.e. sav = a + rat ct.  What is the optimal level of consumption ce?  Use the budget constraints of the first two or three periods to deduce what the amount of saving and asset holdings a, would be in each of the first few periods  Show graphically (putting time t on the horizontal axis) what the time path of labor income, consumption, saving and asset holdings look like (qualitatively). 3. Suppose there is no uncertainty, but labor income is subject to regular, perfectly anticipated fluctuations: @= @ + A in even periods (10, 2, 4, ...) and w=w(1+r)A in odd periods (1=1, 3, 5,...). There is a positive initial wealth ao. Repeat the analysis of the previous question:  What is the optimal path of consumption c?  Use the budget constraints of the first two or three periods to deduce what the amount of saving and asset holdings a, would be in each of the first few periods  Show graphically (qualitatively) the time path of labor income, consumption, saving, asset holdings over time, and compare briefly
Expert Answer:
Answer rating: 100% (QA)
1 a The first order conditions are u ct 1 r E u ct 1 Taking the derivative of the utility function g View the full answer
Related Book For
Microeconomics An Intuitive Approach with Calculus
ISBN: 9780538453257
1st edition
Authors: Thomas Nechyba
Posted Date:
Students also viewed these accounting questions

Madison's preferences are represented by the utility function U(X, Y) = A ln (X) + B ln(Y), where ln stands for the natural logarithm. What is her demand for X as a function of her income M and the...

Douglas Cornfields preferences are represented by the utility function u(x 1 , x 2 ) The prices of x1 and x2 are p1 and p2. (a) The slope of Cornfields indifference curve at the point (x 1 , x 2 ) is...

Alyson's preferences are represented by the CobbDouglas utility function U(X, Y) = XYb. Use formulas (4) and (5) from Chapter 4 MUX = X1 Yb MUY = bX Yb1 to answer the following questions. What are...

The Wall Street Journal reported interest rates of 6 percent, 6.35 percent, 6.65 percent, and 6.75 percent for threeyear, fouryear, fiveyear, and sixyear Treasury notes, respectively. According...

Consider the reaction 2HCl(aq) + Ba(OH)2(aq) BaCl2(aq) + 2H2O(l) H = 118 kJ

Pattys Pies acquired a delivery truck on January 1, 2020, for $86,000. It is expected to last five years and then sell for about $16,000. Calculate depreciation for each year of the trucks life using...

Internally in the computer, with few exceptions, all numerical computation is done using binary numbers. Input, however, often uses ASCII, which is formed by appending 011 to the left of a BCD code....

A company issues a $2,000,000, 9%, fiveyear bond that pays semiannual interest of $90,000 ($2,000,000 9% ), receiving cash of $2,166,332. journalize the bond issuance.

In July 2022 Henry saw a notice in his local newsagents advertising a 'room in a shared flat'. He telephoned and arranged to see the registered freehold owner, Rose, who did not live in the flat....

Janette Douglas is coordinating a bake sale for a nonprofit organization. The organization has acquired $ 2,200 in donations to hold the sale. The following table shows the amounts and costs of...

0.10 mole of a carbohydrate with empirical formula CH2O contains 1 g of hydrogen. Its molecular formula will be : A) C5H10O5 B) C6H12O6 C) C4H8O4 D) C3H6O3

I have estimated a multiple linear regression model with 3 explanatory variables. I have a sample of 200 observations. I wish to test that beta2+beta3=1 and that beta1=0.6. When I compute the F...

(1) Consider the clustering C {C, C2, C3} with C = {x1, 2, 3, x4}, C = {x5, 26, 27, 28}, C3 = {x9, 10} and x; x; for i j. Compute the silhouette coefficient of the clustering with distance function...

Deterministic Modeling and Simulation 1. This problem describes the immune response triggered by encountering foreign antigens. This is called the cytotoxic T cell or CTL response. Suppose that z...

ces An investor buys a newly issued annual bond that pays its coupons once a year. The bonds coupon rate is 11.5% its time to maturity is 4 years, and the yield to maturity is 7.5%. The investor will...

Write a function that finds the monthly car payment of the user once the user enters the credit score and the length of the car loan in years. According to a recent study, car loan APRS depend...

A project's initial Investment is $200,000 straight line depreciated to $20,000 salvage value over 5 year life. Projected sales: 2,500 units @ $88 / unit, variable cost: $50 / unit, Fixed Costs...

The following selected accounts and normal balances existed at yearend. Notice that expenses exceed revenue in this period. Make the four journal entries required to close the books: Accounts...

A: Now consider the same setup as in exercise 13.7 but assume throughout that labor is instantaneously variable, that capital is fixed in the short run and variable in the intermediate run, and that...

I hate grits so much that the very idea of owning grits makes me sick. I do, on the other hand, enjoy a good breakfast of Coco Puffs Cereal. A: In each of the following, put boxes of grits on the...

Consider your tastes for right and left shoes. A: Suppose you, like most of us, are the kind of person that is rather picky about having the shoes you wear on your right foot be designed for right...

Gasoline contains a complex mixture of hydrocarbons. Is gasoline an example of a heterogeneous or a homogeneous mixture?

Which physical state is described as having a fixed shape and fixed volume?

Identify the physical state (solid, liquid, gas) that corresponds to each of the following pictorial representations:
Question Categories