Question: Suppose that a preference relation over R2 is represented by a utility function x(Ux.qu=)1x(u+)2(2), where u: R++ R and u: R++ R are strictly

Suppose that a preference relation over R+ is represented by a utility function 2(U14,2u=)14(14+)22(2), where u: R++ R and U2

Suppose that a preference relation over R2 is represented by a utility function x(Ux.qu=)1x(u+)2(2), where u: R++ R and u: R++ R are strictly increasing, continuous and twice differentiable functions: u, are strictly concave. Prove that there exists numbers a > 0 and b R such that u(x) = au(x) + b.

Step by Step Solution

★★★★★

3.40 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Periodic review system also called fixed interval reorder system has four original econom... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Suppose a quasi-linear preference is represented by a utility function of the form u(x)=x1+(x2,...,xn) . Show that the Hicksian demand functions for goods 2,...,n are independent of utility *WITHOUT*...

Martha Modest has preferences represented by the utility function U (a, b) = ab/100, where a is the number of ounces of animal crackers that she consumes and b is the number of ounces of beans that...

1. A consumer has preferences represented by the utility function u(x1, x2) = (x1x2). If she faces prices p1 = 1 and p2 = 5, and has income m = 10, what are her demands for goods 1 and 2? 2. A...

Consider an individual whose preferences are dened over bundles of non- negative amounts of each of two commodities. Suppose that this individ ual's preferences can be represented by a utility...

6. (20 points) Let X = R2. Let ~ be a preference relation on X. In Lecture notes-2 (see Lecture 2, page 7, Definition 9) we have encountered the definition of additivety property of a preference...

Please prove that the preference relation satisfies the independence axiom (the yellow highlight). Suppose that a preference relation 2 on the space of simple lotteries _ can be represented by a...

Suppose a consumer's preference relation over gambles satises both the substitution and reduction to simple gambles axioms (a) Show that the independence axiom also holds (2) (b) For two gambles,...

Tfie certainty equivalent of a galllble C is /1,e 1111111ber CE tJ,at satisfies tJ,is equation: 11 (CE)= EU (G). The certainty equivalent represents what tJ,e gamble is worth to you. The certainty...

Let Z be a set of prizes. Assume that >, a preference relation over L(Z), satisfies the independence property. Let a and b be two prizes with [a] > [b] and let a and 8 be two numbers between zero and...

Because the Moth Cement Works has a number of subsidiaries, Star Lin is required to prepare a set of consolidated nancial statements for the group. She is concerned about the calculation of the NCI...

L&T is considering expanding its operations in Columbia and has invited a contractor to bid on a construction job. The value of the contract depends on the length of time it takes to complete the...

Express as a single logarithm. ( a ) l n ( 2 1 ) 3 l n ( 7 ) ( b ) 5 l n ( x - 5 ) - l n ( x 2 - 1 1 x 3 0 ) 2 l n ( x - 6 )

You are a senior in college. You sent your resume to a half-dozen companies hoping to get a job. A month ago you interviewed at ABC Corporation and XYZ Corporation. Two weeks ago XYZ Corporation...

Give a context-free grammar that generates the language A = {a i b j c k | i = j or j = k where i, j, k 0}. Is your grammar ambiguous? Why or why not?

The records of Khanna Company show the following amounts in its December 31 financial statements: Khanna made the following errors in determining its ending inventory : 1. The ending inventory...

The unity feedback system shown in Figure P9.1 with G(s) = K/s 2 is to be designed for a settling time of 1.667 seconds and a 16.3% overshoot. If the compensator zero is placed at -1, do the...

A divorce agreement entered into in 2017 requires Alice to pay her former spouse $50,000 a year for the next ten years. Will the payments qualify as alimony? Why or why not?

solve 19 and 20 Write the equation in SLOPE-INTERCEPT FORM with the given information. 19. Passes through (-8, 3) with a slope of -2 20, Passes through (-7, -3) and (5, 6) en |

Network Externalities and the Battle between Microsoft and Apple: Many markets related to technology products operate in the presence of network externalities because the value of such products to...

Consider the problem you face as a student as you determine how much to study for an exam by modeling yourself as a producer of an exam score between 0 and 100. A: Suppose that the marginal payoff to...

In exercise 25.1, we checked how the Bertrand conclusions (that flow from viewing price as the strategic variable) hold up when we change some of our assumptions about fixed and marginal costs. We...

=+50. A random sample of size 25 is selected from a large batch of electronic components, and the proportion of defective items in the sample is recorded. The proportion of defective items in the...

=+c. Which is more likely to lie within .01 cm of 12 cm, the mean of a random sample of size 16 or the mean of a random sample of size 64?

=+b. Answer the questions in part (a) for sample means based on samples of size 64.