Log in
Economics
1
answer
0
watching
70
views

How can we use utility functions, which have actual numbers that can be measured and compared, to model preferences and still say with a straight face that preferences are subjective? Hint: what does it mean for a utility function to be ordinal or cardinal? Why can multiple utility functions describe the same preferences?

Watch
1
answer
0
watching
70
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Nusrat Fatima
Nusrat FatimaLv10
28 Sep 2019

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share

Related textbook solutions

Principles of Economics
2nd Edition, 2017
Openstax
ISBN: 9781947172364
Principles of Macroeconomics
2 Edition,
Openstax
ISBN: 9781947172388
Principles of Microeconomics
2 Edition,
Openstax
ISBN: 9781947172340

Related questions

Kayo is going to dinner in a Spanish restaurant in New York and would love to have some sangrias (s) and tapas (t). Her preferences can be represented by the utility function:

U(s,t) = 2 ln (s) + 3 ln (t).

a. Compute the marginal rate of substitution of sangrias for tapas. Is the MRS increasing or decreasing in s? How do we interpret this?

b. Suppose that the price of sangrias is Ps = 2, the price of tapas is Pt = 5, and Kayo's dinner budget is $25. What exactly should Kayo order for dinner, so that her utility is maximized?

c. Suppose the price of sangria increases to Ps = 4. What should Kayo's new dinner order be?

d. Given the price increase, how much income does Kayo need, to remain as happy (have the same utility) as she was before the price change?

e. What exactly would Kayo order for dinner if she had that additional income, given the new prices?

(4) Consider the plight of two equally skilled economists, Ann and Bill. Ann lives in Ohio, where she pays a monthly rent of $1000 for a 1000 square foot apartment. Bill lives in Oakland in an 800 square foot apartment that is otherwise identical to Ann’s but which costs him $2000 per month. Assume that the only other good that Ann and Bill consume is food, which costs $10 per unit in Ohio and only $5 per unit in Oakland.

a) Suppose that Ann and Bill both have ordinal utility functions U(h, z) = α log(h) + (1 − α) log(z), with 0 ≤ α ≤ 1, where h is housing services (measured in square feet occupied per month) and z is food. Derive Ann and Bill’s Marshallian Demands for housing 2 and food. Give an interpretation of the parameter α; how does it affect choices between housing services and food?

b) Suppose preferences are as in (a) but with α = 0.25. What are the locally prevailing monthly salaries for economists in Ohio and Oakland?

c) Now suppose that we don’t know what Ann and Bill’s incomes are equal to (though they each know, and also know each others’), and that further we don’t know what the value of α is, and Ann’s α may be different from Bill’s α. Either Ann or Bill could choose to move to the other’s location and get a job as an economist there at the prevailing local salary, yet they choose not to. What can you say about the value of Ann’s α relative to Bill’s α? (Hint: Ann’s indirect utility in Ohio must be greater than her indirect utility would be in Oakland; similarly, Bill must be happier in Oakland than in Ohio.)

d) A pollster surveys a random sample of Ohio residents and Oakland residents, and asks each respondent, “Would you say that you’re (1) Very happy; (2) Pretty happy; or (3) Not so happy?” After tabulating the results, the pollster finds that on average people in Ohio are just as happy as people in California. Noting that the cost of living in Ohio is lower than in California, she argues that many Californians should move to Ohio, where they could be just as happy but spend less money. Comment on the quality of this argument. Are you tempted to move?

Given prices for two goods PX = 2 and PY = 3 and a budget of $120 a consumer is trying to maximize the utility function U(X, Y ) = 2X0.3Y 0.7 . Use the Lagrange method to solve this problem, but don’t worry about the second order conditions (if you wish, you can actually check that the MRS is decreasing and this utility function is well behaved). a) Write and solve the utility maximization problem subject to the budget constraint. What is the resulting value of the utility function? (U=49.0481) b) Write and solve the dual problem. Do you get the same optimal solution (the same optimal combination of X and Y)? What is the resulting expenditure? Does that match the budget of your original (primal) problem? (X=18, Y=28 should be the same as for a or very close due to rounding) c) Assume now general values for prices and income. Solve for the optimal amounts of X and Y as functions of PX, PY , and I. What conclusion can you draw regarding how you spend your budget when dealing with Cobb Douglas functions with exponents that add up to 1. You can actually try to solve the general case where we replace the exponents 0.3 and 0.7 with some α and β, where α + β = 1. (Hint: you should find that you spend percent of your income on X and β percent of your income on Y. See if you can get there by solving!)

Weekly leaderboard

Home
Homework Help 3,900,000
Economics 400,000
Start filling in the gaps now
Log in