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# Utility

### Economics: Law of Diminishing Marginal Utility

1. Which gives you greater total utility, 12 gallons of water per day or 20 gallons per day? Why? 2. At which level do you get greater marginal utility, 12 gallons per day or 20 gallons per day? Why?

### 1. Show that, in a second-price sealed bid auction with private values, bidders bid their true valuations of the object for auction. 2. In a second-price sealed bid auction, there are 2 bidders. The value to bidder i of the object for auction is Xi, and the realization of this value is information private to bidder i. The Xi's are uniformly and independently distributed over {0,1}. The object for auction is of no value to the seller. The seller's reserve price is r, and the seller and bidders are risk neutral. What is the seller's expected profit when r=0? What value for r is optimal for the seller, and what then is the seller's expected profit?

1. Show that, in a second-price sealed bid auction with private values, bidders bid their true valuations of the object for auction. 2. In a second-price sealed bid auction, there are 2 bidders. The value to bidder i of the object for auction is Xi, and the realization of this value is information private to bidder i. The Xi's

### Risk, Uncertainty and Information

A firm hires a worker, and the worker chooses between two levels of effort (e), e=1 and e=4. Hiring the worker provides profits (s), and there are two possible levels of profits, s=40 and s=280. If e=1, the probabilities are 0.8 of s=40, and 0.2 of s=280. If e=4, the probabilities are 0.5of s=40 and 0.5 of s=280. The worker's ut

### Risk, Uncertainty and Information

Traders are divided into 2 groups, sellers and buyers. Each seller sells one or no cars, and each buyer buys one or no cars. There are more buyers than sellers and the market is competitive. Cars can be "lemons" with quality q=1 or "peaches" with quality q=3. The proportion of lemons is ½. The von Neumann Morgenstern utility fu

### Risk, Uncertainty and Information

Important Note: Please try to use mathematical notation as much as you can to demonstrate your answer, but don't forget to carefully define each step you make. Question (a) Define "risk averse". (b) Why does a risk averse agent offered actuarially fair insurance choose to insure fully? (c) What does the agent choose if t

### Risk, Uncertainty and Information

Important Note: Please try to use mathematical notation as much as you can to demonstrate your answer, but don't forget to carefully define each step you make. Question (a) What is expected utility theory? (b) On what assumptions is the theory based, and how plausible are these assumptions? (c) Explain the Ellsberg par

### Oyuki's preferences over swords

Oyuki's preferences over swords (good X) and all other consumption (good Y) are given by U(X, Y ) = XY. Her income is \$16, the price of a sword is \$2 and the price of the composite good is \$1.

### Using utility function to solve for optimal choice

Suppose that the typical consumer has the following utility function: U(N, Y) = N×Y, where Y = income or expenditures on goods, and N = leisure (non-work) hours. The wage rate is given by w = \$10. The consumer is initially taxed at the proportional rate of t1 = .4. The consumer has no unearned income (Y* = 0). The time const

### Utility Maximization Exchange Economy

This question is about Walrasian equilibrium in an exchange economy with 2 goods and 2 consumers. Taxes are introduced in the question to solve for the equilibrium and allocation under Pareto theorem. Question (2) Consider an exchange economy with 2 goods and 2 consumers . Consumer 1's initial endowment is and consum

### Consider an exchange economy with two consumers and three goods

The attached question is about 2 consumers with 3 goods in an exchange economy. The consumer's utility functions are given. The question asks to find demand functions for each consumer as well as finding Walrasian equilibrium under certain assumptions. Thanks Question (1) Consider an exchange economy with

### Public Utilities

This is another one of those questions that isn't really discussed in the textbook and, since I'm not really sure about the difficulties the public utilities face, I have not idea where to begin in answering this question. Some guidance please... "Given the difficulties that the regulation of public utilities faces, would

### The utility for citizens

Consider two nations, one a developing nation and the other a developed nation. The population size of each nation is the same. Suppose that each nation experienced an equally large increase in investment. Which nation is likely to receive the most benefit from this increase in investment? Explain your answer.

### Allocating Expenditures Between Goods

Mrs. Wilson buys loaves of bread and quarts of milk each week at prices of \$1 and 80 cents, respectively. At present she is buying these two products in amount such that the marginal utilities from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying the utility-maximizing combination of

### Given that the Arrow-Pratt measure of absolute risk-aversion is a constant, derive the corresponding form of the von Neumann-Morgenstern utility function.

This is a classic graduate/advanced undergraduate level problem in microeconomics/finance. It asks to calculate utility function that corresponds to a constant Arrow-Pratt measure of absolute risk-aversion. Here's a problem from Mas-Colell, Whinston and Green textbook on Microeconomic Theory: Given that the Arrow-Pratt mea

### Calculating maximum insurance premium given a von Neumann-Morgenstern utility function.

1. Consider a von Neumann-Morgenstern individual whose utility function is logarithmic, i.e. u(w)=ln(w), where w is wealth. Given that the individual faces the prospect of gaining or losing an amount of wealth h with equal probability, determine the maximum insurance premium that the individual is prepared to pay.

### Economic Theory on Utility

2- Suppose a person has \$8 to spend only on apples and bananas. Apples cost \$.40 each, and bananas cost \$.10 each. a- If this person buys only apples, how many can be bought? b- If this person buys only bananas, how many can be bought? c- If the person were to buy 10 apples, how many bananas could be bought with the fun

### Agent and Principal Utility

The utility of the agent is given by U(w, a) = √w − a, where w is wage and a is effort. The reservation utility of the agent is 1. There are two profit levels, π;l = \$0 and π;h = \$100. The principal is risk-neutral. The wages are restricted to be non-negative, w ≥; 0. Suppose there are three levels of effort for the agen

### You go to an "all-you-can-eat" buffet. If you maximize utility, the marginal utility of the last bite that you eat will be

You go to an "all-you-can-eat" buffet. If you maximize utility, the marginal utility of the last bite that you eat will be a. equal to the price of the buffet b. as high as possible c. zero d. dependent on how much you like the buffet my answer is A Suzy knows she has maximized her utility, because she is on her budget

### To say that you can't have too much of a good thing means that for any good that you enjoy

To say that you can't have too much of a good thing means that for any good that you enjoy (say pizza), a. higher consumption will always lead to greater utility b. higher consumption will cause utility to increase at an increasing rate c. higher consumption will increase utility but only up to a point; after that utility wil

### Optimal Consumption

For each of the following situations, decide whether the bundle Lakshani is thinking about consuming is optimal or not. If it is not optimal, how could Lakshani improve her overall level of utility? That is, determine which good she should spend more on and which good should she spend less on. a. Lakshani has \$200 to spend on s

### Marginal Utility in Real Life

Use the concept of marginal utility to explain the following: Newspaper vending machines are designed so that once you have paid for one paper; you could take more than one paper at a time. But soda vending machines, once you have paid for one soda, dispense only one soda at a time.

### Diminishing, Increasing and Constant Marginal Utility

For each of the following situations, decide whether Al has increasing, constant, or diminishing marginal utility. a. The more economics classes Al takes, the more he enjoys the subject. And the more classes he takes, the easier each one gets, making him enjoy each additional class even more than the one before. b. Al likes

### Marginal and Total Utility

You go to an auction and set a maximum price of \$100 you are willing to bid on an item. However, you are fortunate and purchase it for \$50. 1) Does the lower price alter the marginal utility you originally placed on the item? 2) Is your potential total utility increased because of the lower price? I struggling with

### Discussion Questions - What are some of the economic consequences of global warming?

Discussion #1 What are some of the economic consequences of global warming? What kind of market failures does this predict? What should the role of government be to correct this market failure? If you were "monarch of the world", what would you do? Who would be hurt by your action? How would you compensate them? Discussio

### Consumption Spending Utility Functions

I am stuck on a question and can use some help with a detailed solution. A utility function of a worker is U(C,L) = C * L where C is Consumption and L is Leisure If the worker has a weekly income of \$600 and has 70 hours a week of Leisure, how many additional dollars of income would it take to make the worker work 10

### Economics and shareholders

See attached file for full problem description.

### Diminishing Marginal Utility: Consumption & Diminishing Returns

Is there a parallel between diminishing marginal utility in consumption and diminishing returns in production? and if so, what would be some possible similarities.

### Computing the Expected Utility

How do I compute the Expected Utility given the probabilities and the utility of each outcome that I am given?

### Macro & Micro Economics in Decision Making

Articulate how macro- and microeconomics come into play in the context of company decision-making in a global business.

### Utility Maximization

Every November, Smith and Jones each face the choice between burning their leaves or stuffing them into garbage bags. Burning the leave sis much easier but produces noxious smoke. The utility values for each person, measured in utils, are listed in the table for each of the four possible combinations of actions: (please see at