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Principles of Mathematical Economics

Consider an industry in which two firms are producing a product.

Consider an industry in which two firms are producing a product. Assume that the two firms are current "colluding together" to set price so to maximize the industry profit. At this collusive price, the industry profit is $100 million - and that profit is split evenly between the two firms. Assume also that if one firm were to

Mergers and P/E Ratios.

Mergers and P/E Ratios. Castles in the Sand currently sells at a price-earnings multiple of 10. The firm has 2 million shares outstanding, and sells at a price per share of $40. Firm Foundation has a P/E multiple of 8, has 1 million shares outstanding, and sells at a price per share of $20. a. If Castles acquires the oth

Maximizing Total Profits and Revenue

A Monopolist's Demand and Total Cost functions are: P= 1624 -4Q TC= 22,000 + 24Q -4Q(squared) + 1/3Q (to the third power) Where Q is output produced and sold a. At what level of output and sales (Q) and price (P) will Total Profits be maximized? b. At What level of output and sales (Q) and price (P) will Total Rev

Probability Frequency Calculation

The number of cars arriving at Joe Kelly's oil change and tune-up place during the last 200 hours of operation is observed to be the following: Number of cars arriving Frequency 3 or less 0 4 10 5 30 6 70 7 50 8

Expected return and Standard Deviation of a portfolio, CAPM

The following four questions need to be addressed with regards to each problem. 1. What financial concept or principle is the problem asking you to solve? 2. In the context of the problem, what are some business decisions that a manager would be able to make after solving the problem? 3. Is there any additional infor

Managerial Economics Question

An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows: Quantity Price ($) Adults Children 5 15 20 6 14 18 7 13 16 8 12 14 9 11 12 10 10 10 11 9 8 12 8 6 13 7 4 1


The __________ is the ratio of __________ to the _____________. a standard deviation; covariance; expected value b coefficient of variation; expected value; standard deviation c correlation coefficient; standard deviation; expected value d coefficient of variation; standard deviation; expected value e

Lagrangian Multipliers

Fixed capital and labor expenses are $1.2 million per year. Variable expenses average $2,000 per van conversion. Q=1,000 - 0.1P where Q is the number of van conversions (output) and P is price. Calculate the profit maximizing output, price and profit levels.

errors in their comparative statistical analysis

When a firm estimates the demand for its product what data collection problems would you anticipate having. For example, at GM how hard is it to list the non-price determinate of demand for its cars? Can they obtain the right set of data? How would they collect the data? What would cause errors in their comparative statistic

Motivations in the Marketing Industry

What motivates people in the marketing industry using incentives, opportunity cost, normative and empirical economics and marginal analysis and marginal benefits?

Queue discipline & simulation

1) A goal of many waiting line problems is to help a firm find the ideal level of services that minimize the cost of waiting and the cost of providing the service. True or False 2) One difficulty in waiting line analysis is that it is sometimes difficult to place a value on customer waiting time. True or False 3) A

Magazine case

A survey of top executives revealed that 35% of them regularly read Time magazine, 20% read Newsweek, and 40% read US News and World Report. Ten percent read both Time and US News and World Report. a)What is the probablility that a particular top executive reads either Time or US News and World Report regularly? Show th

Three defective electric toothbrushes problem

Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 nondefective ones. a.) What is the probability the first two electric toothbrushes sold will be returned to the drugstore because they are defective? b.) What is the probability the first two electric toot

Interest rates associated with price

If there are an increase in interest rates will it be associated with increase in oil prices? If so, what is the connection? (I want more of a written than mathematical explanation if possible).

Economics of internet

You can see the notes that are attached. Please solve the following problems based on the notes. 1. Assume that the disutility of travel for consumers arrayed uniformly along a "Hotelling" line is not t as discussed in class, but t2, (i.e. the utility of a consumer for the product is: Utility(Product i) = 3 - (ideal

Concentration Ratio & Herfindahl-Hirschman index

Please assist and show steps. An industry consists of 5 firms, with sales of $100,000, $500,000, $400,000, $300,000, and $200,000. Now, suppose the largest and smallest firms merge. -Calculate the four-firm concentration ratio (C4) before the merger. -Calculate the Herfindahl-Hirschman index (HHI) before the merger. -C

Deriving maximum value and minimum value functions: an example

See the attached file as equations are contained within the Word file. Consider the following function: (see file) where a > 0 is a parameter. 1. Find the first order condition for a critical point of this function. 2. Is this a maximum or a minimum or an inflection point? 3. Solve for x* (a), the maximizer of the fun

Assets/variance/portfolio question

B. Assume there are only two assets in a portfolio. If this portfolio has a positive weight for each asset, can its (portfolio.s) variance be greater than the variance of returns on the asset in the portfolio that has the higher variance of the two? Explain. Can the variance of the portfolio be smaller than the variance of retur

Per Capita Real GDP Problem

Access the web-site Click on "Most Requested Series" Required 1. Compute Per Capita Real GDP using 4th Quarter data for the period 1991 - 2000. (see Real Gross Domestic Product and Total U.S. Population) 2. Plot Time Series Per Capita Real GDP

Calculating GDP and Summary

Gross Domestic Product (example problem) Nominal Real GDP Per Capita GDP GDP Deflator Inflation Real GDP Population Year ($Billions) ($Billions) (1982 = 100)

Matrices Eigenvalues Examples

I need help with this problem. I've been working on it for a while and unable to solve it. I need to understand how to solve this problem through examples. With step by step breakdown to fully complete the problem. Thank you for your help it is greatly appreciated! (a) Prove that if A and B are both invertible n x n m

Internal economies of scale & six-tenths rule

Please can you help me understand the following question for exam revision purposes. Can you include the step by step workings so i can understand how it should be done, as well as the final solution. Question: The six-tenths rule quantifies the relationship between the relevant costs of a firm's decision to expand and

Applied microeconomics

A. How much time should be spent studying for each class? That is, maximize GPA by determining E* and U* subject to the 12 hour study time constraint. b. Did this allocation of study time maximize or minimize your GPA?