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# Principles of Mathematical Economics

Mathematical economics is the application of mathematical methods to represent theories and analyze problems that apply to economics. The applied methods which are used include integral calculus, difference and differential equations, matrix algebra, mathematical programming and computational methods. Mathematics allows economists to form meaningful, testable proposition about wide-ranging and complex subjects. Most of the economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.

Many theories in classical economics can be presented in simple geometric terms or elementary mathematical notation. Mathematical economics makes use of calculus and matrix algebra in economic analysis in order to make powerful claims that would be more difficult without such mathematical tools. It has become increasingly dependent upon mathematical methods and the mathematical tools it employs.

### Determine the net present worth for Hollingsworth Machine Group

Hollingsworth Machine Group needs a new precision grinding wheel. If 12% is the acceptable return for Hollingsworth, determine the net present worth of one of the best alternatives. Cost =\$80,000 Useful life = 5 years Annual Cost=\$12,000 Salvage Value=\$10,000

### Mathematical Economics-Price and output determination

1. Assume you are the manager of a firm that holds a patent that makes it the exclusive manufacturer of a unique SD card. Based on the estimates provided by a consultant, you know that the relevant demand and cost functions for this SD card are Q = 120 - 2P; C = 20 + 2.5Q2. What are the levels of quantity and price when you

### Capital Budgeting Techniques: IRR Method

See the attached file for full problem. A particular operation at a manufacturing company costs \$100,000 per year in labor costs. A proposal is made to automate this operation with a robot. The cost of the robot, the controller, and ancillary systems is \$200,000 installed. It has a 10-year life and no market value at the end

### Asset replacement and capital budgeting

The plant has accumulated savings of \$60,000 to acquire a new machine for quality assurance of its products. The new quality control machine cost \$80,000. The extra \$20,000 needed to acquire the new machine will be finance through a loan at 6% annual interest with the principal (\$20,000) due at the end of the third year. The inc

### Cash Flow Problems With Gazprom

After reading a financial article, which cash flows (present, future, annuity, or gradient) is implied or mentioned in the article?

### Engineering Economics Problems

2. A machine is under consideration for a new manufacturing process. The interest rate is 10% computed semiannually. Compute the future worth of this alternative: First cost = \$70,000 Semiannual cost = \$6,000 Semiannual income = \$18,000 Salvage value = \$9,000 Life in years = 5 4. You deposit \$5,000 in a savings cert

### Calculating the present equivalent cost for given proposals

The projected annual sales of new product are projected to be \$25,000 the first year and increase by \$10,000 per year until \$55,000 are sold during the fourth year. Sales are then predicted to decrease by \$5,000 per year in the fifth year and each year thereafter until \$25,000 are sold in the tenth year. Proposal A is to pur

### Supply - demand and elasticity

The demand for good X has been estimated to be ln Qxd = 100 − 2.5 ln PX + 4 ln PY + ln M. The income elasticity of good X is: 4.0. 1.0. 2.0. −2.5. What is the value of a preferred stock that pays a perpetual dividend of \$150 at the end of each year when the interest rate is 3 percent? Instructio

### Math Question

Say there is a market for a certain drug consists of domestic (United States) consumers and foreign consumers. The drug's marginal cost is constant at \$5 per dose. The demand schedules for both regions are as follows: US Foreign Price Quantity Quantity \$60 1,000 200 55 1,500 250 50 2,500

### Aggregate Demand Curve and Federal Reserve Policy

1. A change in the real money supply can result either from a change in the normal money supply through Federal Reserve policy (holding the price level constant) or from a change in the price level ( holding the normal money supply constant). The change in the nominal money supply causes a shift of the aggregate demand curve, wh

### Combined Bundle Package Benefits

A cable company offers two basic packages: sports and kids, and a combined package. there are three different types of users: parents, sports fans, and generalists. The following table show the maximum price that each type of consumer is willing to pay for each package. Sports Package

### Second-Degree Price Discrimination Benefits

Suppose that individual demand for a product is given by QD = 1000 - 5P. Marginal revenue is MR = 200 - 0.4Q, and marginal cost is constant at \$20. There are no fixed costs. a. The firm is considering a quantity discount. The first 400 units can be purchased at a price of \$120, and further units can be purchased at a price o

### Breakeven point, shutdown point, and supply curve

The following graph shows the cost curves for perfectly competitive firm. Identify the: (See Graph 02) -Shutdown point -Breakeven point -the firm's short-run supply curve *See attachment for Graph

### Comparison of Web Markup Languages

I) Name the different Web markup languages and explain the differences among them. II) Name five basic functionalities a Web server should provide. III) What are some of the policies that e-commerce businesses must develop before launching a site, and explain why must they be developed?

### Purpose of Price Elasticity

Can you explain the point of price elasticity?

### Economic Character of a Project

Using the information in the attached file, determine both the shortest amount of time in which the project schedule can be crashed without exceeding \$7K and the project critical path that resulted from crashing the project.

### Calculate the retirement payments

An engineer on the verge of retirement has accumulated savings of \$200,000 in an account paying 10% compounded quarterly. 1. The engineer wishes to withdraw \$7000 each quarter for living expenses. For how long can he/she withdraw that full amount? 10 years 12.5 years 15 years 25 years For as long as he/she lives.

### Cinema Theater 3rd-Degree Price Discrimination

Cinema Theater has estimated the following demand functions for its movies: Daytime demand, Qd = 400 - 50Pd Nighttime demand, Qn = 200 - 20Pn The marginal cost of serving another customer is \$5 and its fixed costs are \$100. a. If the theater uses third degree price discrimination, what price will it charge for daytime t

### Herfindahl Index (HHI)

Suppose the market for toy trains is comprised of the following seven competitors with the indicated market shares: Little Toot Toys 55% Trains R Us 3% I Think I Can 25% Thomas Trains 3% Engines, Inc. 8% The Fastest Trains 2% Silver S

### Loan Payment Problems

At the beginning of the year you take out a loan of \$60,000 at 12% annual interest rate compounded monthly. The minimum monthly payment on the first day of each month is 3% of the amount owed or \$10, whichever is greater. You may assume that a year is evenly divided into 12 months. (1) Suppose you make 11 minimum monthly pay

### Interest and Limits

Please see attachment for question. If the annual interest rate is r, then the effective interest for a time period of length T with compounding frequency N is given by the following equation (see that attached file for the equation). (1) Show by algebra that r(T,N) = (1 + rT/N)^N - 1. (2) What is the limit r(T) = lim(N

### Black-Scholes Formula Price

Calculate of the price of a call option by binomial tree models and compare the results with the theoretical Black-Scholes formula. Parameters: Strike price = \$120; Expiration time = 1 year; Annual interest rate = 0.05; Stock volatility = 0.35. For the initial stock price, S0 = 100.45 Requirements: 1. Find the price

### MPC and MPS

Explain the relationship between the marginal propensity to consume and the marginal propensity to save. How do these two components affect GDP?

### Constrained optimization problem

Step by step explanation/solution Brian is taking three courses this semester: economics, statistics, and finance. He has decided to spend 19 hours per week studying (in addition to attending all his classes) and his objective is to maximize his average grade, which means maximizing the total of his grades in the three course

### Two equal sized newspapers have overlap circulation of 10% (10% of the subscribers subscribe to both newspapers.) Advertisers are willing to pay \$10 to advertise in one newspaper but only \$19 to advertise in both, because they're willing to pay twice to reach the same subscriber. What's the likely bargaining

Two equal sized newspapers have overlap circulation of 10% (10% of the subscribers subscribe to both newspapers.) Advertisers are willing to pay \$10 to advertise in one newspaper but only \$19 to advertise in both, because they're willing to pay twice to reach the same subscriber. What's the likely bargaining

### Step by step calculation of company cost of capital and weighted average cost of capital (WACC).

1) A company is 40% financed by risk- free debt. The interest rate is 10%, the expected market risk premium is 8%, and the beta of the company's common stock is 0.5. What is the company cost of capital? What is the after- tax WACC, assuming that the company pays tax at a 35% rate?

### Economics of Merger

An industry consists of 6 firms, with sales of \$100,000, \$500,000, \$400,000, \$300,000, 60,000, and \$75,000. Now, suppose the two smallest firms merge. a. Calculate the four-firm concentration ratio (C4) before the merger. Show your work. b. Calculate the four-firm concentration ratio (C4) after the merger. Show your work. c