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# Principles of Mathematical Economics

### Black-Scholes Formula in Switzerland

You are based in Switzerland. You own two call options both maturing in one year: call option to buy USD at strike 1.2200 CHF/USD and call option to buy EUR at strike 1.5200 CHF/EUR. Spot CHF/USD is 1.2255 and spot CHF/EUR is 1.5255. Which of the option costs more?

### 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

### Federal Reserve problem

Suppose that the Federal Reserve lowers the required reserve ratio from 0.10 to 0.05. How does this affect the simple money multiplier, assuming that excess reserved are held to zero and there are no currency leakages? What are the money multipliers for required reserve ratios of 0.15 and 0.20?

### Earnings Per Share & Price-Earnings Ratio

Attached is a Word document that has the financial documentation provided for the problem. If the market value of the company is 17.2 billion at the end of the year, what was the market to book ratio? If there were 205 million shares outstanding, what were the earnings per share? The price-earnings ratio?

### Per Capita Real GDP Problem

Access the web-site http://www.Economagic.com. 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)

### Bayesian forecasting

Discuss the differences between Bayesian forecasting and the incorportation of intervention analysis into the ARIMA model-building framework.

### Gross Domestic Product Calculation

DATA ARE IN TRILLIONS OF DOLLARS Personal consumption expenditures \$3.0 Net private domestic investment 1.4 Depreciation 0.2 Government purchases of goods and services 2.0 Exports 0.5 Imports 0.3 Foreign factor income 0.1 The economy's GDP is _________ trillion. a. 6.6 b. 6.8 c. 7.2 d. 7.4. The economy's GN

### 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

### Kuhn Tucker conditions

Help to clarify matrices, Jacobian, quasi-concavity, Hessian, and Kuhn-Tucker conditions is provided. 1. (a) Solve the problem of minimizing x2 - 4x + 1 subject to x4 - 1 ≤ 0. (b) Solve the problem of maximizing ƒ(x) = x subject to g(x) = x4 if x ≤ 0, 0 if x Є [0, 1], (x-1)4 if x ≥ 1. Explain why the Kuhn-Tu

### Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions

How to apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions?

### Quasi-Concavity, Hessian, and Kuhn-Tucker Conditions

Apply matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions 1. (a) Given that ƒ(x, y, u, v) = 0 and g(x, y, u, v) = 0, determine ∂u/∂x, ∂u/∂y, and ∂v/∂y. (b) Given that u = ƒ(x,y) and v = g(x,y), prove that there exists a functional relationship between u and v of the form ø(u,v) = 0 if and on

### Matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions

Matrices, Jacobian, quasi-concavity, Hessian, Kuhn-Tucker conditions *******NOTE********** 1 (iii) is (n-2)2 as in "n" minus "2" Squared.. just in case it caused some confusion. Sorry

### 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 allocations

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?