## Win/Win Math

**Mathematics for Management**

Evaluation and graphing of functions, the geometry of straight lines, operations on matrices, solving systems of equations, and set theory and probability theory. Emphasis is on application rather than computational methods of mathematical rigor. The problems of acquiring, measuring, and using economic data

Example A simple example of a relationship in econometrics from the field of labor economics is:

This example assumes that the natural logarithm of a person's wage is a linear function of (among other things) the number of years of education that person has acquired. The parameter β1measures the increase in the natural log of the wage attributable to one more year of education. The term ε is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, β0 and β1 under specific assumptions about the random variable ε. For example, if ε is uncorrelated with years of education, then the equation can be estimated with ordinary least squares.

If the researcher could randomly assign people to different levels of education, the data set thus generated would allow estimation of the effect of changes in years of education on wages. In reality, those experiments cannot be conducted. Instead, the econometrician observes the years of education of and the wages paid to people who differ along many dimensions. Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both theeffect of education on wages and the effect of other variables on wages, if those other variables were correlated with education. For example, people born in certain places may have higher wages and higher levels of education. Unless the econometrician controls for place of birth in the above equation, the effect of birthplace on wages may be falsely attributed to the effect of education on wages.The most obvious way to control for birthplace is to include a measure of the effect of birthplace in the equation above. Exclusion of birthplace, together with the assumption that ε is uncorrelated with education produces a misspecified model. A second technique for dealing with omitted variables is instrumental variables estimation. Still a third technique is to include in the equation additional set of measured covariates which are not instrumental variables, yet render β1identifiable.[15] An overview of econometric methods used to study this problem can be found in Card (1999).[16]

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This example assumes that the natural logarithm of a person's wage is a linear function of (among other things) the number of years of education that person has acquired. The parameter β1measures the increase in the natural log of the wage attributable to one more year of education. The term ε is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, β0 and β1 under specific assumptions about the random variable ε. For example, if ε is uncorrelated with years of education, then the equation can be estimated with ordinary least squares.

If the researcher could randomly assign people to different levels of education, the data set thus generated would allow estimation of the effect of changes in years of education on wages. In reality, those experiments cannot be conducted. Instead, the econometrician observes the years of education of and the wages paid to people who differ along many dimensions. Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both theeffect of education on wages and the effect of other variables on wages, if those other variables were correlated with education. For example, people born in certain places may have higher wages and higher levels of education. Unless the econometrician controls for place of birth in the above equation, the effect of birthplace on wages may be falsely attributed to the effect of education on wages.The most obvious way to control for birthplace is to include a measure of the effect of birthplace in the equation above. Exclusion of birthplace, together with the assumption that ε is uncorrelated with education produces a misspecified model. A second technique for dealing with omitted variables is instrumental variables estimation. Still a third technique is to include in the equation additional set of measured covariates which are not instrumental variables, yet render β1identifiable.[15] An overview of econometric methods used to study this problem can be found in Card (1999).[16]

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**WORK EQUATION**

The equation is to assist in making a decision about accepting a job position or continuing to work: the economics of time and best allocation of assets. Based on the premise of opportunity lost; when we take action towards one thing we lose the possibility of pursing another action. Strategically we have to choose certain daily actions that best suit our personal goals and desires.

**Objective**: Find the value of each variable and applicable sequence to find the win/win solution.

**Variables:**

· Time per day involved in pursuit of job description or work related goals.

· Prospecting cost per lead generation of names and contact information.

· Past worker performance ratios and percentages that can be duplicated.

· Sales cycle, complete time length from contact to pay received.

· Product

· Price of Product

· Company contribution and direct assistance to individual success, such as training and a solidified IMC process in place, current campaigns, promotions, etc to fulfill end goals?

· Pay: salary or commission or both, what benefits, bonuses

· Reputation of Company

The balance of the equation is the representation of the win/win work solution.

The idea is accepting work is an exchange of your time and human resources for monetary compensation, however, to accept this agreement one must equate more than simple pay. A full equation of multiple variables has to be worked out and considered.

In a brief interview or conversation one must be able to ask the right questions or ascertain the necessary information to find the variables values, easily work those into an equation and determine if the equation balances at win/win, thus moving forward with work or accepting a position.

**Desired outcome**: To clarify, this is not based on the idea that win/win is a straight 50% financial portion, but a 50% win /win: 50 equals 50 with all variables considered.

Example: One job offers 10% commission with $3000 base, another job offers 40% commission with no base. Which do I choose? The decision comes from finding the values for the variables in an interview or salary negotiation. Another simple example; two jobs offering the same monetary compensation, which is the best position?

Expectation value is the basis of variable value. For example, if it costs you $3 to roll a dice, and you win dollars equal to the roll, then your expected income is -3+(1+2+3+4+5+6)/6=$.5

Likewise, if you have two options:

earn $50,000 per year

earn $40,000 per year, but have a 50% chance of a $30,000 bonus

Then your expected value in the second option is higher. (but it's riskier)

Ex. One job offers 10% commission with $3000 base, other job offers 40% commission with no base.

What is the expected commission? This will determine which a better deal is.

rate*(estimated gross)+base=earnings.

E=B+sum(Ci*Pi,i=1..N)

earnings=base +Commission*Probability of getting that commission+C2*P2+C3*P3+...

So you're expected to earn an amount that's equal to your base pay, plus the sum over each possible commission or bonus times the probably that you'll earn that commission or bonus based on the required or necessary position duties and responsibilities.

Using this, I can calculate how much I would expect to be paid for each job or how much work I can expect to do based on the pay offered. In the end if the equation balances at win/win or very close to it I accept, negotiate or walk away.