### Only Economics for Ugc Net some basic terminology

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**Only Economics for Ugc Net some basic Terminology **

**Absolute minimum:** The output value of the lowest point on a graph over a given input interval or over all possible input values. An absolute minimum point is a local minimum point and occurs at an endpoint of the given input interval.

**Absolute vs. Relative Price:** Absolute price is the number of dollars that can be exchanged for a specified quantity of a given good. Relative price is the quantity of some other good that can be exchanged for a specified quantity of a given good. Suppose we have two goods A and B. The absolute price of good A is the number of dollars necessary to purchase a unit of good A. The relative price of good A in terms of B is the amount of good B necessary to purchase a unit of good A. The change in relative prices is not the same thing as changes in absolute prices. Sometimes, the absolute prices of goods may change but relative prices may remain constant. In general, we measure absolute prices in terms of dollars and relative prices in terms of units of some other good. However, many times we measure relative prices in terms of dollars also keeping in mind that the word dollar is being used to refer not to a piece of green paper but to a basket of goods. In microeconomics, the word prices always refer to relative prices.**Angle:** The amount of rotation in a turn. An angle can be thought of as the counterclockwise rotation of its initial side into its terminal side. The size of an angle is the measure of this rotation, and a negative sign in front of the size indicates clockwise rotation.**Antiderivative:** A function F is an antiderivative of another function f if the derivative of F is f. If F is an antiderivative of f, where both F and f have input x and C is an arbitrary constant, then y = F(x) + C is called a general antiderivative of f .**Annual percentage rate (APR):** The percentage used in calculating interest each compounding period. In an investment context, the annual percentage rate (or nominal rate) is the advertised rate of interest, 100r%.**Annual percentage yield (APY):** A percentage by which an investment grows over one year. Unlike APR, APY indicates the affect of the compounding periods. APY will be larger than APR any time interest is compounded more frequently than once a year.**Approximate change in a function:** The rate of change of the function times a small change in the input of the function. That is, for the function f with input variable x, the approximate change in f is f ' (x).h where h represents the small change in x. The exact change is f(x + h) - f(x).**Autocorrelation:** A correlation between a component of a stochastic process and itself lagged a certain period of time.**Average cost :** The total production cost divided by the number of units produced.**Average rate of change:** The amount that a quantity changes over an interval divided by the length of the interval. That is, if a quantity changes from a value of m to a value of n over a certain interval, the average rate of change equals n - m length of interval. The average rate of change is the slope of the secant line. Average rates of change have labels of output units per input unit.

**Beta:** A measure of systematic risk.**Bias:** Bias is the difference between the parameter and the expected value of the estimator of the parameter.**Black-Scholes Theory:** Another name for option pricing theory. Differential equations approach is an informal name for derivatives pricing models based upon the original Black-Scholes methodology.**Bootstrapping:** Bootstrapping method is to obtain an estimate by combining estimators to each of many sub-samples of a data set. Often M randomly drawn samples of T observations are drawn from the original data set of size n with replacement, where T is less than n.**Break-even point:** The number of units (produced or sold) for which revenue equals cost so that profit is zero.**Business Cycle Frequency:** The business cycle frequency is often considered to be three to five periods.**Buyer's Market:** A buyer's market is a market for a good (stocks, housing, etc.) where prices are falling and there are more parties interested in selling than in buying.**Business risk:** Exposure to uncertainty in economic value that cannot be marked-to-market.

**Calculus:** The branch of mathematics involving derivatives and integrals.**Capital allocation:** A process of choosing what ventures, deals or trades to engage in, usually based upon some cost or risk-return analysis.**Capital asset pricing model:** A model for valuing financial assets based upon their systematic risk.**Cash instrument:** An instrument whose value, unlike that of a derivative instrument, is determined directly by the markets.**Change:** If a quantity changes from a value of m to a value of n over a certain interval, then the change in the quantity is n - m.**Changes in demand:** A change in price does not lead to a change in demand. But a change in a factor other than price such as income and prices of related goods etc, does lead to a change in demand. In that case the change in demand leads to a shift in the demand curve. A fall in demand shifts the demand curve to the left and a rise in demand shifts the curve to the right. Other factors includes:

- Sales tax is a tax that is paid directly by consumers to the government. A sales tax makes a good less desirable and as such it affects demand. It causes the demand curve to shift towards the left parallel to itself by the amount of the tax.
- So far, we have been concerned with the demand by a single buyer. If there are N buyers in the market, then market demand is the sum of the demand by all the N buyers. The market demand curve is the horizontal summation of individual demand curves.

**Compound interest:**A method of crediting interest in which interest is earned on interest.

**Composition:**A method of combining two functions in which the output of one function (called the inside function) is used as the input of the other function (called the outside function).

**Compound interest formulas:**Exponential formulas that are used to determine the amount A(t) accumulated in an account after t years when P dollars are initially invested, if the nominal interest rate is 100r% compounded n times a year.

**Concavity:**A description of the curvature of a graph. A graph is concave up at a point if the tangent to that point lies below the graph near the point of tangency and concave down if the line tangent to that point lies above the graph near the point of tangency. The point at which the concavity changes to convexity is called an inflection point.

**Constant dollars:**Dollar values that have been adjusted for inflation by means of price indexes to eliminate inflationary factors and allow direct comparison across years. Conversion to constant dollars for a given year t may be calculated as the current dollar value multiplied by the purchasing power of the dollar based on a dollar value of $1 in year t.

**Correlation:**A parameter, related to covariance, that indicates the tendency for two random variables to "move together" of "co-vary."

**Correlation matrix:**A symmetric matrix indicating all the correlations of a random vector.

**Consumer Behavior:**The behavior of consumers in general depends upon two major factors:

1. Tastes (as represented by the concept called indifference curves)

2. Opportunities (as represented by the income or budget line)

**Consumer price index (CPI):**A measure that is 100 times the ratio obtained by comparing the current cost of a specified group of goods and services to the cost of comparable items determined at an earlier date. The consumer price index or CPI is a measure of the level of inflation. CPI measures how much the price of a basket of consumer goods has changed over a given time period.

**Consumers' expenditure:**The actual amount spent by consumers for a certain quantity of goods or services. The consumers' expenditure equals the market price times the quantity in demand.

**Consumers' surplus:**The amount that consumers are willing and able to spend but do not actually spend for a certain quantity of goods or services.

**Consumers' willingness and ability to spend:**The maximum amount that consumers say they will spend and/or actually spend for a certain quantity of goods or services.

**Continuous graph/function:**A continuous graph is an unbroken curve whose set of inputs is assumed to fill up an entire interval of values along the horizontal axis. A continuous graph can be drawn without lifting the writing instrument from the page. A smooth continuous graph is one with no sharp points. A continuous function is a function whose graph is continuous. When modeling real-life situations, continuous functions could be used without restriction or could be discretely interpreted.

**Continuous function used without restriction:**A continuous function for which inputs of any value make sense in context.

**Continuous function with discrete interpretation:**A continuous function whose interpretation makes sense only at certain distinct points.

**Continuous compound interest:**A limiting form of compound interest where the frequency with which interest is credited approaches infinity.

**Contour curve:**A two-dimensional outline of a three-dimensional graph at a given output level. For a three-dimensional function f, the k-contour curve is the collection of all points (x, y) for which f (x, y) = k, where k is a constant. Contour curves are also called level curves.

**Contour graph:**A graph of the contour curves f(x, y) = k for several values of a constant k. Usually, the values of k are equally spaced.

**Count data:**Totals that are reported for a specific time period but that are not cumulative because the counter that tallies the data during the period is reset to zero at the beginning of each period. When working with count data, accumulated change in a quantity is calculated by summing the output data.

**Control Variables:**A control variable is a variable in a model controlled by an agent in order to optimize a specific objective.

**Costs and Efficiency:**A cost is a foregone opportunity. Comparative advantage is the ability to perform a given task at a lower cost. An individual/country is said to be more efficient if it has a comparative advantage in the production of some good. In other words it is said to be more efficient.

**Covariance:**A parameter, related to correlation, that indicates the tendency for two random variables to "move together" or "co-vary."

**Covariance matrix:**A symmetric matrix indicating all the covariances and variances of a random vector.

**Covariance stationarity:**A property of some stochastic processes. A stochastic process is covariance stationary if neither its mean nor its autocovariances depend on the index t.

**Critical point:**A saddle point or a point corresponding to a relative maximum or relative minimum on a multivariable surface.

**Cross section:**For a two-variable function, the curve resulting when the function is intersected with a plane. A cross section of a function will always have one less dimension (variable) than the function itself.

**Cross-sectional function/model:**An equation describing a cross section of a multivariable function.

**Cubic function/model:**A function of the form f (x) = ax

^{3}+ bx

^{2}+ cx + d where a, b, c, and d are constants and not equal to zero. Cubic functions have one change in concavity (i.e., one inflection point) and no end behavior limiting values.

**Cumulative density function:**An accumulation function of a probability density function. The cumulative density function shows how probabilities accumulate as the value of the random variable increases.

**Cyclic function:**A periodic, continuous function that varies between two extremes. The part of the graph of the function that keeps repeating itself is called a cycle of the graph.

**Data:** Real-world information recorded as numerical values.**Decision Rules:** A decision rule is either a function that maps from the current state to the agent's decision or choice, or a mapping from the expressed preferences of each of a group of agents to a group decision. The first is more relevant to decision theory and dynamic optimization; the second is relevant to game theory. The phrase allocation rule is sometimes used to mean the same thing as decision rule. The term strategy-proof has been defined in both contexts.**Decreasing without bound:** A term applied to the output of a function that infinitely decreases in height. Decreasing without bound may describe either the end behavior of a function or the limiting value of a function as the input approaches a certain value.**Degree:** One of 360 equal parts into which a complete revolution is divided. Degree measure is one of the ways angles can be measured and is denoted by a small circle as a superscript.**Delta:** The Greek letter for the factor sensitivities measuring a portfolio's first order (linear) sensitivity to the value of an underlier.**Delta approximation:** A linear approximation for how a portfolio's value will change in response to a small change in an underlier's value.**Delta-gamma approximation:** A quadratic approximation for how a portfolio's value will change in response to a small change in an underlier's value.**Delta-gamma remapping:** A quadratic remapping constructed from a portfolio's deltas and gammas.**Demand:** The amount of a good or service that an individual is willing and able to buy at each possible price.**Demand curve/function:** A graph or equation relating the quantity of goods or services that consumers demand and the price per unit of those goods or services. Mathematicians use price as input and quantity demanded as output; economists use quantity demanded as input and price per unit as output.**Demand curve:** A graph illustrating demand, with prices on the vertical axis and quantity demanded on the horizontal axis. Demand curve slopes downward because of the negative relationship between price and quantity demanded.**Demand vs. Quantity demanded:** Demand is a set of number that lists the quantity demanded corresponding to each possible price whereas quantity demanded is the amount of a good or service that an individual is willing and able to buy at a given price. For instance, the information on price and quantity demanded presented in a table/demand schedule is collectively referred to as the demand.**Derivative:** The mathematical term for an instantaneous rate of change. The terms derivative, rate of change, instantaneous rate of change, slope of a curve, and slope of the line tangent to a curve are synonymous.**Derivative instrument:** An instrument which derives its value from the value of other financial instruments.**Depression:** A depression is a severe downturn in economic activity. These are considerably worse than recessions.**Determinants of demand:** Demand is affected by a number of factors. Price is the most important factor but there are other factors also that can influence demand such as:

- income
- prices of related goods
- taste
- expectation of the future, price and other factors

**Deterministic Functions and Variables:**Deterministic means not random. A deterministic function or variable often means one that is not random, in the context of other variables available. That is, those other variables determine the variable in question unerringly, by a function that would give the same value every time those other variables were given to it as arguments, unlike a random one which with some probability would give different answers.

**Differential equation:**An equation involving one or more derivatives. A general solution for a differential equation is a function that has derivatives that satisfy the differential equation, and a particular solution is a function obtained from the general solution and the initial conditions stated in a specific problem.

**Diminishing marginal utility:**Each additional unit of X yields less utility than the previous ones. This is known as the law of diminishing marginal utility. For instance, a thirsty person would derive more utility from the first glass of water than the successive ones.

**Direct proportionality:**For variables x and y, y is proportional to x if there exists some constant k such that y = kx. The terms proportional and directly proportional are used interchangeably. The constant k is referred to as the constant of proportionality.

**Discrete:**Discrete information is represented by a scatter plot or a table of data. Discrete graphs are scatter plots of data. In some situations, continuous functions are interpreted discretely; that is, outputs of the function have meaning in the context of a real-life situation only at some, not all, input values in an interval.

**Diverge:**A term applied to an improper integral for which the limit does not exist.

**Dynamic Optimization:**Dynamic optimizations are maximization problems to which the solution is a function; equivalently, optimization problems in infinite-dimensional spaces.

**Econometric Model:** An econometric model is an economic model formulated so that its parameters can be estimated if one makes the assumption that the model is correct.**Economics:** Economics is the study of how scarce resources are allocated to satisfy unlimited and competing ends.**Efficiency:** Efficiency activity or turnover ratios provide information about management's ability to control expenses and to earn a return on the resources committed to the business, for example:

- Cash Turnover = Net Sales / Cash
- Inventory Turnover = Cost of Goods Sold / Average Inventory

**Efficient frontier:**A theoretical set of portfolios offering optimal risk-reward tradeoffs.

**Elasticity:**A measure of responsiveness. The responsiveness of behavior measured by variable Z to a change in environment variable Y is the change in Z observed in response to a change in Y. Specifically, elasticity = (percentage change in Z) / (percentage change in Y).

**(Price) Elasticity of Demand:**It is a measure of how much the quantity demanded of a good responds to a change in the price of that good, computed as the percentage change in quantity demanded divided by the percentage change in price:

Ed = Price Elasticity of demand = (Percentage change in quantity demanded) / (Percentage change in Price)

Inelastic: If percentage change in quantity demanded is less than the percentage change in price.

Unit Elastic: If percentage change in quantity demanded is exactly equal to the percentage change in price.

Elastic: If percentage change in quantity demanded is greater than the percentage change in price.

**Elasticity and the Shape of the Demand curves:**A steep demand curve represents inelastic demand whereas a flat demand curve represents elastic demand. A vertical demand curve represents perfectly inelastic demand. A horizontal demand curve represents perfectly elastic demand curve.

**(Price) Elasticity of Supply:**It is a measure of how much the quantity supplied of a good responds to a change in the price of that good, computed as the percentage change in quantity supplied divided by the percentage change in price.

Es = Price Elasticity of supply = (Percentage change in quantity supplied) / (Percentage change in Price)

Inelastic: If percentage change in quantity supplied is less than the percentage change in price.

Unit Elastic: If percentage change in quantity supplied is exactly equal to the percentage change in price.

Elastic: If percentage change in quantity supplied is greater than the percentage change in price

**Elasticity and the Shape of the Supply curves:**A steep supply curve represents inelastic supply whereas a flat supply curve represents elastic supply. A vertical supply curve represents perfectly inelastic supply. A horizontal supply curve represents perfectly elastic supply curve. Since the economic incidence of a sales or an excise tax is independent of its legal incidence. In other words, the burden of the tax is shared by both buyers and sellers regardless of whether it is a sales tax or an excise tax. The magnitude of the burden however depends upon the elasticity of demand and supply curves. For instance, buyers will share a greater burden of the tax if demand is less elastic and sellers will share a greater burden if supply is less elastic.

**End behavior:**The behavior of the output of a graph as the input becomes infinitely large or infinitely small.

**Endogenous:**A variable is endogenous in a model if it is at least partly a function of other parameters and variables in a model, in contrast to exogenous.

**Equilibrium:**Equilibrium is some balance that can occur in a model, which can represent a prediction if the model has a real-world analogue. The standard case is the price-quantity balance found in a supply and demand model. If the term is not otherwise qualified, it often refers to the supply and demand balance.

**Equilibrium point:**The point at which the demand curve and the supply curve intersect. At this point, there is market equilibrium; that is, the supply of a product is equal to the demand for that product.

**Event:**An outcome of some happening whose results are subject to chance.

**Exogeneous:**A variable is exogenous to a model if it is not determined by other parameters and variables in the model, but it is set externally and any changes to it come from external forces, in contrast to endogenous.

**Expected value :**The expected value is a parameter indicating the "center of gravity" of a probability/density distribution. It is also the average of the data. The expected value is a parameter indicating the "center of gravity" of a probability distribution.

**Exponential function/model:**A function with an equation of the form f(x) = ab

^{x}or f (x) = ae

^{kx}. Exponential models are characterized by constant percentage change (percentage differences) in output values when input values are evenly spaced.

**Extrapolation:**The process of predicting an output value using an input value that is outside a given interval of input data. Extrapolation should always be viewed with caution.

**Extreme point:**A point at which a maximum or minimum output occurs. At an extreme point on a graph, the slope of the line tangent to the curve at that point is zero or the slope does not exist at that point (but the function output exists at that point). Extreme points occur at an input value, but the extreme value is an output value. For multivariable functions, relative extreme points cannot be visually identified on the edges of tables or contour graphs.

**First differences:** The changes in successive output values. It is helpful to calculate first differences for a data set only if all input data values are evenly spaced.**Fixed costs:** Also called start-up costs, these costs do not vary with the number of items produced or the amount of service performed.**Four-Step Method:** An algebraic method of finding the derivative of a function using the definition of the derivative.**Function:** A function is a rule that assigns exactly one output to each input. Functions are represented verbally by word descriptions, numerically in tables, visually with graphs, or algebraically with equations. If x is the input symbol and f is the rule, then f(x) symbolizes the output. Input/output diagrams display the input, how the input is measured (input units), the rule that relates the input and output; and the output, including how the output is measured (output units).**Future value:** The value of an investment at some time in the future. Future value for discrete situations is calculated using the appropriate compound interest formula. The future value of a continuous income stream is the total accumulated value of the income stream and its earned interest.

**Gamma:** The Greek letter for the factor sensitivities measuring a portfolio's second order (quadratic) sensitivity to the value of an underlie.**Generalized Linear Model:** A generalized linear model is a model where y is a vector of dependent variable, and x is a column vector of independent variables. The model is often called a link function.**Graph:** One of the ways to represent a function or a real-life situation by plotting output and input points on coordinate axes. Discrete graphs are scatter plots. Continuous graphs can be drawn without lifting the writing instrument from the page.

**Hedging:** The taking of offsetting risks.**Hessian Matrix:** The Hessian matrix is the matrix of second derivatives of a multivariate function. That is, the gradient of the gradient of a function. Properties of the Hessian matrix at an optimum of differentiable function are relevant in many places in economics and finance.**Histogram:** A graph that is composed of rectangles and constructed so that the area of each rectangle is the percentage of outputs in the corresponding input interval. These histograms are also called probability histograms because the area of each rectangle is the probability that the value of the random variable under discussion is in the interval that forms the base of the rectangle.

**Identification:** A parameter in a model is identified, if and only if, complete knowledge of the joint distribution of the observed variables gives enough information to calculate the parameter exactly.

If the model has been written in such a way that its parameters can be consistently estimated from the observables, then the parameters are identified. A model is identified if there is no observationally equivalent model. That is, potentially observable random variables in the model have different distributions for different values of the parameter.**Indifference curve (IC):** IC is a locus of points representing different baskets of commodities X and Y that may give consumers the same level of utility or satisfaction so that he is indifferent among them.**Income stream :** A flow of money into an interest-bearing account over a period of time. When the money flows continuously into the account, the flow is called a continuous income stream. A discrete income stream is a one into which money flows at specific intervals of time (quarterly, monthly, daily, and so on.)**Increasing without bound:** A term applied to the output of a function that infinitely increases in height. Increasing without bound may describe either the end behavior of a function or the limiting value of a function as the input approaches a certain value.**Inflation:** An ongoing rise in the average level of absolute prices.**Inflection point :** A point where the concavity of a graph changes. Cubic and logistic functions have one point. Sine and cosine functions have two inflection points in each cycle and an infinite number of inflection points over all real number inputs. In real-life applications, the inflection point is interpreted as the point of most rapid change or least rapid change in an area near the inflection point.**Initial condition :** A known point on the graph of a particular solution for a differential equation.**Instantaneous rate of change:** The instantaneous rate of change at a point on a curve is the slope of the curve at that point and the slope of the line tangent to the curve at that point. Instantaneous rates of change have labels of output units per input unit.**Integration:** The process of evaluating a definite integral to determine the accumulation of change or the process of recovering a quantity function from a rate-of-change function.**Interpretation of a result:** A simple non-technical sentence explaining the real-life meaning of a result.**Intercept:** The input value where the graph crosses or touches the horizontal axis or the output value where the graph touches or crosses the vertical axis.**Interpolation:** The process of predicting an output value using an input value that is within a given interval of input data.**Inverse function:** If a rule obtained by reversing the input and output of a function is also a function, then it is called an inverse function.**Ito Process:** An Ito process is a stochastic process: a generalized Wiener process with normally distributed jumps. A generalized Wiener process is a continuous-time random walk with a drift and random jumps at every point in time.

**Jackknife Estimator:** A jackknife estimator creates a series of estimates, from a single data set by generating that statistic repeatedly on the data set, leaving one data value out each time. This produces a mean estimate of the parameter and a standard deviation of the estimates of the parameter.**Joint proportionality:** For variables x, y, and z, y is jointly proportional to x and z if there exists some constant k such that y = kxz. The constant k is the constant of proportionality.

**Kurtosis:** A parameter describing the peakedness and tails of a probability distribution.

**Law of demand:** All else equal, if the price of a good goes up, quantity demanded goes down and vice versa.**Least squares method:** A procedure to determine the line that best fits a set of data using the criterion that the sum of the squares of the deviations of all the data points from the fitted line, i.e., SSE is at a minimum.**Least squares line:** The linear function that best fits a set of data, where best fit is defined according to the least squares method.**Legal Incidence vs. Economic Incidence of a Tax** Legal incidence refers to the division of a tax burden according to who is required by law to pay the tax, while economic incidence refers to the division of a tax burden according to who actually pays the tax after all price adjustments are taken into account. A change in the legal incidence of a tax will have no effect on the economic incidence. If the legal incidence of a per-unit tax is entirely on suppliers, the supply curve will shift up by the amount of the tax. On the other hand, if the legal incidence is entirely on demanders, the demand curve will shift down by the amount of the tax. In both situations, the equilibrium quantity will fall, suppliers will receive a lower post-tax price, and demanders will pay a higher post-tax price.**Leverage Ratios:** Leverage ratios measure the degree of protection of suppliers of long-term funds and can also aid in judging a firm's ability to raise additional debt and its capacity to pay its liabilities on time, for example:

- Total Debts to Assets = Total Liabilities / Total Assets
- Capitalization Ratio= Long-Term Debt /(Long-Term Debt + Owners' Equity)

**Limit:**A number to which the output of a function becomes closer and closer as the input becomes closer and closer to a stated value.

**Linear function/model:**A function that repeatedly and at even intervals adds the same value to the output. A linear model is a function of the form f(x) = ax + b representing a situation in which incremental change is constant. In the linear function, a is the constant rate of change of the output, i.e., the slope of the graph of the linear function and b is the output corresponding to an input of zero, i.e., the vertical axis intercept. When input values in a set of data are evenly spaced and the first differences of the output values are constant, the data should be modeled by a linear function.

**Linear system of equations:**Two or more equations in which all the variables occur to the first power and there are no terms in which two different variables are multiplied or divided.

**Liquidity Ratios:**Liquidity ratios measure a firm's ability to meet its current obligations, for example:

- Acid Test or Quick Ratio = (Cash + Marketable Securities + Accounts Receivable) / Current Liabilities
- Cash Ratio = (Cash Equivalents + Marketable Securities) / Current Liabilities

**Local linearity:**The principle that if we graph a smooth, continuous function over a small enough interval around a point, then the graph looks like the line tangent to the curve at that point. That is, the tangent line and the curve are basically indistinguishable over the interval.

**Logarithmic (log) function/model:**A function with an equation of the form f(x) = a + blnx. This function is the inverse of the exponential function y = AB , where A = e

^{x/b}and B = e

^{-a/b}.

**Logistic function/model:**A function of the form f(x) = L + Ae

^{-bx}. The graph of a logistic function is bounded by the horizontal axis and the line f(x) = L. We refer to L as the limiting value (or carrying capacity or saturation level) of the function.

**Marginal analysis:** A type of approximation of change used in economics. The rates of change of cost, revenue, and profit with respect to the number of units produced or sold are called marginal cost, marginal revenue, and marginal profit. These rates are often used to approximate the actual change in cost, revenue, or profit when the number of units produced or sold is increased by one.**Marginal utility**: The marginal utility of a good say X is defined to be the amount of additional utility derived from the consumption of an additional unit of X while keeping the quantity of the other good say Y as constant.**Market price:** The actual price that a consumer pays for one unit of goods or services.**Mathematical modeling:** The process of translating a real-world problem into a useable mathematical equation.**Matrix:** A rectangular arrangement of numbers in rows and columns. Matrices are useful in solving systems of linear equations.**Mean:** One of the measures of the center of a probability distribution, the mean (also called the expected value or average) is the input value of the "balance point" of the region between the density function and the horizontal axis.**Microeconomics:** Microeconomics is the study of the economic choices made by individual economic units such as consumers, households and firms etc.**Model:** A mathematical model is an equation, along with descriptions and units of the variables, that describes a real-life situation. There are four important elements to every model: an equation, a label denoting the units on the output, a description (including units) of what the input variable represents, and an indication of the interval of input values over which the model is valid.**Monopoly:** If a certain firm is the only one that can produce a certain goodsor service, it has a monopoly in the market for that goods or service.**Mortgage Terms:**

- "Good faith" estimate: It is an estimate of the fees that you will pay to close your loan.
- A cash-out option? If your equity in your property qualifies, you can refinance with a loan amount greater than your current mortgage - and keep the difference! Use it for home improvement, debt consolidation, or whatever you desire.
- Housing-to-income ratio: Your income, debt, and mortgage payments are the primary factors that affect whether you qualify for a loan. If you do qualify for a loan, you can apply, and ditech.com will move to the next step of checking to see if you can be approved.
To determine your qualification, the first thing ditech.com will do is divide the monthly payment of your proposed loan by your gross monthly income. This provides your housing-to-income ratio. If the resulting percentage falls within a certain range, the next step is to divide your total monthly debt by your gross monthly income. This provides your debt-to-income ratio. Again, if the ratio falls within prescribed limits, you are qualified for the loan.

The limits within which your housing and debt ratios must fall are determined primarily by the size of the loan, the value of the property, and the ratio between the two (known as the loan-to-value ratio, or LTV). This loan-to-value ratio is one of the most important factors in determining a home loan.

- Appraisal: The appraisal determines the value of the property in question, which becomes a prime factor in determining the loan-to-value - or LTV - ratio (the amount of your loan divided by the value of your property). Your LTV is important because it determines your equity in the property. With the exception of leveraged equity and some second mortgages, ditech.com will arrange an appraisal of your property to verify its value. An appraiser is an authorized professional who estimates the value of the property and sends the information to ditech.com and to you.
- An impound/escrow account: An impound account or an escrow account (the terms are interchangeable; each is used in different states) is the name of the account in which a lender collects payments you make toward your property taxes and hazard/fire insurance. If you have an impound/escrow account, each of your monthly payments will contain a fraction of your annual property tax and insurance costs. Your lender keeps these funds in the impound/escrow account and then pays your taxes and insurance directly when they become due.
An impound/escrow account can be a convenient and trouble-free manner of ensuring that your insurance and tax payments are made on time. Additionally, choosing the convenience of an impound/escrow account allows ditech.com to offer you a better rate or lower fee. Please note that impound/escrow accounts are mandatory for purchase or refinance Loans where the loan amount is 80.01 percent or more of the property value (loan-to-value ratios of 80.01 percent or more), unless otherwise restricted by laws in your property's state (in California, impound accounts are required for refinance loans, purchase loans with LTV of 90 percent or greater, and for second mortgages with LTVs of 80.01 percent or greater).

- Income-to-debt ratio: Your income, debt, and mortgage payments make up your income-to-debt ratio. These are the primary factors that affect whether or not you qualify for a loan. If you do qualify for a loan, you can apply, and ditech.com will move to the next step of checking to see if you can be approved. To determine your qualification, the first thing ditech.com will do is divide the monthly payment of your proposed loan by your gross monthly income. This provides your housing-to-income ratio.
If the resulting percentage falls within a certain range, the next step is to divide your total monthly debt by your gross monthly income. This provides your debt-to-income ratio. Again, if the ratio falls within prescribed limits, you are qualified for the loan.

The limits within which your housing and debt ratios must fall are determined primarily by the size of the loan, the value of the property, and the ratio between the two (known as the loan-to-value ratio, or LTV). This loan-to-value ratio is one of the most important factors in determining a home loan.

- Owner's estimate of value: For the 125% Freedom loan product, ditech.com relies on your estimate of the value of your property. You can estimate the value by reviewing neighborhood comparable properties (comps). A good way to do this is to simply call a local real estate agent. You can also visit open house events in your neighborhood. This may give you an indication of what prices are being asked for various properties.
- PITI: PITI is the acronym for Principal, Interest, Taxes and Insurance. That is, each month your payment to your lender will consist of:
- Funds to be applied to the
**principal**- to repay the actual money you borrowed - Funds to be applied to the
**interest**- to repay the interest you're being charged on the loan, over the life of the loan - Funds being collected in an impound/escrow account to pay your property
**taxes**when they come due - Funds being collected in an impound/escrow account to pay your hazard/fire
**Insurance**when it comes due

- Funds to be applied to the
- PMI: Private Mortgage Insurance (PMI) is usually mandatory for loans when the ratio of the loan amount to the value of the subject property is greater than 80 percent; that is, 80.01 percent or more of the property is being paid for by the loan. This is known as the loan-to-value ratio, or LTV. Basically, the lower your loan-to-value ratio, the higher your equity in the property will be. You can think of equity as the part of your property you actually own. If you sold your property (for its appraised value), equity is the amount of cash you'd have left after you repay your loan balance in full.
Common wisdom holds that the more equity a borrower has in a property, the lower the risk of defaulting on the loan. Thus, Private Mortgage Insurance (PMI) must be paid for lower equity (high LTV) loans to safeguard the lender from possible loan defaults.

- What is prequalification vs. preapproval: Ditech.com simultaneously gives prequalification and preapproval based upon the information you provide in the online application. Because this preapproval is based on information provided to ditech.com verbally and as set forth on the application, it is considered conditional loan approval.
The conditional approval is subject to the verification and/or receipt of additional information. Once all closing conditions and lender requirements are satisfied, the loan will receive final approval.

- Refinancing: Rolling in your loan costs is especially attractive when refinancing. By rolling in your costs, you incur no expenses, thus you have no "payback period." The payback period is the time required to recoup the cost of your new loan through the monthly savings you get from the difference between your new lower payments and your old ones. For example, if your new loan's payments are $100 a month less than your old one, but you had to pay $1,200 to refinance, you'd have a payback period of 12 months before you'd actually start saving. By rolling in the cost of your refinance, your actual savings begin immediately. Rolling in your costs is particularly appropriate if you are planning to sell or refinance again in a few years because, in this case, it doesn't really matter that your loan amount is higher as long as you enjoy savings right now.
- Equity Line of Credit and another type of second mortgage: An Equity Line of Credit is money in an account that can be used as you need it. You can use any portion of it at any time and pay it back at any time. The interest rate is usually variable and is tied to the prime rate. Other types of second mortgages, such as the Home Equity Loan and 125 percent Freedom Loans are simple interest products. You borrow a lump sum and pay it back over a period of years with interest. The interest rate for these products is fixed.
- Closing costs: Closing costs are sometimes also called settlement costs. These are the costs a lender charges for funding and completing your loan and are generally charged at the time of closing (or settlement). They often include discount points, which are fees paid to lower your interest rate. Settlement costs/closing costs vary greatly depending on your state, county, and/or metropolitan area. They also vary from one lender to another, so it pays to shop around.
- Income, debt, and mortgage payments: These are the primary factors that effect whether you qualify for a loan. In order to determine if you qualify for a loan, your lender will calculate two defining ratios: the housing-to-income ratio and the debt-to-income ratio. The first of the two ratios, the housing-to-income ratio, is calculated by dividing the monthly payment of your proposed loan by your gross monthly income. If the resulting percentage falls within a predetermined range, the lender will then go on to calculate your debt-to-income ratio. The debt-to-income ratio is calculated by dividing your total monthly debt by your gross monthly income. Once again, if this ratio falls within prescribed limits, the lender will qualify you for the loan. The limits within which your housing and debt ratios must fall are determined primarily by the size of the loan, the value of the property, and the ratio between the two (known as the loan-to-value ratio, or LTV). This loan-to-value ratio is one of the most important factors in determining a home loan.
- Prepaid interest and impound/escrow funds: Prepaid interest and impound/escrow funds are costs generally associated with a mortgage. At the time of closing your loan, a lender will often require you to provide the funds to establish your impound/escrow accounts (so your taxes and insurance can be paid on time) and to pay the interest for the time period between the loan closing date and the end of the closing month.
- Rates, terms, and APR: All mortgages have an interest rate, a term, and an annual percentage rate (APR). For example, a mortgage might be defined as a 30-year fixed-rate loan at 7.625 percent, with an APR of 7.800 percent. In this example, the mortgage term is 30 years. As the borrower, you will pay back the loan in installments over the course of 30 years.
The interest rate in this example is 7.625 percent. This means you must pay interest on the money you've borrowed at a rate of 7.625 percent per year. That is, in addition to paying back the loan, you will pay your lender an additional 7.625 percent of the current loan balance every year. This interest is basically the fee your lender charges you in return for lending you the money.

The annual percentage rate (APR) is a measure of the cost of credit, expressed as a yearly rate. Because APR includes points and other costs such as origination fees, it's usually higher than the advertised rate. The APR allows you to compare different mortgages based on actual annual costs.

- "Locking in a rate": You can secure your rate by completing a written agreement in which ditech.com guarantees a specified interest rate for a specified period of time. Locking in a mortgage rate protects you against interest rate changes from the date of the rate lock until the date of the closing as long as your rate lock has not expired. Should interest rates rise during that period, ditech.com is obligated to honor the committed rate. Should interest rates fall during that period, you must honor the lock.
- Mortgage: A mortgage is a loan you acquire in order to purchase property, but you can also get cash for other purposes using the property as equity. In return for the loan, you pledge real property (land and/or a building) as security in case you fail to live up to your obligation.
When you borrow money against property, you commit to two financial documents:

- The NOTE that is a personal obligation to repay the loan on a timely basis
- The MORTGAGE DEED OF TRUST that is the pledge of the property as security; the mortgage deed of trust defines your obligations to your lender, as well as your rights and those of the lender.

You are pledged to repay the mortgage loan, along with an additional charge for the lender's service of lending you the money.

The cost of borrowing the money is the interest rate specified in your note. The amount of time you have to pay back the loan is the note's term.

- Amortization:Amortization means paying down your principal. You repay your loan in monthly installments. If you have a fixed mortgage (that is, an interest rate that remains fixed for the entire term of the loan), your payments will always be the same amount. Part of the payment goes toward the payment of the interest, and part toward the repayment of the money you've borrowed (the principal).
The balance of the principal (what you still owe at any given time) is reduced with each payment. As a result, your monthly payment will pay the principal in increasing amounts over time. With a fixed-interest rate, the amount of interest you owe will decrease as your principal balance decreases.

You can create an amortization schedule for fixed loans when they are originated. This schedule will show how much of each payment will go toward interest and how much will go toward principal over the life of the loan.

As your principal decreases, your equity in the mortgaged property increases. Equity is a very important factor in mortgage financing.

- Equity: Equity is a crucial aspect of home loans. Equity is simply the value of a homeowner's unencumbered interest on real estate. Equity is computed by subtracting the total of the unpaid mortgage balance and any outstanding liens or other debts against the property from the property's fair market value. A homeowner's equity increases as he or she pays off his or her mortgage or as the property appreciates in value. When a mortgage and all other debts against the property are paid in full, the homeowner has 100 percent equity in his or her property.
Equity exists in conjunction with your loan-to-value ratio (or LTV). Your LTV is a ratio expressing the value of your property to the amount of your loan. You determine your LTV by dividing your loan amount by your property's value or selling/purchase price, whichever is lower.

For example, you buy a $100,000 home with a $20,000 down payment of your own money, and cover the remaining $80,000 with a mortgage - 80,000 divided by 100,000 gives you a loan-to-value ratio of 80 percent and equity of 20 percent.

Equity and LTVs are important because lenders prefer a borrower to have as much equity as possible. Traditional wisdom holds that the higher the LTV on a loan, the higher the risk of default; alternatively, the higher the equity, the lower the risk - and therefore the lower the interest rate, cost, and fees associated with doing the loan. Equity also determines how much a lender will allow you to refinance your property for and how much they will lend you for a second mortgage.

Another way to think of equity is as the amount that you'll receive when you sell the property and pay back the remaining loan balance. Again, for a $100,000 house bought with an $80,000 loan and sold for $100,000, you would get $20,000 in cash back - or 20 percent of the home's value.

**Multivariable function:**A function that has two or more input variables and one output variable. Multivariable functions with two input variables can be illustrated with graphs of three-dimensional surfaces, tables of data, and/or contour graphs.

**Normal distribution:** A continuous probability distribution whose probability density function has a "bell" shape.

**Oligopoly:** A market for a good where a few major suppliers account for a large majority of sales.**Operational risk:** Risk to financial or other institutions from inadequate or failed internal processes, people and systems or from external events.**Optimization:** The process of finding relative or absolute extreme points.**Option:** A type of derivative instrument. A contract which gives the holder of the contract the right to buy or sell a commodity or financial asset for a given price before a specified date.

**Partial derivative:** A derivative of a multivariable function found by taking the derivative of the function with respect to one of the input variables while all the other input variables are held constant.**Partial rate of change:** The rate of change of a cross-sectional function that is computed as a partial derivative.**Percentage change:** A quantity calculated from data with increasing input values by dividing each first difference by the output value of the lesser input value and multiplying by 100%. That is, if a quantity changes from a value of m to a value of n over a certain interval, then the percentage change equals n-mm×100%.**Percentage rate of change :** A quantity that is useful in describing the relative magnitude of a rate of change. A percentage rate of change at a point is found by dividing the rate of change at the point by the function value at that same point and multiplying the result by 100%. Percentage rates of change have labels of percent per input unit.**Piecewise continuous function:** A function formed by combining two or more pieces of continuous functions. A piecewise continuous function is not necessarily a continuous function.**Point of diminishing returns:** An inflection point on the graph of a function beyond which the function output increases at a decreasing rate.**Point of tangency:** The point at which the line tangent to a curve touches the curve and at which the slope of the line tangent to the curve is the instantaneous rate of change of the curve.**Polynomial function:** A function that has the form f(x) = a_{n}x^{n}+ a_{n-1}x^{n-1}+ … + a_{1}x + a_{0} , where a_{0}, a_{1}, … , a_{n} are constants and n is a positive integer called the degree of the polynomial. If n = 1, then the polynomial function is a linear function; if n = 2, it is a quadratic function; and if n = 3, it is a cubic function.**Portfolio:** The entire collection of financial assets held by an investor.**Premium:** The purchase price of an option.**Present value:** The amount of money that would have to be invested now in an interest-bearing account in order for the amount to grow to a given future value.**Probability:** A measure of how likely an event is to happen. The probability of an event is always a number between 0 (for an impossible event) and 1 (for a sure event). One of the methods for computing probabilities is to find areas under probability density functions.**Probability density function:** A continuous or piecewise continuous function with input consisting of some interval of real numbers and output satisfying the conditions that each output value is greater than or equal to 0 and the area of the region between the density function and the horizontal axis is 1.**Probability distribution:** When all outcomes of a particular situation are considered, the pattern indicated by the variability in the data is called the distribution of the quantity being studied.**Producers' revenue:** The actual amount of money that producers receive for supplying a certain quantity of goods or services. The producers' revenue equals the market price times the quantity supplied.**Producers' surplus:** The amount of money that producers receive above the minimum amount they are willing and able to accept for a certain quantity of goods or services.**Producers' willingness and ability to receive:** The minimum amount of money that producers are willing and able to receive for supplying a certain quantity of goods or services.**Profit:** Revenue minus total cost.**Profitability Ratios:** Profitability ratios profitability ratios measure management's ability to control expenses and to earn a return on the resources committed to the business, for example:

- Operating Income Margin = Operating Income / Net Sales
- Gross Profit Margin = Gross Profit / Net Sales

**Properties of indifference curves (IC):**

- All points on the same indifference curve carry same level of satisfaction or utility. A point with higher level of utility will be on a higher indifference curve while a point with lower level of satisfaction will be on a lower indifference curve.
- Indifference curves slope downward. This is because when a person moves along an indifference curve, he/she faces a tradeoff. In order to get more of one good, one has to give up some amount of the other.
- Indifference curves do not intersect each other. The IC's are convex to the origin. The indifference curves slope downward.
- The Marginal Rate of Substitution / The marginal value and the Slope of IC. The marginal rate of substitution is the rate at which the consumer is just willing to substitute one good for another. For instance the marginal rate of substitution of Y for X is the amount of Y that a consumer is willing to give up in order to get one additional unit of X. The marginal rate of substitution is in fact the slope of the indifference curve. The steeper the indifference curve is, higher would be the slope and so higher would be the marginal rate of substitution.
- Shape of the Indifference Curves and the Law of Diminishing Marginal Utility. Indifference curves are convex to the origin. In other words, they are steeper in the beginning and then flatten out towards the end. Since the slope of the IC is simply the marginal rate of substitution of X for Y , therefore we can say that the marginal rate of substitution of X for Y declines as we move along the curve. This is due to the law of diminishing marginal utility. As we move along the indifference curve, we are having more and more units of Y (measured on horizontal axis) and according to the law of diminishing marginal utility, each additional unit gives less and less marginal utility compared to the previous ones. So as we get more of Y, it becomes less valuable for us and we are willing to give up less of the other good in order to get more Y.

**Quadratic function/model :** A function of the form f(x) = ax^{2}+ bx + c where a, b, and c are constants and a is nonzero. In this function, a is called the leading coefficient. The graph of a quadratic model is called a parabola. If a is less than zero, the parabola is cocave and if a If a is more than zero, the parabola is concvex. When input values of a set of data are evenly spaced and the second differences of the output values are constant, the data should be modeled by a quadratic function.**Quadratic portfolio:** In the context of value-at-risk (VaR), a portfolio whose portfolio mapping function is a quadratic polynomial.

**Random variable:** A variable whose numerical values are determined by the results of a situation involving chance.**Ratings transition matrix:** A matrix indicating probabilities of upgrades or downgrades in bonds' credit ratings.**Reduced form model:** Intensity model.**Relative maximum:** An output value that is larger than all other output values in some interval around the maximum. A graph increases to the relative maximum and decreases after it. For a multivariable function, a relative maximum is an output value that is greater than all values around it.**Relative minimum:** An output value that is that is smaller than all other output values in some interval around the minimum. A graph decreases to the relative minimum and increases after it. For a multivariable function, a relative minimum is an output value that is smaller than all values around it.**Replacement cost :** The cost of replacing an obligation of a counterparty.**Revenue:** Quantity sold times price per unit.**Risk:** Comprises two components: uncertainty and exposure.**Risk averse:** Preferring less risk to more.

**Saddle point:** For a multivariable function, a saddle point appears to be a maximum point when approached from one direction and a minimum point when approached from another direction. Saddle points cannot be visually identified on the edges of tables or contour graphs.**Scatter plot:** A discrete graph showing points in isolation from one another on a rectangular grid. A graph of data is a scatter plot.**Secant line:** A line through two points on a scatter plot or a function graph. The slope of the secant line through two points is the average rate of change of the quantity between the input values of those two points.**Second derivative:** The derivative of the derivative (provided it exists). At a point of inflection on a graph, the second derivative is zero or does not exist. Where the second derivative of a function is positive, the function graph is convex up, and where the second derivative of a function is negative, the function graph is concave.**Second differences :** The differences between the first differences. Separation of variables : A technique for solving certain differential equations in which all terms containing one variable are put on one side of the equation, all terms involving the other variable are put on to the other side of the equation, and then antiderivatives of both sides are taken.**Shutdown price:** The price below which producers are not willing or able to supply any quantity of particular goods or services to consumers. The point on the supply curve that corresponds to the shutdown price is called the shutdown point.**Signed area :** The negative of the area of a region.**Semi-variance:** An alternative to variance that focuses on negative values of a distribution.**Slope:** A measure of how steeply tilted a line or curve is. The rate of change of a linear function is its slope. The slope of the line tangent to a curve at a point is the limiting value of the slopes of nearby secant lines. The slope of a curve (graph) at a point is the slope of the line tangent to the curve at that point (provided the slope exists). The instantaneous rate of change (also called the derivative or rate of change) at a point on a curve is the slope of the curve at that point (provided that slope exists).**Slope graph:** Also called the rate-of-change graph or derivative graph, a slope graph depicts the changing nature of the slopes of lines tangent to a graph of a function. Where a function is increasing, its slope graph is positive; where a function is decreasing, its slope graph is negative. Where a function has a maximum, has a minimum, or levels off, the slope graph is zero. Where a function has an inflection point, the slope graph has a maximum or minimum point.**Smooth:** A continuous function is smooth if it has no sharp points; that is, no points where two pieces of a function have different slopes at the point where they meet.**Solvency Ratios:** These ratios measure the financial soundness of a business and how well the company can satisfy its short- and long-term obligations:

- Quick Ratio – This ratio, also called "acid test" or "liquid" ratio, considers only cash, marketable securities (cash equivalents) and accounts receivable because they are considered to be the most liquid forms of current assets. A Quick Ratio less than 1.0 implies dependency on inventory and other current assets to liquidate short-term debt. This ratio is calculated using the following formula:
Cash + Accounts Receivable / Current Liabilities

- Current Ratio – This ratio is a comparison of current assets to current liabilities, commonly used as a measure of short-run solvency, i.e., the immediate ability of a business to pay its current debts as they come due. Potential creditors use this ratio to measure a company's liquidity or ability to pay off short-term debts. This ratio is calculated using the following formula:
Current Assets / Current Liabilities

- Current Liabilities to Net Worth Ratio – This ratio indicates the amount due creditors within a year as a percentage of the owners or stockholders investment. The smaller the net worth and the larger the liabilities, imply the less security for creditors. Normally a business starts to have trouble when this relationship exceeds 80%. This ratio is calculated using the following formula:
Current Liabilities / Net Worth

- Current Liabilities to Inventory Ratio – This ratio shows, as a percentage, the reliance on available inventory for payment of debt (how much a company relies on funds from disposal of unsold inventories to meet its current debt). This ratio is calculated using the following formula:
Current Liabilities / Inventory

- Total Liabilities to Net Worth Ratio – This ratio shows well how all of a company's debt relates to the equity of the owners or stockholders. The higher this ratio, the less protection there is for the creditors of the business. This ratio is calculated using the following formula:
Total Liabilities / Net Worth

- Fixed Assets to Net Worth Ratio – This ratio shows the percentage of assets centered in fixed assets compared to total equity. Generally the higher this percentage is over 75%, the more vulnerable a concern becomes to unexpected hazards and business climate changes. Capital is frozen in the form of machinery and the margin for operating funds becomes too narrow for day-to-day operations. This ratio is calculated using the following formula:
Fixed Assets / Net Worth

**Standard deviation:**A measure of how closely the values of a probability distribution cluster about its mean.

**Standard position:**An angle drawn so that one side, called the initial side, is along the positive x-axis and the other side, called the terminal side, is in one of the four quadrants.

**Stochastic process:**A model for a time series.

**Sum of squared errors (SSE):**A measure of best fit for linear functions. SSE is calculated as the sum of the squares of the deviations where the deviation for each data point is the data output minus the output of the fitted linear function y = ax + b.

**Supply:**Supply is the amount of a good or service that a producer is willing and able to offer for sale at each possible price. Supply is affected by a number of factors. Price is the most important factor but there are other factors also that can influence supply such as technology, future expectations and

prices of inputs: A change in price leads to a change in quantity supplied. A change in price does not lead to a change in supply. All else equal, if the price of a good goes up, quantity supplied goes up and vice versa.

**Supply vs. Quantity supplied:**Supply is a set of number that lists the quantity supplied corresponding to each possible price whereas quantity supplied is the amount of a good or service that a producer is willing to offer for sale at a given price. For instance, the information on price and quantity supplied presented in a table/demand schedule is collectively referred to as the supply.

**Supply curve:**A graph illustrating supply, with prices on the vertical axis and quantity supplied on the horizontal axis. Supply curve slopes upward because of the positive relationship between price and quantity. A change in supply leads to a shift in the supply curve. A fall in supply shifts the supply curve to the left and a rise in supply shifts the curve to the right supplied.

**Supply and the Excise Tax:**An excise tax is a tax that is paid directly by suppliers to the government. An excise tax affects the supply curve. It causes the curve to shift to the left parallel to itself by the amount of the tax.

**Supply Market:**Market supply is the sum of the individual supplies by all the sellers. Market supply curve is the horizontal summation of individual supply curves.

**Demand and Supply Equilibrium:**The points where the demand and supply curves intersect each other. Shifts in demand, supply or both the curves changes the equilibrium. In order to find the effect of a certain event on equilibrium, we have to know first whether the event shifts the demand or supply curve and then trace the effect on equilibrium systematically. Both the sales tax and excise tax reduce the equilibrium quantity. In both cases, the price paid by demanders increase and the price received by suppliers decrease. In other words, both the suppliers and demanders are worse off regardless of whether it is a sales tax or an excise tax. In other words, both the demanders and the suppliers bear the burden of the tax. The magnitude of burden however, depends upon the shapes of the demand and supply curves.

**Supply curve/function:**A graph or equation that expresses the quantity supplied relative to the price per unit.

**Symmetric difference quotient:**A method of approximating instantaneous rates of change from data or an equation by using a close point on either side of the point of interest and the same horizontal distance away. The symmetric difference quotient is the difference between the outputs of the two close points divided by the corresponding difference in inputs of the two close points.

**Systematic risk:**That component of an instrument or portfolio's market risk that is correlated with the overall market.

**Tangent line:** A line that touches a graph at a point and is tilted exactly the way the graph is tilted at that point. The tangent line at a point on a smooth continuous graph is the limiting position of the secant lines between nearby points and that point (if the limiting position exists). Provided the slope exists, the slope of the tangent line at a point is a measure of the slope of the graph at that point and gives the instantaneous rate of change of the graph at that point.**Time series:** A series of observations made over a period of time.**Total cost:** The sum of the fixed costs and the variable costs.**Total social gain:** The benefit to society whenever consumers and/or producers have surplus funds. When the market price of a product is the equilibrium price for that product, the total social gain is the consumers' surplus plus the producers' surplus.**Trend :** As associated with limits, a trend is a value to which a quantity becomes closer and closer as the input becomes infinitely large or infinitely small.

**Unexpected loss:** A risk metric related to the second moment of a portfolio's losses due to default over a specified horizon.**Uniform distribution:** A continuous probability distribution that has constant probability on a finite interval.**Unit of measure:** A word or short phrase telling how a quantity is measured, not an entire description telling what the variable represents.**Utility:** Utility is a measure of pleasure or satisfaction. Suppose we have two goods: X and Y and there is a basket containing 5 units of X and 7 units of Y, and the consumption of this basket gives 6 units of utility, then we can write: U(5,7) = 6.**Utilization:** Given a risk limit, the amount of risk being taken as a fraction of the limit.**Value-at-risk (VaR):** A category of market risk measures.**Variable costs:** Costs that change according to the number of items produced or the amount of service performed.**Variation:** the spread of a set of observations or of a random variable, usually measured by the variance, the standard deviation, the range or the inter-quartile range.**Vertical Line Test:** A method of visually determining whether a graph with inputs located along the horizontal axis and outputs located along the vertical axis is a function. If there is no input at which a vertical line crosses or touches the graph in two or more places, then the graph represents a function.**Why People Trade?** Everyone benefits when each person specializes in his area of comparative advantage and then engages in trade. Trade can help people specialize in different activities and helps them enjoy a variety of goods and services. Trade can take place because of two major reasons: difference in tastes and difference in abilities.**Volatility:** A metric of variability in a stochastic process.**Work Simplification:** Analysis of any aspects of work with the objective of removing any unnecessary obstacles to its effective achievement, such as motion and time study.

**X-bar chart: **A quality control chart for the mean of a process.

**Yates' correction for continuity:** An old correction to adjust chi-square for a 2 by 2 table for the fact that cell frequencies are integer, rather than continuous; however, rarely recommended any longer.

**Zero Defects:** A type of quality control in which the objective is to make no mistake or produce no reject material whatsoever.**Z score:** Number of standard deviations above or below the mean

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