Show
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) = ax3+ bx2 + 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.
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.
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) = abx or f (x) = aekx . 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.
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:
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 = ex/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.
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). When you borrow money against property, you commit to two financial documents: 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. 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.
Properties of indifference curves (IC):
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. The Copyright Statement: The fair use, according to the 1996 Fair Use Guidelines for Educational Multimedia, of materials presented on this Web site is permitted for non-commercial and classroom purposes only. Kindly e-mail me your comments, suggestions, and concerns. Thank you. This site was launched on 2/18/1994, and its intellectual materials have been thoroughly revised on a yearly basis. The current version is the 9th Edition. All external links are checked once a month. What is the relationship between demand and income?In the case of normal goods, income and demand are directly related, meaning that an increase in income will cause demand to rise and a decrease in income causes demand to fall.
What is the inverse relationship between price and quantity demanded?Inverse Relationship of Price and Demand
Thus, the price of a product and the quantity demanded for that product have an inverse relationship, as stated in the law of demand. An inverse relationship means that higher prices result in lower quantity demand and lower prices result in higher quantity demand.
What is the relationship between price level and quantity demanded?Key points. The law of demand states that a higher price leads to a lower quantity demanded and that a lower price leads to a higher quantity demanded. Demand curves and demand schedules are tools used to summarize the relationship between quantity demanded and price.
What is the relationship between price and quantity?Price is what the producer receives for selling one unit of a good or service. An increase in price almost always leads to an increase in the quantity supplied of that good or service, while a decrease in price will decrease the quantity supplied.
|