When there are more than one independent variable such as X1, X2, and they have a quadratic relationship with the dependent variable Y, such a function is called multivariable quadratic function. Share Your PDF File In Figure 5.1 we have noted these price-quantity combinations on a graph and have obtained demand curve DD of the commodity representing the given demand function (Qd = 7- 0.5P). A linear function can be stated in the following general form: Where a and b are positive constants and are called parameters of the function. Many economic phenomena are dichotomous in nature; in other words, the outcome either occurs or does not occur. We now turn to explain how slope of a non-linear function, say, a quadratic function (Y= a + bX+ cX2) can be measured. In quadratic function one or more of the independent variables are squared, that is, raised to the second power. In the field of economics we find both linear and nonlinear functions. Thus, here ∆X = 4 – 1 = 3 and ∆y = 33 – 9 = 24. Thus, b represents the slope of the linear function. In case of two independent variables X1 and X2 such a function may be expressed as under: If such a function is graphically shown, it will be represented by a three dimensional surface and not a two dimensional curve. Thus, the slope of the function (Y=2 + 0.5X) is: This implies that value of Y increases by 0.5 when value of X increases by 1. An important function which is extensively used in economics is a demand function which expresses quantity … Let us take the following specific quadratic function: In Table 5.2 we have calculated the various values of Y by taking different values of X (0, 1, 2, 3, etc.). Term dependent variable Definition: A variable that is identified within the workings of the model. A = advertising expenditure incurred by the firm. It will be seen from this linear function that when the value of X is zero, the value of Y will be equal to a. If price (P) is zero, the second term (0.5P) in the demand function drops out and the quantity demanded is equal to 7. It will be seen from this Figure 5.5 that slope of the line AB which connects two points A and B on a curve representing quadratic function can be measured by taking the change in the value of Y divided by the change in value of X. A cubic function may have the following form: a is the intercept term, the dependent variable X has the first degree, second degree and third degree terms. The values of constants a and b determine the specific nature of a linear function. It should be noted that slope of a linear function is constant throughout. However, if we represent quantity demanded (Qd) on the y-axis, and price (Px) on the x-axis; the slope of the demand curve so drawn would be equal to ∆Q/∆P. A function describes the relation between two or more than two variables. Scenarios 1 Coach Jones has noticed that her players tend to shoot a higher percentage from the free throw line when they play away, rather than at home. Similarly, slope of straight line AC in Fig.5.5. When value of X rises from 3 to 4, value of Y increases from 3.5 to 4. Linear demand function with more than one independent variables, can be written in the following way: Qx = a + b1 Px + b2 Py+ b3 M + b4 T + b5 A. For example, demand for a product is generally considered to be a function of its own price prices of other commodities (which may be substitutes or complements) income of the consumers, tastes and preferences of the consumers and advertising expenditure made by a firm to promote its product. can be measured. 5.4. Similarly, supply function of a commodity X is expressed as: When the value of the variable Y depends on more than two variables X1, X2….. Xn this function is written in general form as: This shows the variable Y depends on several independent variables X1, X2……Xn where n is the number of independent variables. Again note that in economics we write ’causes’ as the independent variables and ‘effect’ as the dependent variable. are raised to the first power only. Before publishing your Articles on this site, please read the following pages: 1. That is, if price of a commodity falls, its quantity demand increases and vice versa. We can obtain the different values of Y for taking different values of the independent variable X. Quadratic functions are of two types: convex quadratic functions and concave quadratic functions. The dependent variable is the condition that you measure in an experiment. All rights reserved. It was 8 of the line AB 7 of the line AC and 6 of the line AD. Welcome to EconomicsDiscussion.net! Thus in function (1) Y is called the dependent variable and its value depends on the value of X Further, the independent variable is Interpreted as the cause and the dependent variable as the effect. In economics power functions of the quadratic and cubic forms are extensively used. Permalink: https://glossary.econguru.com/economic-term/dependent+variable, © 2007, 2008 Glossary.EconGuru.com. Further, we have plotted the different values of Table 5.1 on a graph shown in Fig. That is, a function expresses dependence of one variable on one or more other variables. « demographic variables | deposit ». TOS4. The exact nature of relation of dependent variable with the independent variables can be known from the specific form of the function. An important function which is extensively used in economics is a demand function which expresses quantity demanded of a commodity is a function of its price, other factors being held constant. This implies that value of the dependent variable Y depends on the constant a plus the coefficient b times the value of the independent variable X plus the coefficient c times the square of the variable X Suppose a = 4, b = 3 and c = 2 then quadratic function takes the following specific form. The linear multivariate function is written in the following form: In this function the coefficients 0.4, 0.2, 0.3 and 0.5 show the precise impact of the independent variables X1, X2, X3, X4 on the dependent variable Y. In Table 5.1 we have calculated the values of the variable Y by taking different values of X such as 1, 2, 3, 4 etc. Graph of linear demand function is shown in Figure 5.1. However, the slope of a linear function can be directly known from the linear function itself and for that purpose there is no need to plot the data. As AX further decreases, slope of the line connecting two points of the non-linear curve will further decline. Content Guidelines 2. It should be compared with an exogenous variable this is the "input" of the model. It should be noted that, contrary to mathematical practice, by convention in economics to represent demand function we show the independent variable (price in the above case of demand function) on the y-axis and the dependent variable (the quantity demanded in the present case) on the x-axis. You are assessing how it responds to a change in the independent variable, so you can think of it as depending on the independent variable. In economics the effect of variables other than the own price of a commodity in the demand function are depicted by shifts in the demand curve. Thus, a cubic functions may have first degree, second degree and third degree terms. Privacy Policy | Terms of Use | Disclaimer | Contact Us, https://glossary.econguru.com/economic-term/dependent+variable. We can take various values of P and find out different quantities (Qd) of a commodity demanded at them. Let us first take the slope of a linear function. If a equals 7 and b equals 0.5, the linear demand function can be expressed in the following specific form: The above specific demand function shows that a unit fall in price of the commodity will cause 0.5 units increase in the quantity demanded of the commodity. That is, slope = ∆Y / ∆X. For example, a student who applies to graduate school will be admitted or not. It is worth noting that slope of the demand function curve in Figure 5.1 will represent ∆P/ ∆Q. Consider the following linear function. In linear function Y= 2 + 0.5X, 2 is the Y-intercept, that is, value of Y when X is zero, 0.5 is the b coefficient which measures the slope of the linear function. The linear functions stated above are known as first degree functions where the independent variables X1, X2, X3, etc. Sometimes the dependent variable is called the "responding variable." T = tastes and preferences of the consumer for the product. Therefore, the slope at a point on the non-linear function curve can be measured by the slope of a tangent drawn to the curve at that point. Thus. Share Your PPT File, Differentiation Calculus: Concept and Rules of Differentiation | Optimisation Technique. Also termed an endogenous variable, a dependent variable is in essence the "output" of the model. Dichotomous outcomes are the most common type of discrete or qualitative dependent variables analyzed in economics. However, when the signs of various coefficients differ in the cubic function, that is, some have positive signs and some have negative signs, then the graph of the function may have both convex and concave segments depending on the values of the coefficients. For instance when income (M) of the consumers increases consumers will demand more of the product X at a given price. On plotting the non-linear function in a graph, we get a non-linear curve. For example, at point A of the given function value of variable X is 3 and corresponding to it the value of variable Vis 3.5. This implies that every value of the variable Y is determined by a unique value of the variable X. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. Further, in this function b is the coefficient of X and measures change in Y due to change in X that is, ∆Y/∆X. Privacy Policy3. The specific form of a unction can take a variety of mathematical forms. It should also be noticed that the slope of the straight line AD connecting points and D is very close to the slope of the tangent drawn to the curve at point As AX becomes smaller and smaller slope of the line connecting the two points on a curve will become extremely close to the slope of the tangent drawn to the curve at point A. The condition that you measure in an experiment by a unique value of the model further decline left-hand... 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