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). All rights reserved. can be measured. Welcome to EconomicsDiscussion.net! It should be compared with an exogenous variable this is the "input" of the model. In quadratic function one or more of the independent variables are squared, that is, raised to the second power. See DEMAND FUNCTION, SUPPLY FUNCTION. Share Your PDF File We explain below some specific types of functions. For example, it is important to know the rate at which quantity demanded of a commodity changes in response to a change in price of a commodity. That is, a function expresses dependence of one variable on one or more other variables. Dichotomous outcomes are the most common type of discrete or qualitative dependent variables analyzed in economics. An important function which is extensively used in economics is a demand function which expresses quantity … 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. 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. Also termed an endogenous variable, a dependent variable is in essence the "output" of the model. The quadratic function, Y = a + bX + cX2, where the coefficient c of X2 is positive (i.e. That is, slope = ∆Y / ∆X. 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. n-shaped) as shown in Figure 5.3. If you’re interested in determining which factors […] are raised to the first power only. 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. The linear functions stated above are known as first degree functions where the independent variables X1, X2, X3, etc. Privacy Policy3. It should be compared with an exogenous variable this is the "input" of the model. Term dependent variable Definition: A variable that is identified within the workings of the model. We now turn to explain power functions. When the signs of all the coefficients a, b, c and d are positive, then the values of y will increase by progressively larger increments as the value of X increases. On plotting the non-linear function in a graph, we get a non-linear curve. 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. 5.4. On the other hand, if coefficient of X2 is negative (c < 0), that is, when Y= a + bX- cX2 then we have concave quadratic function because its graphs is of inverted ᴒ- shape (i.e. We now turn to explain how slope of a non-linear function, say, a quadratic function (Y= a + bX+ cX2) can be measured. The data so obtained have been plotted to get a curve in Figure 5.5. Let us first take the slope of a linear function. Thus, a cubic functions may have first degree, second degree and third degree terms. 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. 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. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. In economics it is important to know the rate at which a variable changes in response to a change in another variable, the slope of a variable measures this rate. Further, in this function b is the coefficient of X and measures change in Y due to change in X that is, ∆Y/∆X. A function describes the relation between two or more than two variables. 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. 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. Such a cubic function where signs of the coefficients of variables differ may be expressed as follows: In which the sign of the coefficient c of variable X^ is negative whereas the coefficients of others are positive. Consider the following linear function. In the field of economics we find both linear and non­linear functions. The values of constants a and b determine the specific nature of a linear function. 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.
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