Demand Function and Demand Equation
The demand equation is the mathematical expression of the relationship between the quantity of a good demanded and those factors that affect the willingness and ability of a consumer to buy the good. For example, Qd = f(P; Prg, Y) is a demand equation where Qd is the quantity of a good demanded, P is the price of the good, Prg is the price of a related good, and Y is income; the function on the right side of the equation is called the demand function. The semi-colon in the list of arguments in the demand function means that the variables to the right are being held constant as we plot the demand curve in (quantity, price) space. A simple example of a demand equation is Qd = 325 - P - 30Prg + 1.4Y. Here 325 is the repository of all relevant non-specified factors that affect demand for the product. P is the price of the good. The coefficient is negative in accordance with the law of demand. The related good may be either a complement or a substitute. If a complement, the coefficient of its price would be negative as in this example. If a substitute, the coefficient of its price would be positive. Income, Y, has a positive coefficient indicating that the good is a normal good. If the coefficient was negative the good in question would be an inferior good meaning that the demand for the good would fall as the consumer's income increased. Specifying values for the non price determinants, Prg = 4.00 and Y = 50, results in the demand equation Q = 325 - P - 30(4) +1.4(50) or Q = 275 - P. If income were to increase to 55 the new demand equation would be Q = 282 - P. Graphically this change in a non price determinant of demand would be reflected in an outward shift of the demand function caused by a change in the x intercept.
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