Demand Functions

Demand Functions - Economics 101 400 Class Notes Demand and...

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Economics 101 – 400 Class Notes Demand and Supply Functions 1. Introduction The simple supply and demand model is a powerful tool. With little other than the conviction that supply curves slope upward and demand curves slope downward, we can generate a great many insights into changes in prices and sales volumes in competitive markets. For example, if I know that beer and wine are substitute goods, and that the price of beer rises, then the supply and demand model allows me to predict that wine prices will increase and that wine consumption will increase. But what if I wish to know more than simply the direction of the changes in market price and quantity traded? What if I wish to know by how much the price of wine rises when the price of beer increases? Or how much more wine will be consumed? To generate quantitative results like these, I need to have more information about the shape of the supply and demand curves. This information is most easily captured in the mathematical representation of the curves: the supply and demand functions . These are equations that capture the relationship between the quantity demanded or supplied and the price of the good (and any other explanatory variables). 2. The Demand Function In its most basic form, the demand function expresses the quantity of a good demanded as a function of the good’s price. Consider the discussion from class, relating to the quota imposed on sugar imports into the United States. In that scenario, we were informed that 20.3 billion pounds of sugar are demanded when the price of sugar is $0.21/pound, and that 24.3 billion pounds would be demanded when the price of sugar is $0.08/pound. A demand function that reflects that information is the following: Q d sugar = 26.76 – 30.77 P sugar where P sugar is the price per pound of sugar and Q d sugar is the quantity of sugar demanded, measured in billions of pounds. We can check to see whether this demand function is consistent with what we know about demand for sugar. By substituting a price of P = $0.08/pound of sugar into this expression, we find that the quantity of sugar demanded is (approximately) Q d sugar = 24.3 billion pounds. Similarly, if P = $0.21/pound of sugar, then the quantity of sugar demanded is (approximately) Q d sugar = 20.3 billion pounds. Therefore, the graph of this function will pass through both of the points we have been given from the domestic demand curve for sugar (marked A and B in Figure 1 below).
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Notice, we have information about two points that lie on the demand function (A and B), and have found a function associated with a curve that goes through those points. But a little reflection should convince you that there are many curves that pass through points A and B, and therefore many functions that could represent demand for sugar. The particular demand function we have generated here is just one of these possible demand functions. It has a specific characteristic: its graph is a straight line.
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