15varianbergstrom - Chapter 15 N AME Market Demand...

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Chapter 15 NAME Market Demand Introduction. Some problems in this chapter will ask you to construct the market demand curve from individual demand curves. The market demand at any given price is simply the sum of the individual demands at that price. The key thing to remember in going from individual demands to the market demand is to add quantities . Graphically, you sum the individual demands horizontally to get the market demand. The market demand curve will have a kink in it whenever the market price is high enough that some individual demand becomes zero. Sometimes you will need to find a consumer’s reservation price for a good. Recall that the reservation price is the price that makes the consumer indifferent between having the good at that price and not hav- ing the good at all. Mathematically, the reservation price p satisfies u (0 , m ) = u (1 , m p ), where m is income and the quantity of the other good is measured in dollars. Finally, some of the problems ask you to calculate price and/or in- come elasticities of demand. These problems are especially easy if you know a little calculus. If the demand function is D ( p ), and you want to calculate the price elasticity of demand when the price is p , you only need to calculate dD ( p ) /dp and multiply it by p/q . 15.0 Warm Up Exercise. (Calculating elasticities.) Here are some drills on price elasticities. For each demand function, find an ex- pression for the price elasticity of demand. The answer will typically be a function of the price, p . As an example, consider the linear demand curve, D ( p ) = 30 6 p . Then dD ( p ) /dp = 6 and p/q = p/ (30 6 p ), so the price elasticity of demand is 6 p/ (30 6 p ). (a) D ( p ) = 60 p . p/ (60 p ) . (b) D ( p ) = a bp . bp/ ( a bp ) . (c) D ( p ) = 40 p 2 . 2 . (d) D ( p ) = Ap b . b . (e) D ( p ) = ( p + 3) 2 . 2 p/ ( p + 3) .
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192 MARKET DEMAND (Ch. 15) (f) D ( p ) = ( p + a ) b . bp/ ( p + a ) . 15.1 (0) In Gas Pump, South Dakota, there are two kinds of consumers, Buick owners and Dodge owners. Every Buick owner has a demand func- tion for gasoline D B ( p ) = 20 5 p for p 4 and D B ( p ) = 0 if p > 4. Every Dodge owner has a demand function D D ( p ) = 15 3 p for p 5 and D D ( p ) = 0 for p > 5. (Quantities are measured in gallons per week and price is measured in dollars.) Suppose that Gas Pump has 150 con- sumers, 100 Buick owners, and 50 Dodge owners. (a) If the price is $3, what is the total amount demanded by each indi- vidual Buick Owner? 5.
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