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Unformatted text preview: Chapter 3: Answers to Questions and Problems 1. a. When P = $12, R = ($12)(1) = $12. When P = $10, R = ($10)(2) = $20. Thus, the price decrease results in an $8 increase in total revenue, so demand is elastic over this range of prices. b. When P = $4, R = ($4)(5) = $20. When P = $2, R = ($2)(6) = $12. Thus, the price decrease results in an $8 decrease total revenue, so demand is inelastic over this range of prices. c. Recall that total revenue is maximized at the point where demand is unitary elastic. We also know that marginal revenue is zero at this point. For a linear demand curve, marginal revenue lies halfway between the demand curve and the vertical axis. In this case, marginal revenue is a line starting at a price of $14 and intersecting the quantity axis at a value of Q = 3.5. Thus, marginal revenue is 0 at 3.5 units, which corresponds to a price of $7 as shown below. $0 $2 $4 $6 $8 $10 $12 $14 1 2 3 4 5 6 Quantity Price Demand MR Figure 31 31 2. a. At the given prices, quantity demanded is 700 units: ( 29 ( 29 1000 2 154 .02 400 700 d x Q = + = . Substituting the relevant information into the elasticity formula gives: , 154 2 2 0.44 700 x x x Q P x P E Q =  =  =  . Since this is less than one in absolute value, demand is inelastic at this price. If the firm charged a lower price, total revenue would decrease. b. At the given prices, quantity demanded is 300 units: ( 29 ( 29 1000 2 354 .02 400 300 d x Q = + = . Substituting the relevant information into the elasticity formula gives: , 354 2 2 2.36 300 x x x Q P x P E Q =  =  =  . Since this is greater than one in absolute value, demand is elastic at this price. If the firm increased its price, total revenue would decrease. c. At the given prices, quantity demanded is 700 units: ( 29 ( 29 1000 2 154 .02 400 700 d x Q = + = . Substituting the relevant information into the elasticity formula gives: , 400 .02 .02 0.011 700 x Z Z Q P x P E Q = = = . Since this number is positive, goods X and Z are substitutes. 3. a. The own price elasticity of demand is simply the coefficient of ln P x , which is 0.5. Since this number is less than one in absolute value, demand is inelastic. b. The crossprice elasticity of demand is simply the coefficient of ln P y , which is 2.5. Since this number is negative, goods X and Y are complements. c. The income elasticity of demand is simply the coefficient of ln M , which is 1. Since this number is positive, good X is a normal good. d. The advertising elasticity of demand is simply the coefficient of ln A , which is 2. 4. a. Use the own price elasticity of demand formula to write % 2 5 d x Q =  . Solving, we see that the quantity demanded of good X will decrease by 10 percent if the price of good X increases by 5 percent....
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 Summer '10
 HOLLAND

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