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.

Price $14 $12 $10 $8 $6 $4 $2 Demand $0 0 1 2 3

MR 4

5

6 Quantity

Figure 3-1

Managerial Economics and Business Strategy, 7e

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2. a. At the given prices, quantity demanded is 700 units: d Qx = 1000 − 2 (154 ) + .02 ( 400 ) = 700 . Substituting the relevant information into

Px 154 = −2 = −0.44 . Since this is less 700 Qx 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: d Qx = 1000 − 2 ( 354 ) + .02 ( 400 ) = 300 . Substituting the relevant information into the elasticity formula gives: EQx ,Px = −2
⎛P ⎞ ⎛ 354 ⎞ the elasticity formula gives: EQx ,Px = −2 ⎜ x ⎟ = −2 ⎜ ⎟ = −2.36 . Since this is ⎝ 300 ⎠ ⎝ Qx ⎠ 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: d Qx = 1000 − 2 (154 ) + .02 ( 400 ) =