CHAPTER 3 DEMAND THEORY
1. A frm has estimated the ollowing demand unction or its product: Q = 58 − 2P + 0.10I + 15 A where Q is uantit! demanded per month in thousands" P is product price" I is an inde# o consumer income" and A is ad$ertising e#penditures per month in thousands. Assume that P = %10" I = 120" and A = 10. &se the point ormulas to complete the elasticit! calculations indicated 'elow. 'elow. (i) *alculate uantit! demanded. (ii) *alculate the price elasticit! o demand. s demand elastic" inelastic" or unit elastic, (iii) *alculate the income elasticit! o demand. s the good normal or inerior, s it a necessit! or a lu#ur!, (i$) *alculate the ad$ertising elasticit! o demand. Solution:
(i) Q = 58 − (2)(10) + (0.10)(120) + (15)(10) = 200 (ii) (−2)(10-200) = −0.10 so demand is inelastic (iii) (0.10)(120-200) = 0.0 so the good is normal and a necessit! (i$) (15)(10-200) = 0./5 2. A frm has estimated the ollowing demand unction or its product: Q = 100 − 5 P + 5I + 15 A where Q is uantit! demanded per month in thousands" P is product price" I is an inde# o consumer income" and A is ad$ertising e#penditures per month in thousands. Assume that P = %200" I =150" and A = 0. &se the point ormulas to complete the elasticit! calculations indicated 'elow. 'elow. (i) *alculate uantit! demanded.
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(ii) *alculate the price elasticit! or demand. s demand elastic" inelastic" or unit elastic, (iii) *alculate the income elasticit! o demand. s the good normal or inerior, s it a necessit! or a lu#ur!, (i$) *alculate the ad$ertising elasticit! o demand. Solution:
(i) Q = 100 − (5)(200) + (5)(150) + (15)(0) = 00 (ii) (−5)(200-00) = −. so demand is elastic (iii) (5)(150-00) = 2.50 so the good is normal and a lu#ur! (i$) (15)(0-00) = 1.50 . A frm has ept trac o the uantit! demanded o its output during our time periods. roduct price" consumer income" and ad$ertising e#penditures were also recorded or each time period. 3he inormation is pro$ided in the ta'le that ollows. &se it to calculate the arc elasticit! o demand with respect to price" income" and ad$ertising. 3ime eriod 1 2 4 uantit! 120 80 100 80 rice 20 0 0 0 ncome 150 150 250 250 Ad$ertising 50 50 50 0 Solution:
3he price elasticit! o demand (using time periods 1 and 2) is 6(120 − 80)-(20 − 0)76(20 + 0)-(120 + 80)7 = −1 3he income elasticit! o demand (using time periods 2 and ) is 6(80 − 100)-(150 − 250)76(150 + 250)-(80 + 100)7 = 0.44 3he ad$ertising elasticit! o demand (using time periods and 4) is 6(100 − 80)-(50 − 0)76(50 + 0)-(100 + 80)7 = 0.44 4. A frm has ept trac o the uantit! demanded o its output (ood X ) during our time periods. 3he price o X and the prices o two other goods (ood Y and ood Z ) were also recorded or each time period. 3he inormation is pro$ided in the ta'le that ollows. &se it to calculate the own9price arc elasticit! o Managerial Economics: Principles and Worldwide Applications, 7/e
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demand and the two cross9price elasticities o demand. etermine whether ood Y and ood Z are complements or su'stitutes or ood X . 3ime eriod 1 2 4 uantit! o X 220 80 250 20 rice o X 15 25 15 25 rice o Y 10 10 5 10 rice o Z 20 20 20 0 Solution:
3he own9price elasticit! o demand (using time periods 1 and 2) is 6(220 − 80)-(15 − 25)76(15 + 25)-(220 + 80)7 = −1.8/ 3he cross9price elasticit! o demand or ood X with respect to the price o ood Y (using time periods 1 and ) is 6(220 − 250)-(10 − 5)76(10 + 5)-(220 + 250)7 = −0.1; ood X and ood Y are complements. 3he cross9price elasticit! o demand or ood X with respect to the price o ood Y (using time periods 2 and 4) is 6(80 − 20)-(20 − 0)76(20 + 0)-(80 + 20)7 = 2.5 ood X and ood Z are su'stitutes. 5. 3he price o a good increases rom %; to %11 and" as a result" the uantit! o the good demanded declines rom 120 to 80. *alculate the price elasticit! o demand using the arc ormula and determine whether demand is elastic" inelastic" or unit elastic. Solution:
6(80 − 120)-(11 − ;)76(11 + ;)-(80 + 120)7 = −2.00 so demand is elastic. . 3he demand unction or a good is defned as Q = 20 − 0.5 P. *alculate the price elasticit! o demand using the point ormula or P = 8 and determine whether demand is elastic" inelastic" or unit elastic. Solution:
(−0.5)(8-1) = −0.25 so demand is inelastic.
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/. 3he demand unction or ood X is defned as QX = 20 − 0.5PX + 1.2PY " where PY is the price o ood Y . *alculate the price elasticit! o demand using the point ormula or PX = 12 and PY = 10. etermine whether demand is elastic" inelastic" or unit elastic with respect to its own price and whether ood Y is a su'stitute or a complement with respect to ood X . Solution:
(−0.5)(12-2) = −0.2 so demand is inelastic with respect to its own price. (1.2)(10-2) = 0.2 so the two goods are su'stitutes. 8. 3he demand unction or a good is defned as Q = 20 − 1.5 P + 0.2I" where I is a measure o consumer income. *alculate the price elasticit! o demand using the point ormula or P = 1 and I = 110. etermine whether demand is elastic" inelastic" or unit elastic with respect to its own price and whether the good is normal or inerior and whether it is a lu#ur! or a necessit!. Solution:
(−1.5)(1-18) = −1. so demand is elastic with respect to its own price. (0.2)(110-18) = 1.22 so the good is normal and is a lu#ur!. ;. A frm has estimated the ollowing demand unction or its product: Q = 8 − 2P + 0.10I + A where Q is uantit! demanded per month in thousands" P is product price" I is an inde# o consumer income" and A is ad$ertising e#penditures per month in thousands. Assume that P = %10" I = 120" and A = 10. &se the point ormulas to complete the elasticit! calculations indicated 'elow. (i) *alculate uantit! demanded. (ii) *alculate the price elasticit! o demand. s demand elastic" inelastic" or unit elastic, (iii) *alculate the income elasticit! o demand. s the good normal or inerior, s it a necessit! or a lu#ur!, (i$) *alculate the ad$ertising elasticit! o demand.
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Solution:
(i) Q = 8 − (2)(10) + (0.10)(120) + (1)(10) = 10 (ii) (−2)(10-10) = −2.0 so demand is elastic (iii) (0.10)(120-10) = 1.2 so the good is normal and a lu#ur! (i$) (1)(10-10) = 1.0 10. A frm has estimated the ollowing demand unction or its product: Q = 400 − 5 P + 5I + 10 A where Q is uantit! demanded per month in thousands" P is product price" I is an inde# o consumer income" and A is ad$ertising e#penditures per month in thousands. Assume that P = %200" I = 100" and A = 20. &se the point ormulas to complete the elasticit! calculations indicated 'elow. (i) *alculate uantit! demanded. (ii) *alculate the price elasticit! o demand. s demand elastic" inelastic" or unit elastic, (iii) *alculate the income elasticit! o demand. s the good normal or inerior, s it a necessit! or a lu#ur!, (i$) *alculate the ad$ertising elasticit! o demand. Solution:
(i) Q = 400 − (5)(200) + (5)(100) + (10)(20) = 100 (ii) (−5)(200-100) = −10.0 so demand is elastic (iii) (5)(110-100) = 5.0 so the good is normal and a lu#ur! (i$) (10)(20-100) = 2.0 11. 3he price o a good increases rom %8 to %10" and as a result the uantit! o the good demanded declines rom 120 to 80. *alculate the price elasticit! o demand using the arc ormula and determine whether demand is elastic" inelastic" or unit elastic. Solution:
6(80 − 120)-(10 − 8)76(10 + 8)-(80 + 120)7 = −1.80 so demand is elastic
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12. 3he demand unction or a good is defned as Q = 20 < 0.5 P. *alculate the price elasticit! o demand using the point ormula or P = 0 and determine whether demand is elastic" inelastic" or unit elastic. Solution:
(−0.5)(0-5) = −.0 so demand is elastic 1. 3he demand unction or ood X is defned as QX = /5 − 2PX − 1.5PY " where PY is the price o ood Y . *alculate the price elasticit! o demand using the point ormula or PX = 20 and PY = 10. etermine whether demand is elastic" inelastic" or unit elastic with respect to its own price and whether ood Y is a su'stitute or a complement with respect to ood X . Solution :
(−2)(20-20) = −2.0 so demand is elastic with respect to its own price. (−1.5)(10-20) = −0./5 so the two goods are complements.
14. 3he demand unction or a good is defned as Q = 45 − 2.5P − 0.2I" where I is a measure o consumer income. *alculate the price elasticit! o demand using the point ormula or P = and I = 100. etermine whether demand is elastic" inelastic" or unit elastic with respect to its own price and whether the good is normal or inerior and whether it is a lu#ur! or a necessit!. Solution:
(−2.5)(-10) = −1.5 so demand is elastic with respect to its own price. (−0.2)(100-10) = −2.0 so the good is inerior. 15. 3he demand unction or a good is defned as Q = 50 − P. *alculate the price elasticit! o demand using the point ormula or P = 25 and determine whether the demand is elastic" inelastic" or unit elastic. Solution:
(−1)(25-25) = −1.0 so demand is unit elastic. Managerial Economics: Principles and Worldwide Applications, 7/e
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