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16.CSEC Maths JANUARY 2012.pdf

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The demand curve for gardeners is Ed = 39 - 2w, where E = the number of gardeners, and w = the hourly wage. The supply curve is Es= 4 + 3w. a) Graph the demand and the supply curve. b) What is the equilibrium wage and equilibrium number of gardeners hired? c) Suppose the town government imposes a $3 per hour tax on all gardeners. i. Draw the new (after-tax) demand curve in terms of the employee wage. ii. What is the effect on the equilibrium wage and the equilibrium number of gardeners hired? iii. How much does the gardener receive? iv. How much does the customer pay? v. How much does the government receive as tax revenue? Solution a) Ed=39-2w Es=4+3w At w=1, Ed=37, Es=7 w=2,Ed=35, Es=10 w=3 Ed=33, Es=13 w=4, Ed=31, Es=16 a graph can be plotted on these values. b) At Equilibrium, Ed=Es 39-2w=4+3w Equilibrium wage=w=7 c) i) the new formula for Ed after tax would be Ed=39-2(Ws+3)=33-2Ws so you can plot the demand curve for various values of w ii) the new equilibrium wage when 33-2Ws=4+3Ws W=5.8 iii) we have after tax, the new Wd=Ws+3 substituting it Ed=1=33-2Ws Ws=16 (gardener receives) iv) Customer pays =Ws+tax 16+3=19 v) Tax revenue received by government = Number of gardeners employed X Tax rate = (4+3w) X 3 at equilibrium, when w=7 Tax revenue is Rs 75 .

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- The demand curve for gardeners is Ed = 39 - 2w, where E = the number of gardeners, and w = the hourly wage. The supply curve is Es= 4 + 3w. a) Graph the demand and the supply curve. b) What is the equilibrium wage and equilibrium number of gardeners hired? c) Suppose the town government imposes a $3 per hour tax on all gardeners. i. Draw the new (after-tax) demand curve in terms of the employee wage. ii. What is the effect on the equilibrium wage and the equilibrium number of gardeners hired? iii. How much does the gardener receive? iv. How much does the customer pay? v. How much does the government receive as tax revenue? Solution a) Ed=39-2w Es=4+3w At w=1, Ed=37, Es=7 w=2,Ed=35, Es=10 w=3 Ed=33, Es=13 w=4, Ed=31, Es=16 a graph can be plotted on these values. b) At Equilibrium, Ed=Es
- 39-2w=4+3w Equilibrium wage=w=7 c) i) the new formula for Ed after tax would be Ed=39-2(Ws+3)=33-2Ws so you can plot the demand curve for various values of w ii) the new equilibrium wage when 33-2Ws=4+3Ws W=5.8 iii) we have after tax, the new Wd=Ws+3 substituting it Ed=1=33-2Ws Ws=16 (gardener receives) iv) Customer pays =Ws+tax 16+3=19 v) Tax revenue received by government = Number of gardeners employed X Tax rate = (4+3w) X 3 at equilibrium, when w=7 Tax revenue is Rs 75

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