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Problem 2 of MIDTERM Page 279 #14 Group 6 Ritchie Roi Chua Ramon Jose Miguel Naguiat Mary Jane L. Paglumotan Mark Anthony Salazar Charlotte Tang Tong Ya(Nicole) Problem 2 (Page 279 # 14) In the demand function given, a point is specified with one given coordinate A. Find the value of the other coordinate B. Find the coordinates of the new point corresponding to the changed (increased or decreased) price or demand level C. Approximate the price elasticity of demand at the specified (first) point, using the results of (a) and (b) D. Find the arc price elasticity of demand at the specified point. Classify and interpret this result 5 X= (36-P2), P=2, price increase by 1 (monetary) unit 4 Solution A. VALUE OF X X=(5/4)(36-P2) P=2 X=(5/4)(36-4) X=40 B. When price increases by 1 monetary unit : P=2+1=3 X=(5/4)(36-P2) X=(5/4)(36-9) X=33.75 Solution C. Price Elasticity of demand at P=2 ΔX = 33.75-40 = - 6.25 ΔP=3-2 =1 η=EX/EP= (P/X)(ΔX/ΔP) η= (2/40)(-6.25/1) η= -0.3125 Solution D. The arc price elasticity of demand between the points is : η=EX/EP=[(3+2)/(33.75+40)]*(-6.25/1) =(5/73.75)*(-6.25/1) = - 0.37 Solution E. Exact elasticity of demand at P=2 E = EX/EP = (P/X)*(dx/dp) To get dx/dp: X = (5/4)(36-P2) dx/dp =(5/4)(-2P) dx/dp = - 5p/2 E=EX/EP= (P/X)*(dx/dp) =(P/X)*(-5p/2) At P=2, X=40 : E=(EX/EP)=(2/40)*(-10/2) = -1/4 Conclusion: A 4% increase in price is expected to decrease demand for the commodity by 1%, when the prevailing price is Php2 and the corresponding demand is 40 units Graph X=(5/4)(36-P2) Web Links http://people.hofstra.edu/faculty/Stefan_Wan er/RealWorld/Calcsumm5.html http://www.howardcc.edu/math/ma145/3.5/3. 5.htm http://www.pinkmonkey.com/studyguides/sub jects/eco/chap2/e0202401.asp