Suppose a demand curve for good x is given by Qx = 60 - 2Px + 0.5Py - 0 1M (For

Question

Suppose a demand curve for good x is given by Qx = 60 - 2Px + 0.5Py - 0 1M (For those of you who don't like math, don't be afraid that this demand curve looks complicated because Py and M are in it, just plug the values in). If Py = 10 and M = 100, graph the demand curve and show the quantities demanded for Px = 20 and Px = 10. Calculate the own price arc elasticity over this price range using the average price and quantity as your base. Assuming that Px = 10 and that M = 100. suppose the price of Py goes from 10 to 20. Calculate the cross price elasticity of demand for goods x and y. Are they complements or substitutes? Assuming that Px = 10 and that Py = 10, suppose income changes from $100 to $200. Calculate the income elasticity of demand for good x. Is x a normal or inferior good?

Explanation / Answer

a) Qx = 60 - 2Px + 0.5Py - 0.1 M ; If Py = 10 ; M =100 and Px = 20 then Qx = 60 - 2*20 + 0.5*10 - 0.1*100 = 60 - 40 + 5 - 10 = 15 ; If Px = 20 then Qx = 15 ; If Px = 10 ; then Qx = 60 - 2*10 + 0.5*10 - 0.1*100 = 60 -20 + 5 - 10 = 35; if Px = 10 then Qx = 35; change in Qx = 35 - 15 = 20 change in Px = 10-20 = -10 Average Q = (35+15)/2 = 25 Average P = (10+20)/2 = 15 so arc elasticity = (dQ/Q)*(P/dP) = - 20*25/(10*15) = - 3.3333 b) when Py = 10 ...Qx = 35 and when Py = 20 .... Qx = 40 Change in Qx = 40 - 35 = 5 Change in Py = 20 - 10 = 10 Average Qx = (35+40)/2 = 37.5 Average P = 15 so arc elasticity = (dQ/Q)*(P/dP) = (5/37.5)*(15/10) = 0.2 c) Qx for M = 100 is Qx = 35 Qx for M = 200 is Qx = 60 - 2*10 + 0.5*10 - 0.1*200 = 25 Change in Qx = 25-35 = -10 Change in Income = 200 - 100 = 100 Average Qx = 30 Average M = 150 so Elasticity = (dQ/Q)*(P/dP) = (-10/30)*(150/100) = - 0.5 Since income elasticity is negative this means Qx decreases (Quantity Bought) as Income increases ...so good must be inferior .

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