Seminar Questions Given the demand function Q 200 2P PA

Seminar Questions Given the demand function: Q = 200 - 2P - P_A + 0.1 Y^2 Where P = 10, P_A = 15 and Y = 100, find: The price elasticity of demand The cross-price elasticity of demand The income elasticity of demand. Estimate the percentage change in demand if P_A rises by 3%. Is the alternative good substitutable or complementary?

Solution

Price elasticity of Demand = dQ/dP=-2

Cross elasticity of demand = dQ/dP (P/Q)

= -2(10/Q)

To find Q when P = 10

Q = 200-2(10)-15+0.1(10000)

= 200 -35+1000 = 1165

Hence cross elas of demand = -2(10/1165) = -0.01717

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Income elasticity of demand = dQ/dY = 2y = 200

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3) If PA raises by 3% then PA =10.3

Alternative good is substituttable.