The demand for Airplanes is represented by this equation : Qd=53,230 - .8V+.05Vr

Question

The demand for Airplanes is represented by this equation : Qd=53,230 - .8V+.05Vr-3,600Vh + 4T

V is the Price for Airplanes
Vr is the price per trip in boats
Vh is the price per gallon of gasoline
T is the average income of a consumer

Imagine that the current price per boat is $5.
That the price per gallon of gas is $10
The average income is $50
The equilibrium price for Airplanes is $60,000

After getting the market-equilibruim quantity of airplanes (-30,569.8)

Calculate : price elasticity of demand for airplanes, income elasticity of demand for airplanes, cross-elasticity of demand relative to boat transportation, and cross-elasticity of demand relative to gas.

Explanation / Answer

I hope you know how to find the market-equilibrium of airplanes i.e. (30,569.8)...steps are as follows: Market-equilibrium of airplanes = 53,230 - .8V+.05Vr-3,600Vh + 4T = 53,230 - 0.8(60,000)+0.05(5)-3,600(10) + 4(50) = -30,569.75 = -30,569.8 Then: a) price elasticity of demand for airplanes = P.E.D P.E.D = - [?Qd/?P x P/Q ] ?Qd/?P = dp/dq (calculus - change in Q with respect to P) = -0.8 p (price of airplanes) = 60,000 q (qty. demanded of airplanes) {*calculated above}= -30,569.8 P/Q = 60,000/-30,569.8 = -1.96 therefore, P.E.D = - [-0.8 x -1.96] P.E.D = -1.57 .....Interpretation= INELASTIC DEMAND. b) income elasticity of demand for airplanes = I.E.D Y = Income I.E.D = ?Qd/?Y x Y/Q ?Qd/?Y = dQ/dY (calculus - change in Q with respect to Y) = 4 Y = 50 , Q = -30,569.8 Y/Q = 50/-30,569.8 = -0.00163 I.E.D = 4 x -0.0016 I.E.D = -0.0065.... Interpretation= NEGATIVE RELATIONSHIP c) cross-elasticity of demand relative to boat transportation = C.E.D Let - Airplane be product A and Boats be product B C.E.D = ?Qda/?Pb x Pb/Qa ?Qda/?Pb = dQda/dPb = 0.05 Pb = 5 and Qa = -30,569.8 Pb/Qa = 5/-30,569.8 = - 0.00016 C.E.D = 0.05 x -0.00016 C.E.D = -0.000008178...Interpretation= COMPLIMENTARY d) cross-elasticity of demand relative to gas = C.E.D Let - Airplane be product A and Gasoline be product B C.E.D = ?Qda/?Pb x Pb/Qa ?Qda/?Pb = dQda/dPb = -3,600 Pb = 10 and Qa = -30,569.8 Pb/Qa = 10/-30,569.8 = - 0.000327 C.E.D = -3,600 x -0.00016 C.E.D = 1.18...Interpretation= POSITIVE RELATION

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