Assume that the demand for the Mazda 6 is given by Q D = 500 ? 12 P M +10 P A ?

Question

Assume that the demand for the Mazda 6 is given by QD = 500?12PM +10PA ?5PG + 0.0001M, where PM is the price of the Mazda 6 (in thousands), PA is the price of the Honda Accord (in thousands), PG is the price of gas (per liter) and M is disposable income. The supply for Mazda 6 is given by QS = 20PM ? 55.

a.[5] Provide the demand curve for the Mazda 6 if the price of the Accord is $25,000, the price of gas is $2 per liter and the disposable income is $50,000.

b.[10] Calculate the equilibrium price and quantity in the market for the Mazda 6. c.[5] Indicate whether the demand is elastic or inelastic at equilibrium.

d.[5] Calculate the cross-price elasticity of demand between the Mazda 6 and the Accord at equilibrium.

e.[5] Calculate the income elasticity of demand for the Mazda 6 at equilibrium.

Explanation / Answer

a. Demand for mazda 6 : QD = 500 - 12PM + 10PA - 5PG + 0.0001M

=> QD = 500 - 12PM + 10(25) - 5(2) + 0.0001(50000)

=> QD = 500 - 12PM + 250 - 10 + 5

=> QD = 745 - 12PM

b. For equlibrium price QD = QS

=> 745 - 12PM = 20PM - 55 => 800 = 32PM => PM = 25 (in thousands)

=> PM = $25000

Equlibrium quantity Q = 445

c. Inelastic

d. (PA/QD)d(QD)/d(PA) = (25/445)(10) = 0.562

e. (M/QD)d(QD)/d(M) = (50000/445)*(0.00001)=0.011

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