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uppose the annual demand function for the Honda Accord is Qd = 430 – 10 PA + 10 PC – 10 PGwhere PA and PC are the prices of the Accord and the Toyota Camry respectively (in thousands), and PGis the price of gasoline (per gallon). What is the elasticity of demand of the Accord with respect to the price of Camry when both cars sell for $20,000 and fuel costs $3 per gallon? What is the elasticity with respect to the price of gasoline?

Sagot :

Answer:

Qd = 400 units

elasticity of demand of the Accord with respect to the price of Camry = 0.5

elasticity with respect to the price of gasoline = -0.075

Explanation:

Solution:

The annual demand function for the Honda Accord is:

Qd = 430 – 10 PA + 10 PC – 10 PG

Where,

PA = Price of Honda Accord

PC = Price of Honda Camry

PG = Price of Gasoline per gallon.

Selling Price of both cars = $20,000

Fuel Cost = $3 per gallon.

a) Elasticity of Demand of the Accord with respect to the price of Camry.

First, we need to calculate the number of units demanded.

Qd = 430 – 10 PA + 10 PC – 10 PG

Qd = 430 – 10 (20) + 10 (20) – 10 (3.00)

Qd = 430 - 200 + 200 - 30

Qd = 430 - 30

Qd = 400 units

Cross-price elasticity of the Accord with respect to the price of the Camry will be:

Cross Price = (dQd/dPC) x (PC)/(Qd)

dQd/dPC = 10

PC = 20

Qd = 400

So,

Cross Price = 10* 20/400

Cross Price  = 0.5

b) Elasticity with respect to the price of gasoline?

Elasticity =  (dQd/dPG)*(PG/Qd)

dQd/dPG = -10

PG = 20

Qd = 400

Elasticity  = (-10)*(3/400)

Elasticity  =  -0.075

a) The Qd is = 400 units

b) When The elasticity of demand of the Accord regarding the price of Camry is = 0.5 then elasticity concerning the price of gasoline is = -0.075

Calculation Elasticity of demand

When The annual demand function for the Honda Accord is:

Then Qd = 430 – 10 PA + 10 PC – 10 PG

Where,

PA is = Price of Honda Accord

PC is = Price of Honda Camry

PG is = Expense of Gasoline per gallon.

Selling Price of both cars is = $20,000

Fuel Cost is = $3 per gallon.

a) When the Elasticity of Demand of the Accord about the price of Camry.

First, we need to estimate the number of units demanded.

Qd is = 430 – 10 PA + 10 PC – 10 PG

Qd is = 430 – 10 (20) + 10 (20) – 10 (3.00)

Qd is = 430 - 200 + 200 - 30

Qd is = 430 - 30

Qd is = 400 units

When the Cross-price elasticity of the Accord with respect to the price of the Camry will be:

Cross Price is = (dQd/dPC) x (PC)/(Qd)

dQd/dPC is = 10

PC is = 20

Qd is = 400

So,

Cross Price is = 10* 20/400

Cross Price is = 0.5

b) When is the Elasticity affecting the price of gasoline?

Elasticity is = (dQd/dPG)*(PG/Qd)

dQd/dPG = -10

PG = 20

Qd is = 400

Elasticity is = (-10)*(3/400)

Elasticity is = -0.075

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