Question

A) Suppose that, initially, the price of a car is $10,000, the average consumer makes $50,000 per year, and 4,000 of these cars are sold every month.

Then suppose that, a month later, the price of the car is $10,000, the average consumer makes $40,000 per year, and 5,000 of these cars are sold every month.

Calculate the income elasticity of demand for these cars.

Enter your answer as a decimal number rounded to 3 decimal places.

B)

Suppose that, initially, the price of a plate of eggs is $3.60, the price of bacon is $2.50, and the diner with these prices sells 80 plates of eggs per day.

Then suppose that, after updating their menu prices, the price of a plate of eggs is $3.60, the price of bacon is $3.00, and the diner sells 64 plates of eggs per day.

Calculate the cross-price elasticity of demand for eggs, with respect to bacon.

Enter your answer as a decimal number rounded to 3 decimal places.

The cross-price elasticity of demand is:

The income elasticity of demand is:

Answer 1

Income elasticity of demand can be calculated using the following formula

%ΔQ Ey = WAY

Using mid point method

Ev - (Q2 – Qı)(Y2 + Y1) (Q2+2)(Y) - Y)

Given, Q1 = 4000,Y1 =.50000

Q2 = 5000, Y2 = 40,000

Ey = 14.000+ (5000 – 4000 (40.000 + 50,000) (4,000 + 5,000) (40,000 – 50,000)

Ey = (1000)(90,000 (9000) (-10,000)

Ey = -1.000

This is for the first time I am seeing negative sign in case of cars. As car is considered as normal / luxury but in this case with the rise in income the demand for car has declined therefore it is an inferior good. You take annual or monthly value will get the same elasticity.

Cross elasticity of demand can be determined using the following formula

ΔΟΕ Εχ - ΔΡΒ

Ex=TO (QE, - QE)(PB, + PB.) (QE + QE)(PB, – PB1) +QE

Given, Q^E₁ = 80, P^B₁ = $ 2.50

Q^B₂ = 64, P^B₂= $ 3.00

Plug in these values in the above equation we get

Ex= (64 – 80) (3 + 2.5) (64 + 80) (3 – 2.5)

=Ex = -16 x 5.5 144 x 0.5

Ex = -1.222

Since sign is negative thus it means that Eggs and Bacon's are complementary to each other.

The cross elasticity of demand = - 1.222

The income elasticity of demand = - 1.000

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