Question

A car dealer wants to get rid of the stock of last year's model. Assume that the dealer knows from past experience that the price elasticity of demand for cars is unitary (= 1). If the price of the cars is currently $20,000 and the dealer wants to increase the quantity demanded from 30 units to 50 units, what must the new price be if the dealer is to sell the 20 additional cars?

Answer 1

Answer: $6,600

Explanation: According to the question, The price elasticity of demand for cars is unitary meaning that any percentage increase or decrease in price of a product will give an equal increase or decrease in the demand for the product.

If cars are sold at $20,000 and current sales is 30 units. To increase the quantity sold to 50 units, there must be a price reduction.

what percentage of increase in quantity to be sold do we have? 50 - 30 = 20

20/30 = 66.67 appx 67%

Meaning that a 67% decrease in price of the car will give an equal 67% increase in sales quantity.

The new price of the car will be $20,000 * 67% = $13,400

new price = $20,000 - $13,400 = $6,600

Answer 2

Answer: The answer is $6,600

Explanation:

The unitary elasticity of demand means that the quantity and price must change in the same proportion .

Using the formula

Old quantity - New quantity / Old quantity × 100%

Old quantity = 30 units, New quantity = 50units

30 - 50 / 30 × 100%

-20/30 × 100%

= -0.666 × 100 ignore the minus sign)

= 67% approximately

The percentage change in cars is 67%

0.67 × 20,000 = 13,400

Therefore the new price is

20,000 - 13,400

= 6,600

Therefore the new price is $6,600