Question

The equation for a demand curve is P = 48 – 3Q.

What is the elasticity in moving from a quantity of 5 to

a quantity of 6?

Short answer

The price elasticity in moving from a quantity of 5 to

a quantity of 6 is - 2.20.

Step-by-step solution

Step 1. Meaning

• Elastic demand indicates the quantity demanded as a response to changes in price in a more than proportional manner.

Price elasticity of demand=

percentage change in the quantity demanded of a good or service/percentage change in the price.

Step 2. Explanation 

Given equation,

P = 48 – 3Q.(the demand curve)

At Q=5

P= 48- 3$\times$5

=48-15

=33

At Q=6

P = 48 – 3 $\times$6

=48-18

=30

As price increases, the quantity demanded decreases.

Step 3. Calculation.

.Price elasticity using the formula from percentage method,

percentage change in the Quantity = $△$in Quantity$÷$initial quantity $\times$100, ($△$Q= Q₁-Q)

= 6 -5$÷$5 $\times$100

= 20 %

percentage change in the Price = $△$in Price /initial price $\times$100, ($△$P= P₁-P)

= 30-33 /33 $\times$100

= -9.09 %

E_d = % $△$in Quantity demanded $÷$% $△$in price

= 20 / - 9.09

= - 2.20.

The price elasticity in moving from a quantity of 5 to

a quantity of 6 is - 2.20.