Question

Suppose a firm sells 100 units when the price is $6, but sells 250 units when the price falls to $4.

1-Calculate the firm's revenue at each of the prices.

2-Calculate the price effect and the quantity effect.

3-Use the price effect and the quantity effect to determine whether demand is elastic or inelastic over this range.

4-Verify your previous answer by calculating the elasticity of demand using the midpoint formula.

Answer 1

1)Firm revenue = price * quantity sold

Firm revenue at price $6 = 6*100 = 600$

At price $4 = 4*250 = 1000$

2 )Price effect means after a price increase each unit sold sells at a higher price, raising revenue.

Quantity effect - after a price increase ,fewer units are sold,lowering revenue.

The price elasticity determines which effect is stronger.

3. Price elasticity = % change in quantity demanded ÷ % change in price

= -1.50 ÷ 0.3333

= - 4.50

% change in quantity demanded = (100-250) ÷ 100 = -1.50

% change in price = (6-4) ÷ 6= 0.3333

price demand is elastic because it is greater than 1.

4. Mid point formula = q2-q1 ÷((q2+q1 )÷ 2) / P2 -p1 ÷ (( p2+p1 ) ÷ 2)

= 250-100 ÷ ((250+ 100) ÷2 / 4-6 ÷ ( (4+6 )÷ 2

= 150 ÷ 175 / -2 ÷ 5

= 0.86 / -0.4

= -2.15

Here price elasticity of demand is greater then 1 hence it is elastic .