To calculate the Price Elasticity of Demand (PED), we use the formula:

$\text{Price Elasticity of Demand} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}$

where the percentage change in quantity demanded and the percentage change in price are given by the following formulas:

$\%\ \text{change in quantity demanded} = \frac{Q_2 - Q_1}{Q_1} \times 100$ $\%\ \text{change in price} = \frac{P_2 - P_1}{P_1} \times 100$

Let's calculate PED for each price point.

When the price is $90:

• The initial quantity demanded at $60 is 22,000, and the new quantity demanded at $90 is 18,000.
• The initial price is $60, and the new price is $90.

Step 1: Calculate percentage change in quantity demanded:

$\%\ \text{change in quantity demanded} = \frac{18,000 - 22,000}{22,000} \times 100 = \frac{-4,000}{22,000} \times 100 \approx -18.18\%$

Step 2: Calculate percentage change in price:

$\%\ \text{change in price} = \frac{90 - 60}{60} \times 100 = \frac{30}{60} \times 100 = 50\%$

Step 3: Calculate PED:

$\text{PED} = \frac{-18.18\%}{50\%} \approx -0.36$

Since the absolute value of PED is less than 1, the demand is inelastic at a price of $90.

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When the price is $150:

• The initial quantity demanded at $120 is 14,000, and the new quantity demanded at $150 is 12,000.
• The initial price is $120, and the new price is $150.

Step 1: Calculate percentage change in quantity demanded:

$\%\ \text{change in quantity demanded} = \frac{12,000 - 14,000}{14,000} \times 100 = \frac{-2,000}{14,000} \times 100 \approx -14.29\%$

Step 2: Calculate percentage change in price:

$\%\ \text{change in price} = \frac{150 - 120}{120} \times 100 = \frac{30}{120} \times 100 = 25\%$

Step 3: Calculate PED:

$\text{PED} = \frac{-14.29\%}{25\%} \approx -0.57$

Since the absolute value of PED is less than 1, the demand is also inelastic at a price of $150.

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Conclusion:

At both prices ($90 and $150), the demand for the good is inelastic, meaning the percentage change in quantity demanded is less than the percentage change in price.

Would you like further details or clarification?

Here are some related questions to explore:

1. How would you calculate the price elasticity of supply?
2. What happens if the price elasticity of demand is greater than 1?
3. How do factors like necessity or availability of substitutes affect elasticity?
4. How can elasticity help businesses with pricing strategies?
5. How do governments use elasticity in taxation policies?

Tip: Inelastic goods tend to be those with fewer substitutes or are necessities, where consumers don't easily reduce quantity demanded in response to price increases.