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Figure 5.2 Calculating the Price Elasticity of Demand

We calculate the price elasticity of demand as the percentage change in quantity divided by the percentage change in price.

First, apply the formula to calculate the elasticity as price decreases from [tex]$\$[/tex] 70[tex]$ at point $[/tex]B[tex]$ to $[/tex]\[tex]$ 60$[/tex] at point [tex]$A$[/tex]:

[tex]\[
\begin{aligned}
\% \text{ change in quantity} & = \frac{3,000 - 2,800}{(3,000 + 2,800) / 2} \times 100 \\
& = \frac{200}{2,900} \times 100 \\
& = 6.9 \\
\% \text{ change in price} & = \frac{60 - 70}{(60 + 70) / 2} \times 100 \\
& = \frac{-10}{65} \times 100 \\
& = -15.4 \\
\text{Price Elasticity of Demand} & = \frac{6.9\%}{-15.4\%} \\
& = 0.45
\end{aligned}
\][/tex]



Answer :

GinnyAnswer
Sure, let’s go through the step-by-step solution to find the Price Elasticity of Demand.

### Step 1: Calculate the Percentage Change in Quantity

First, we need to determine the initial and final quantities. Here, the initial quantity ([tex]\(Q_i\)[/tex]) is 3000 units and the final quantity ([tex]\(Q_f\)[/tex]) is 2800 units.

[tex]\[ \text{\% change in quantity} = \frac{Q_f - Q_i}{\frac{Q_i + Q_f}{2}} \times 100 \][/tex]

Substitute the given values:

[tex]\[ \text{\% change in quantity} = \frac{2800 - 3000}{\frac{3000 + 2800}{2}} \times 100 \][/tex]

Calculate the average quantity:

[tex]\[ \frac{3000 + 2800}{2} = 2900 \][/tex]

Calculate the change in quantity:

[tex]\[ 2800 - 3000 = -200 \][/tex]

Now, plug these values back into the formula:

[tex]\[ \text{\% change in quantity} = \frac{-200}{2900} \times 100 \][/tex]

Simplify the fraction:

[tex]\[ \frac{-200}{2900} \approx -0.06896551724137931 \][/tex]

Convert to a percentage:

[tex]\[ -0.06896551724137931 \times 100 \approx -6.896551724137931 \][/tex]

### Step 2: Calculate the Percentage Change in Price

Next, determine the initial and final prices. Here, the initial price ([tex]\(P_i\)[/tex]) is [tex]$70 and the final price (\(P_f\)) is $[/tex]60.

[tex]\[ \text{\% change in price} = \frac{P_f - P_i}{\frac{P_i + P_f}{2}} \times 100 \][/tex]

Substitute the given values:

[tex]\[ \text{\% change in price} = \frac{60 - 70}{\frac{70 + 60}{2}} \times 100 \][/tex]

Calculate the average price:

[tex]\[ \frac{70 + 60}{2} = 65 \][/tex]

Calculate the change in price:

[tex]\[ 60 - 70 = -10 \][/tex]

Now, plug these values back into the formula:

[tex]\[ \text{\% change in price} = \frac{-10}{65} \times 100 \][/tex]

Simplify the fraction:

[tex]\[ \frac{-10}{65} \approx -0.15384615384615385 \][/tex]

Convert to a percentage:

[tex]\[ -0.15384615384615385 \times 100 \approx -15.384615384615385 \][/tex]

### Step 3: Calculate the Price Elasticity of Demand

Finally, the Price Elasticity of Demand (PED) is calculated as the percentage change in quantity divided by the percentage change in price:

[tex]\[ \text{Price Elasticity of Demand} = \frac{\text{\% change in quantity}}{\text{\% change in price}} \][/tex]

Substitute the percentages we found:

[tex]\[ \text{Price Elasticity of Demand} = \frac{-6.896551724137931}{-15.384615384615385} \][/tex]

Simplify the division:

[tex]\[ \text{Price Elasticity of Demand} \approx 0.44827586206896547 \][/tex]

### Conclusion

So, the calculations yield the following results:
- Percentage change in quantity: [tex]\(-6.90\%\)[/tex]
- Percentage change in price: [tex]\(-15.38\%\)[/tex]
- Price Elasticity of Demand: [tex]\(0.45\)[/tex]

These values indicate that the demand is inelastic since the absolute value of the Price Elasticity of Demand is less than 1.

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