university of mumbai calculate the Price Elasticity of Demand

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Prompt
Consider the following scenario: The price of a popular widget has increased from $800
to $900. Consequently, demand for the widget decreased from 500,000 units to 450,000 units.
Calculate this widget’s Price Elasticity of Demand (PED) and interpret the result.
We can use the simple formula to calculate the **PED** for this particular widget. It’s
more precise and better suited than the simple midpoint formula when products experience
significant price or demand fluctuations.
**Price Elasticity of Demand (PED)** = [**(Q~0~** + **Q~1~)** / **(Q~0`** **Q~1~)**] / [**(P~0~** + **P~1~)** / **(P~0~** – **P~1~)**]
Where
* **Q~0~** = *New Quantity*
* **Q~1~** = *Original Quantity*
* **P~0~** = *New Price*
* **P~1~** = *Original Price*
—
Given:
* **New Quantity (Q~0~)** = 450,000 units
* **Original Quantity (Q~1~)** = 500,000 units
* **New Price (P~0~)** = $900
* **Original Price (P~1~)** = $800
—
### Step 1: Calculate the Changes and Sums for Quantity and Price
#### Quantity (Demand)
* Sum of Quantities: **Q~0~** + **Q~1~** = *450,000* + *500,000* = **950,000**
units
* Change in Quantity: **Q~0~** – **Q~1~** = *450,000* – *500,000* = **-50,000**
units
#### Price
* Sum of Prices: **P~0~** + **P~1~** = *\$900* + *\$800* = **\$1,700**
* Change in Price: **P~0~** – **P~1~** = *\$900* – *\800* = **\$100**
—
### Step 2: Calculate PED Using the Midpoint Formula
**PED** = [*950,000* / *-50,000*] / [*1,700* / *100*]
**Calculate each part**:
* *Sum of Quantities / Change in Quantity* = *950,000* / *-50,000* = **-19.0**
(approximately)
* *Sum of Prices* / *Change in Price* = *1,700* / *100* = **17.00** (approximately)
Finally, calculate the **PED**:
* **PED** = *-19.00* / *17.00* = **-1.118** (approximately)
—
### Interpretation
This widget’s PED is approximately **-1.118**, indicating a **proportional
relationship** between its supply and demand, which is relatively standard. In relative terms, a
PED of more than one, as in this case, signifies that **the product is elastic**, meaning that the
percentage change in demand is more than the percentage change in price. Specifically, **a one
percent decrease in price leads to a more than one percent increase in demand**, potentially
attributable to factors like brand loyalty, excessive adequate alternatives, or perceived necessity.