Demand Function and Price Elasticity of Demand

The demand function is a mathematical expression that relates the quantity demanded of a product to its price, along with other factors such as income, preferences, and the prices of related goods. Price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It helps us understand how sensitive consumers are to changes in price, and it is an important concept in economics.

Demand Function: Q = 75
The given demand function is Q = 75, where Q represents the quantity demanded. This means that regardless of the price, the quantity demanded will always be 75 units. This is known as a perfectly inelastic demand, where the quantity demanded remains constant regardless of price changes.

Price Elasticity of Demand
Price elasticity of demand (PED) is calculated using the following formula:
PED = (% Change in Quantity Demanded) / (% Change in Price)

It measures the percentage change in quantity demanded relative to the percentage change in price. The PED value indicates the responsiveness of demand to price changes. There are three possible scenarios:
- If PED > 1, demand is elastic, meaning that quantity demanded is highly responsive to price changes.
- If PED = 1, demand is unit elastic, meaning that quantity demanded changes proportionally to price changes.
- If PED < 1,="" demand="" is="" inelastic,="" meaning="" that="" quantity="" demanded="" is="" not="" very="" responsive="" to="" price="" />

Calculating Price Elasticity of Demand

To calculate the price elasticity of demand at P = 3 and P = 5, we need to determine the percentage change in quantity demanded and the percentage change in price.

Price = 3
Given that Q = 75, the quantity demanded remains constant. Therefore, there is no change in quantity demanded, and the percentage change is 0.

Using the formula, PED = (% Change in Quantity Demanded) / (% Change in Price), we have:
PED = (0) / (% Change in Price)
PED = 0

The price elasticity of demand at P = 3 is 0. Since the value is less than 1, demand is inelastic. This means that quantity demanded is not very responsive to price changes.

Price = 5
Similarly, at P = 5, the quantity demanded remains constant at Q = 75. Therefore, there is no change in quantity demanded, and the percentage change is 0.

Using the formula, PED = (% Change in Quantity Demanded) / (% Change in Price), we have:
PED = (0) / (% Change in Price)
PED = 0

The price elasticity of demand at P = 5 is also 0. Again, since the value is less than 1, demand is inelastic, indicating that quantity demanded is not very responsive to price changes.

Conclusion
In summary, the demand function Q = 75 represents a perfectly inelastic demand, where the quantity demanded remains constant regardless of price changes. The price elasticity of demand at P = 3 and P = 5 is 0, indicating that quantity demanded is not very responsive to price changes. This suggests that consumers are not highly sensitive to changes in price, and the demand for the product is relatively inelastic.