Total Revenue Curve for a Negatively Sloping Straight Line Demand Curve

A demand curve shows the relationship between the price of a product and the quantity demanded by consumers. If the demand curve is a straight line with a negative slope, it means that as the price of the product increases, the quantity demanded decreases. In this case, the total revenue curve will have a specific shape, which is an inverted vertical parabola. Let's understand this concept in detail.

Definition of Total Revenue

Total revenue is the total amount of money earned by a company by selling its products. It is calculated by multiplying the price of a product with the quantity sold. Mathematically, we can represent it as:

Total Revenue = Price x Quantity

Shape of Total Revenue Curve

The shape of the total revenue curve depends on the slope of the demand curve. If the demand curve is perfectly elastic, which means that the quantity demanded changes infinitely for a small change in price, the total revenue curve will be a horizontal line. On the other hand, if the demand curve is perfectly inelastic, which means that the quantity demanded remains the same irrespective of the change in price, the total revenue curve will be a vertical line.

However, in the case of a negatively sloping straight line demand curve, the shape of the total revenue curve is unique. When the price of a product is high, the quantity demanded is low, and hence the total revenue earned is also low. Similarly, when the price of a product is low, the quantity demanded is high, and hence the total revenue earned is also low. Therefore, the total revenue curve reaches its maximum point at the midpoint of the demand curve, where the price and quantity are both moderate. As we move away from the midpoint, the total revenue curve starts to fall.

The shape of the total revenue curve in this case is an inverted vertical parabola because it has a maximum point at the top and slopes downwards on both sides. It is concave to the origin because the rate of change of total revenue decreases as we move away from the midpoint.

Conclusion

In conclusion, the shape of the total revenue curve for a negatively sloping straight line demand curve is an inverted vertical parabola, which is concave to the origin. The maximum point of the curve is at the midpoint of the demand curve, where the price and quantity are both moderate. As we move away from the midpoint, the total revenue curve starts to fall.