Marginal revenue and elasticity of demand:

Marginal revenue:
Marginal revenue (MR) is the additional revenue generated from selling one extra unit of a product. It is calculated by dividing the change in total revenue by the change in quantity sold.

Elasticity of demand:
Elasticity of demand measures the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. Elasticity values can be negative, positive, or zero.

Relation between marginal revenue and elasticity of demand:
The relationship between marginal revenue and elasticity of demand can be explained using the concept of price elasticity of demand.

If elasticity of demand is less than 1:
If the elasticity of demand is less than 1 (inelastic demand), it means that the percentage change in quantity demanded is less than the percentage change in price. In this case, marginal revenue will be negative.

When demand is inelastic, a decrease in price leads to a proportionately smaller increase in quantity demanded. As a result, the reduction in total revenue from selling the additional units at a lower price outweighs the increase in revenue from selling more units. This leads to a negative marginal revenue.

If elasticity of demand is more than 1:
If the elasticity of demand is more than 1 (elastic demand), it means that the percentage change in quantity demanded is greater than the percentage change in price. In this case, marginal revenue will be positive.

When demand is elastic, a decrease in price leads to a proportionately larger increase in quantity demanded. As a result, the increase in total revenue from selling the additional units at a lower price outweighs the reduction in revenue from selling fewer units. This leads to a positive marginal revenue.

If elasticity of demand is equal to 1:
If the elasticity of demand is equal to 1 (unitary elastic demand), it means that the percentage change in quantity demanded is equal to the percentage change in price. In this case, marginal revenue will be zero.

When demand is unitary elastic, a decrease in price leads to an equal percentage increase in quantity demanded. The increase in revenue from selling more units at a lower price exactly offsets the reduction in revenue from selling fewer units. This results in a marginal revenue of zero.

If elasticity of demand is equal to zero:
If the elasticity of demand is equal to zero (perfectly inelastic demand), it means that quantity demanded does not change regardless of the change in price. In this case, marginal revenue will be negative or zero.

When demand is perfectly inelastic, changes in price do not affect quantity demanded. As a result, the reduction in total revenue from selling the additional units at a lower price outweighs the increase in revenue from selling more units, leading to a negative or zero marginal revenue.

Conclusion:
In summary, marginal revenue will be negative if the elasticity of demand is less than 1, positive if the elasticity of demand is more than 1, zero if the elasticity of demand is equal to 1, and negative or zero if the elasticity of demand is equal to zero. The relationship between marginal revenue and elasticity of demand is based on how changes in price affect quantity demanded and total revenue.

Use this formula:
MR = AR(1- 1/e)

putting e=0.5
MR = AR(1 - 1/0.5)