**Calculating MR using the formula:**

To calculate MR (marginal revenue), we can use the formula:

MR = AR * (1 - 1/|e|)

Where:
- MR represents marginal revenue
- AR represents the average revenue
- e represents the elasticity of demand

**Step 1: Understanding Average Revenue (AR):**

Average revenue (AR) is the total revenue divided by the quantity sold. It represents the price per unit of a product.

In this case, since AR is given as 5, it means that the average revenue per unit is $5.

**Step 2: Understanding Elasticity of Demand (e):**

The elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It tells us how sensitive demand is to price changes.

In this case, the elasticity of demand is given as 2. An elasticity of demand greater than 1 indicates elastic demand, meaning that demand is highly responsive to price changes.

**Step 3: Calculating Marginal Revenue (MR):**

Using the formula mentioned earlier, we can calculate MR.

MR = AR * (1 - 1/|e|)

Substituting the given values:

MR = 5 * (1 - 1/|2|)

MR = 5 * (1 - 1/2)

MR = 5 * (1 - 0.5)

MR = 5 * 0.5

MR = 2.5

Therefore, the marginal revenue (MR) is $2.5.

**Explanation:**

Marginal revenue (MR) represents the change in total revenue that results from selling one additional unit of a product. It is calculated by finding the difference between the total revenue of two consecutive quantities sold.

In this case, the elasticity of demand is 2, indicating that demand is elastic. If the price is increased by 1%, the quantity demanded would decrease by 2%. As a result, the average revenue (AR) of $5 would need to be adjusted to maintain profitability.

The formula for MR takes into account the elasticity of demand. When demand is elastic, reducing the price leads to a proportionately larger increase in quantity demanded. Therefore, MR is lower than AR.

By substituting the given values into the formula, we find that the marginal revenue (MR) is $2.5. This means that for each additional unit sold, the total revenue would increase by $2.5.