6. Given the demand function as Q_(1)=b_(0)-b_(1)P Derive the Average Revenue and Marginal Revenue functions and compare the two (5 marks)

To derive the Average Revenue (AR) and Marginal Revenue (MR) functions from the given demand function , we need to follow these steps:1. **Determine the Total Revenue (TR) function:** - Total Revenue is calculated as the product of price (P) and quantity (Q). - Given , the Total Revenue function is: - Simplifying this, we get: 2. **Derive the Average Revenue (AR) function:** - Average Revenue is the Total Revenue divided by the quantity. - Using the Total Revenue function , we have: 3. **Derive the Marginal Revenue (MR) function:** - Marginal Revenue is the additional revenue from selling one more unit of the good. - To find MR, we take the derivative of the Total Revenue function with respect to quantity (Q). - Given , we need to express in terms of . From the demand function , we solve for : - Substitute into the Total Revenue function: - Simplify the expression: - Differentiate with respect to to find : 4. **Compare Average Revenue (AR) and Marginal Revenue (MR):** - The Average Revenue function is: - The Marginal Revenue function is: - To compare the two, we can express in terms of from the demand function: - Substitute into the AR function: \[ AR = \frac{b_0 \left(\frac{b_0 - Q_1}{b_1}\right) - b_1 \left(\frac{b_0 - Q_1}{b_1}\right)^2}{b_0 - b_1 \left(\frac{b_0 - Q