Question

The average revenue \( R_A \) is 50 and elasticity of demand \( \eta \) is 5, the marginal revenue \( R_M \) is ..............

Hint:

This formula is a key application of derivatives in economics. It helps businesses understand how a change in price will affect their total revenue, based on how sensitive demand is to price changes.

Answer 1

Step 1: Recall the formula that relates marginal revenue (\(R_M\)), average revenue (\(R_A\)), and the elasticity of demand (\(\eta\)). \[ R_M = R_A \left(1 - \frac{1}{\eta}\right) \] Step 2: Substitute the given values \( R_A = 50 \) and \( \eta = 5 \) into the formula. \[ R_M = 50 \left(1 - \frac{1}{5}\right) \] Step 3: Simplify the expression. \[ R_M = 50 \left(\frac{4}{5}\right) = 10 \times 4 = 40 \]