$$MR = ARleft( {1 - rac{1}{e}} ight)$$
$$AR = MRleft( { rac{{e - 1}}{e}} ight)$$
$$MR = ARleft( { rac{1}{{e - 1}}} ight)$$
$$AR = left( { rac{{MR}}{e}} ight)$$
Answer is Right!
Answer is Wrong!
The correct answer is: A. $$MR = AR\left( {1 – \frac{1}{e}} \right)$$
The formula for marginal revenue (MR) is:
$$MR = \frac{dQ}{dP} \cdot P$$
The formula for average revenue (AR) is:
$$AR = \frac{TR}{Q} = P$$
The formula for elasticity of demand (e) is:
$$e = \frac{dQ}{dP} \cdot \frac{P}{Q}$$
Therefore, the formula for MR in terms of AR and e is:
$$MR = AR\left( {1 – \frac{1}{e}} \right)$$
Here is a brief explanation of each option:
- Option A: This is the correct formula. It is derived from the formulas for MR, AR, and e.
- Option B: This formula is incorrect. It does not take into account the elasticity of demand.
- Option C: This formula is incorrect. It does not take into account the price.
- Option D: This formula is incorrect. It does not take into account the quantity demanded.