Question

5. (15 points) A firm with market power sells its product for $9/unit, and its marginal cost is MC per unit. (7 pts)(a) What is this firm's Lerner Index? $6 (8 pts)(b) Beginning with the way we write marginal revenue in terms of market price, show mathematically how we can obtain the formula for the Lerner Index. Explain what range of values the LI can take, and which value indicates more market power

Answer 1

Lerner Index = (P-MC)/P

= (9-6)/9 = 0.33

we know that total revenue is the product of price and quantity

TR = P*Q, now next we take first order derivative

dTR/dQ = P + QdP/dQ

MR = P(1+dP/dQ*(Q/P))

MR = P(1+dP/dQ*(Q/P)), we know e = dQ/dP*P/Q which is equal to 1/e

at profit max position MR=MC, so

MR =MC = P*(1+1/e)

MC/P = (1+1/e)

-1/e = 1-MC/P

-1/e = P/P - MC/P

-1/e = (P-MC)/P (This is the lerner index) The right hand side is also called markup.

Lerner index would be anywhere between 0 and 1, 0 indicating competitive market and 1 indicating absolute market power.