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A firm’s Lerner index is given by L=(P-MC)/P and the firm’s marginal revenue, MR is related to its price elasticity E_d by the following formula: MR=P×(1+1/E_d ).

 a. Using the firm’s profit-maximizing condition MR=MC, show that the Lerner index L is L=(-1)/E_d  

b. What happens to the Lerner index when the demand become more elastic? Explain

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Related questions

1.Lerner Index

A firm sells 10 units at a price of 20. The marginal cost of production for this firm is MC(q)=5+q.

a) What is this firm’s Lerner Index?

b) Provide an interpretation of this value.

2. Heterogeneous consumers

A monopolist offers a single price to two consumers with the following demand functions:

p1(q1) = 120 − q1

p2(q2) = 45 − 1/2 q2.

The firm experiences a constant marginal cost of production, c = 10.

a) Graph aggregate demand, marginal revenue and marginal cost on a single graph

b) Find the optimal price and resulting demands of consumers 1 and 2 (P ∗ , q∗ 1 and q ∗ 2 ).

The demand curve for a mineral product (gold) is given by 𝑄𝑥𝑑 = 1,200 − 3𝑃𝑥 − 0.1𝑃𝑧, where 𝑃𝑧 = $300.00

a. What is the own-price elasticity of demand when 𝑃𝑥 = $140.00? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price below $140.00? Explain

b. What is the own-price elasticity of demand when 𝑃𝑥 = $240.00? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price above $240.00? Explain

c. What is the cross-elasticity of demand between good X and good Z when 𝑃𝑥 = $140.00? Are goods X and Z substitutes or complements? Explain

1. Assume a monopoly has the following demand schedule:

Price (P) Quantity (Q)

$20            200

15              300

10              500

5                700

(a) Calculate total revenue (TR) at each P and Q combination.

(b) Calculate marginal revenue per unit for each decrease in price.

(c) For the change in price from $20 to $15, calculate the interval elasticity of demand. Is demand elastic or inelastic?

(d) For the change in price from $20 to $15, obtain the Lerner index.

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