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EC311 · Intermediate Microeconomics

EC311 / TOPIC 35

8.9 Differentiated Bertrand and follower advantages

How can differentiated products create upward-sloping price best responses?

When a rival raises price, our demand improves, often making a higher own price optimal under strategic complements.

Follow the cause and effect

  1. Write profit (pi−c)qi(pi,pj).

  2. Differentiate with respect to pi for BRpi(pj).

  3. Solve the intersection or substitute follower BR into the leader problem.

The model you are using

KEY MODEL
q₁=20−2p₁+p₂
q₂=20−2p₂+p₁
MC=4
BRp₂=7+p₁/4

Conditions for this model

Both demands positive, no fixed costs, differentiated products and binding leader price commitment in the sequential game.

The exam trap

Do not apply homogeneous-Bertrand P=MC when demand reflects product differentiation.

Connect the reasoning to the graph

What changes

  • Price best responses can slope upward, and their intersection is the differentiated-Bertrand Nash equilibrium.

What stays fixed

Both demands positive, no fixed costs, differentiated products and binding leader price commitment in the sequential game.

Keep these conditions throughout the comparison; change only what the case above specifies.

What to inspect

Solve the intersection or substitute follower BR into the leader problem.

Compare before and after, and locate the conclusion on the graph.

5 MINUTES · TRANSFER THE IDEA

Can you explain it without the lesson?

Explain how a larger cross-price coefficient changes best-response slope.

Lesson references

  • Pindyck & Rubinfeld, Microeconomics, 9th Global ed., pp. 479–480
  • Varian, Intermediate Microeconomics, 8th ed., pp. 504–507
  • Original differentiated sequential-pricing extension; not the common-price dominant-firm model
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