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Pindyck and Rubinfeld: arc elasticity (§2.4) and the markup pricing rule (Example 10.1)

ToolBreak-Even and Pricing
SourcePindyck, R. S., and Rubinfeld, D. L. (2013). Microeconomics, 8th ed. Pearson, Boston. Section 2.4 and Chapter 10, Example 10.1.
LevelUndergraduate

Problem

Demand falls from 6 to 4 units when the price rises from $8 to $10. Find the arc elasticity and the point elasticities at the two prices from the linear demand through them; then show the price a profit-maximizing seller sets over marginal cost when the elasticity is −10, −5 or −4.

Inputs to Enter

  • Price elasticity analysis: observations 8 6 / 10 4; unit cost (marginal cost) entered
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Answers

  • Arc elasticity −1.8 (the same in either direction); linear fit q = 14 − p, point elasticities −1.33 at (8, 6) and −2.5 at (10, 4)
  • Markup rule P = MC/(1 + 1/E): E = −10 → 1.11 MC, −5 → 1.25 MC, −4 → 1.33 MC; Lerner index (P − MC)/P = −1/E
  • Varian's linear monopoly (p = 50 − y/2, MC 10): y* = 40, p* = 30, profit 800, elasticity at p* −1.5

Notes

Choose the price-elasticity analysis and paste the two observations; the optimal price is printed from both the constant-elasticity and the linear demand fits.

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