8.17. EFFICIENCY LOSS UNDER COURNOT. Consider a market where two firms simultaneous set quantities of a homogeneous product with demand given by Q = 37.5-P/4. Each firm has constant marginal cost equal to 30. (a) Determine equilibrium output and price. (b) Compute the efficiency loss as a percentage of the efficiency loss under monopoly.

Microeconomic Theory
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Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.10P: Inverse elasticity rule Use the first-order condition (Equation 15.2 ) for a Cournot firm to show...
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8.17
(f) Show that, in equilibrium, consumer surplus is given by
CS = (na-₁c)²/(n + 1)²
8.16. ELASTICITY RULE (REPRISE). Show that the elasticity rule derived in Chapter 3,
that is (p-MC)/MC = -1/e, holds under Cournot competition with linear demand and
costs, where MC is firm i's marginal cost and e its demand elasticity (not the market
elasticity).
8.17. EFFICIENCY LOSS UNDER COURNOT. Consider a market where two firms simultaneous
set quantities of a homogeneous product with demand given by Q = 37.5 - P/4. Each
firm has constant marginal cost equal to 30.
(a) Determine equilibrium output and price.
(b) Compute the efficiency loss as a percentage of the efficiency loss under
monopoly.
8.18. EQUILIBRIUM PRICE UNDER COURNOT. Show analytically that equilibrium price
under Cournot is greater than price under perfect competition but lower than monopoly
price.
8.19. COURNOT WITH INCREASING MARGINAL COST. Consider a duopoly for a homoge-
uct with demand Q=10-P/2. Each firm's cost function is given by
Transcribed Image Text:(f) Show that, in equilibrium, consumer surplus is given by CS = (na-₁c)²/(n + 1)² 8.16. ELASTICITY RULE (REPRISE). Show that the elasticity rule derived in Chapter 3, that is (p-MC)/MC = -1/e, holds under Cournot competition with linear demand and costs, where MC is firm i's marginal cost and e its demand elasticity (not the market elasticity). 8.17. EFFICIENCY LOSS UNDER COURNOT. Consider a market where two firms simultaneous set quantities of a homogeneous product with demand given by Q = 37.5 - P/4. Each firm has constant marginal cost equal to 30. (a) Determine equilibrium output and price. (b) Compute the efficiency loss as a percentage of the efficiency loss under monopoly. 8.18. EQUILIBRIUM PRICE UNDER COURNOT. Show analytically that equilibrium price under Cournot is greater than price under perfect competition but lower than monopoly price. 8.19. COURNOT WITH INCREASING MARGINAL COST. Consider a duopoly for a homoge- uct with demand Q=10-P/2. Each firm's cost function is given by
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