Market demand for gizmos is P = 750 0.5Q. Suppose there are two firms in the gizmo industry, selling identical products. Firm 1's cost function is C₁(Q₁) = 0.25Q1, and firm 2's cost function is C₂(Q2) = 10Q2. (a) Suppose that the gizmo firms compete on quantity and move simultaneously (i.e., they are in a Cournot duopoly). i. Derive each firm's best response function. ii. Find the Cournot equilibrium levels of output for each firm. iii. Find the market price and profits for each firm. (b) Suppose instead that firm 1 is able to start production before firm 2. i. Find the Stackelberg equilibrium levels of output for each firm. ii. Find the market price and profits for each firm. (c) Comparing the two duopoly situations, does the Cournot or Stackelberg duopoly result in greater industry profits? Which situation does firm 1 prefer? Which situation does firm 2 prefer?

Market demand for gizmos is P = 750 0.5Q. Suppose there are two firms in the gizmo industry, selling identical products. Firm 1's cost function is C₁(Q₁) = 0.25Q1, and firm 2's cost function is C₂(Q2) = 10Q2. (a) Suppose that the gizmo firms compete on quantity and move simultaneously (i.e., they are in a Cournot duopoly). i. Derive each firm's best response function. ii. Find the Cournot equilibrium levels of output for each firm. iii. Find the market price and profits for each firm. (b) Suppose instead that firm 1 is able to start production before firm 2. i. Find the Stackelberg equilibrium levels of output for each firm. ii. Find the market price and profits for each firm. (c) Comparing the two duopoly situations, does the Cournot or Stackelberg duopoly result in greater industry profits? Which situation does firm 1 prefer? Which situation does firm 2 prefer?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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**Market demand for gizmos is $ P = 750 - 0.5Q $. Suppose there are two firms in the gizmo industry, selling identical products. Firm 1's cost function is $ C_1(Q_1) = 0.25Q_1^2 $, and firm 2's cost function is $ C_2(Q_2) = 10Q_2 $.**

(a) Suppose that the gizmo firms compete on quantity and move simultaneously (i.e., they are in a Cournot duopoly).

i. Derive each firm's best response function.

ii. Find the Cournot equilibrium levels of output for each firm.

iii. Find the market price and profits for each firm.

(b) Suppose instead that firm 1 is able to start production before firm 2.

i. Find the Stackelberg equilibrium levels of output for each firm.

ii. Find the market price and profits for each firm.

(c) Comparing the two duopoly situations, does the Cournot or Stackelberg duopoly result in greater industry profits? Which situation does firm 1 prefer? Which situation does firm 2 prefer?

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Step 2: (a) (i) Derive each firm's best response function

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Step 3: a) (ii) Find the Cournot equilibrium levels of output for each firm.

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Step 4: a) (iii) Find the market price and profits for each firm

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Step 5: b) (i) Find the Stackelberg equilibrium levels of output for each firm

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Step 6: b) (ii) Find the market price and profits for each firm

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Step 7: c) Compare the two duopoly situations

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