# HW3a - Econ 419 Industrial Organization Jura Liaukonyte Homework 3 Due Wed March 21st in class Submit ONE version per study group Write legibly I

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Econ 419 – Industrial Organization Jura Liaukonyte Homework 3 Due Wed, March 21 st , in class Submit ONE version per study group. Write legibly. I reserve a right not to grade messy or illegible answers. Include a title page, listing the homework number and the names of all members of the study group. PART I – Analytical Problems 1. Two firms are Stackelberg competitors. The Stackelberg leader has the total cost function C 1 ( q ) = 12 q and the follower has the total cost function C 2 ( q ) = 16 q . The inverse demand curve for this market is P D ( Q ) = 64 - Q . a. Find the reaction function for the Stackelberg follower. The follower’s revenue function is R 2 ( q 1 , q 2 ) = (64 – q 1 q 2 ) q 2 , so that marginal revenue is MR 2 ( q 1 , q 2 ) = 64 – 2 q 1 q 2 . The firm’s marginal cost is MC 2 = 16. Setting marginal revenue equal to marginal cost and solving for q 2 yields q 2 = 24 – 0.5 q 1 . b. How much output will the Stackelberg leader produce? The leader’s revenue function is R 1 ( q 1 , q 2 ) = (64 – q 1 q 2 ) q 1 . Since the leader knows the follower’s reaction function, he substitutes 24 – 0.5 q 1 for q 2 , leaving his revenue function as R 1 ( q 1 ) = (40 – 0.5 q 1 ) q 1 . The leader’s marginal cost is 12. Setting marginal revenue equal to marginal cost and solving for q 1 yields q 1 = 28. c. How much output will the Stackelberg follower produce? If the leader produces 28, then the follower’s reaction function tells us that the follower produces 10. d. Now suppose that the two firms are Cournot rather than Stackelberg competitors.

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## This note was uploaded on 04/30/2008 for the course ECON 419 taught by Professor Jura during the Spring '07 term at UVA.

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HW3a - Econ 419 Industrial Organization Jura Liaukonyte Homework 3 Due Wed March 21st in class Submit ONE version per study group Write legibly I

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