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Econ100C-Summer2011-Final-sols

# Econ100C-Summer2011-Final-sols - Economics 100C...

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Economics 100C: Microeconomics C Final Exam Solutions: Summer I 2011 1. (20 pts) Exactly two firms are competing by sequentially choosing quantity in a market. First firm 1 chooses q 1 . Firm 2 observes this quantity and then chooses q 2 . Firm 1 has the cost function   2 11 1 2 Cq q . Firm 2 has the cost function   2 22 2 2 q . Inverse market demand is P D ( Q ) = 68 – Q where Q = q 1 + q 2 . a. Calculate the Stackelberg equilibrium quantities and the resulting market price.  2 1 2 21 2 2 2 122 2 1 2 2 1 1 1 1 1 2 max 68 2 First order condition: 68 2 4 0 68 6 68 max 68 2 6 First order condition: 34 68 2 4 0 33 10 68 10 29 9.67 63 29 145 68 10 q q S S S qqq q qqq q q q q qq q q q q q P        38.33 b. Give an intuitive explanation about the direction in which each firm’s Stackelberg equilibrium quantity will be different from the Cournot equilibrium quantity. Firm 1’s Stackelberg quantity is above its Cournot quantity because it can increase its profit by producing more which causes firm 2 to produce less relative to Cournot.

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2. (20 pts) Exactly two firms are competing by simultaneously choosing price in a market. Each has the long run cost function of C i ( q i ) = 0. Market demand is Q d ( P ) = 80 – P . All consumers will purchase from the firm with the lowest price if that price is at least \$8 less than the other firm’s price. If the prices are (strictly)
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Econ100C-Summer2011-Final-sols - Economics 100C...

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