Suppose that there are two firms and they each have MC=2. No fixed costs. They each produce a slightly differentiated product; that is, consumers substitute imperfectly between products. This means demand for firm 1's product is decreasing in their price and increasing in their competitor's price. Demand functions are as follows: Firm 1: Q1 = 10 - 2P1 + P2 Firm 2: Q2 = 10- 2P2+ Pi %3! Firm 1 chooses their Pi first, then Firm 2 observes their choice and selects P2. Solve backwards, i.e., start by setting up Firm 2's profit maximization problem and solving it for their best response function. Plug this into Firm l's maximization problem. Once you have each firm's best response functions, solve for the SPNE prices. Calculate equilibrium profits to see whether there is a first mover advantage or a second mover advantage.

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Econ 306
HW 7 Applied Problems: Dynamic Games
You will develop the most skill by trying these on your own first and then comparing responses
with fellow students. Come see me or your TA for assistance.
Research Prompt
Joseph Bertrand was a 20th century French mathematician who challenged Antoine Cournot on
the idea that oligopolies compete over quantities. Bertrand believed firms compete through price
setting instead. For this assignment you will be an economic historian, using modern economic
tools to analyze a classic economic issue from the past. Specifically, you will use dynamic game
theory to solve a duopoly problem where firms choose prices instead of quantities.
Suppose that there are two firms and they each have MC=2. No fixed costs. They each produce
a slightly differentiated product; that is, consumers substitute imperfectly between products.
This means demand for firm 1's product is decreasing in their price and increasing in their
competitor's price.
Demand functions are as follows:
Firm 1: Qi = 10- 2P1+ P2
Firm 2: Q2 = 10 - 2P2 + Pi
Firm 1 chooses their Pi first, then Firm 2 observes their choice and selects P2.
Solve backwards, i.e., start by setting up Firm 2's profit maximization problem and solving it for
their best response function. Plug this into Firm 1's maximization problem. Once you have each
firm's best response functions, solve for the SPNE prices. Calculate equilibrium profits to see
whether there is a first mover advantage or a second mover advantage.
Transcribed Image Text:Econ 306 HW 7 Applied Problems: Dynamic Games You will develop the most skill by trying these on your own first and then comparing responses with fellow students. Come see me or your TA for assistance. Research Prompt Joseph Bertrand was a 20th century French mathematician who challenged Antoine Cournot on the idea that oligopolies compete over quantities. Bertrand believed firms compete through price setting instead. For this assignment you will be an economic historian, using modern economic tools to analyze a classic economic issue from the past. Specifically, you will use dynamic game theory to solve a duopoly problem where firms choose prices instead of quantities. Suppose that there are two firms and they each have MC=2. No fixed costs. They each produce a slightly differentiated product; that is, consumers substitute imperfectly between products. This means demand for firm 1's product is decreasing in their price and increasing in their competitor's price. Demand functions are as follows: Firm 1: Qi = 10- 2P1+ P2 Firm 2: Q2 = 10 - 2P2 + Pi Firm 1 chooses their Pi first, then Firm 2 observes their choice and selects P2. Solve backwards, i.e., start by setting up Firm 2's profit maximization problem and solving it for their best response function. Plug this into Firm 1's maximization problem. Once you have each firm's best response functions, solve for the SPNE prices. Calculate equilibrium profits to see whether there is a first mover advantage or a second mover advantage.
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