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2.[**] Consider a differentiated product duopoly market with symmetric, linear demand system $y_1 = 12 - 2p_1 + p_2$ $y_2 = 12 - 2p_2 + p_1$ and in which both firms have constant unit costs of $5 per unit. The firms compete in prices, with Firm 1 choosing first (the leader) and Firm 2 second (the follower). When answering the following questions, please round figures to 2 dec- imal places when necessary. (a) Write down the profit function of Firm 1. (b) Write down the reaction function of Firm 2. (You can use the formula derived in the Class Prep video for Week 5.) (c) Substitute Firm 2's reaction function into Firm 1's profit function and determine Firm 1's profit-maximising choice of $p_1$. (d) What price will Firm 2 choose? (e) Draw a diagram with $p_1$ measured on the horizontal axis and $p_2$ on the vertical axis. Sketch the reaction function for Firm 2 in your diagram, and indicate the point corresponding to the values of $p_1$ and $p_2$ that you found in (c) and (d). (f) Does this market have a first-mover or a second-mover advantage?

          2.[**] Consider a differentiated product duopoly market with symmetric,
linear demand system
$y_1 = 12 - 2p_1 + p_2$
$y_2 = 12 - 2p_2 + p_1$
and in which both firms have constant unit costs of $5 per unit. The
firms compete in prices, with Firm 1 choosing first (the leader) and
Firm 2 second (the follower).
When answering the following questions, please round figures to 2 dec-
imal places when necessary.
(a) Write down the profit function of Firm 1.
(b) Write down the reaction function of Firm 2. (You can use the
formula derived in the Class Prep video for Week 5.)
(c) Substitute Firm 2's reaction function into Firm 1's profit function
and determine Firm 1's profit-maximising choice of $p_1$.
(d) What price will Firm 2 choose?
(e) Draw a diagram with $p_1$ measured on the horizontal axis and $p_2$
on the vertical axis. Sketch the reaction function for Firm 2 in
your diagram, and indicate the point corresponding to the values
of $p_1$ and $p_2$ that you found in (c) and (d).
(f) Does this market have a first-mover or a second-mover advantage?

2.[**] Consider a differentiated product duopoly market with symmetric,
linear demand system
y1 = 12 - 2p1 + p2
y2 = 12 - 2p2 + p1
and in which both firms have constant unit costs of 5 per unit. The
firms compete in prices, with Firm 1 choosing first (the leader) and
Firm 2 second (the follower).
When answering the following questions, please round figures to 2 dec-
imal places when necessary.
(a) Write down the profit function of Firm 1.
(b) Write down the reaction function of Firm 2. (You can use the
formula derived in the Class Prep video for Week 5.)
(c) Substitute Firm 2's reaction function into Firm 1's profit function
and determine Firm 1's profit-maximising choice ofp1.
(d) What price will Firm 2 choose?
(e) Draw a diagram withp1measured on the horizontal axis andp2on the vertical axis. Sketch the reaction function for Firm 2 in
your diagram, and indicate the point corresponding to the values
ofp1andp2that you found in (c) and (d).
(f) Does this market have a first-mover or a second-mover advantage?

Added by Sarah J.

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