Two multinational Dynamic Games of Industrial Organisation companies produce the same good. In the first period, firm 1 sells its prod- uct as a monopolist in Paris. In the second period, firm 1 competes with firm 2 in Berlin as a Cournot duopolist. There is no discounting between the two pe- riods. Firm 1 produces quantity xp < c/a in Paris at cost cxp. Interestingly, in Berlin, firm 1 produces quantity xg at cost (c-axp)xg, where 0

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Chapter16: Government Regulation
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part B

Two multinational
3. Dynamic Games of Industrial Organisation
companies produce the same good. In the first period, firm 1 sells its prod-
uct as a monopolist in Paris. In the second period, firm1 competes with firm 2
in Berlin as a Cournot duopolist. There is no discounting between the two pe-
riods. Firm 1 produces quantity xp <c/a in Paris at cost cXp. Interestingly, in
Berlin, firm 1 produces quantity xg at cost (c - axp)xB, where 0< a <c < 1/2.
The parameter a captures a form of learning by doing: the more firm 1 pro-
duces in Paris, the lower the marginal costs are going to be in Berlin. As for
firm 2, it produces x, in Berlin with cost cx. The inverse demand functions
are pp(xp) = 1- Xp and pa(xg, X2) = 1- xg-X2. Each firm maximises profit. In
particular, firm 1 maximises the total profit from its Paris and Berlin operations.
(a) Consider first the case of simultaneous choice. Assume that firm 2 does
not observe xp before making its production decision. This means that,
although formally firm 1 chooses output xp first, this game should be anal-
ysed as a simultaneous game between firm 1 and firm 2.
What solution concept should we use here?
ii.
* Write down the profit functions for firm 1 and firm 2, and
the maximisation programme each firm faces.
iji
, Find the first order condition for each firm with respect to
each of their products.
* Solve for the Nash equilibrium quantities of each product,
iv. .
xp, X, x
V.
rium quantities found in the previous part, determine how the equi-
librium quantities change with a. Provide an intuition for this.
By differentiating each of the expressions for the equilib-
vi.
Compute the profit of firm 2 in equilibrium. How does this
profit level vary with a? Why are firm 2's profits affected by a even
though the parameter a does not directly enter the cost function of
Firm 2?
Transcribed Image Text:Two multinational 3. Dynamic Games of Industrial Organisation companies produce the same good. In the first period, firm 1 sells its prod- uct as a monopolist in Paris. In the second period, firm1 competes with firm 2 in Berlin as a Cournot duopolist. There is no discounting between the two pe- riods. Firm 1 produces quantity xp <c/a in Paris at cost cXp. Interestingly, in Berlin, firm 1 produces quantity xg at cost (c - axp)xB, where 0< a <c < 1/2. The parameter a captures a form of learning by doing: the more firm 1 pro- duces in Paris, the lower the marginal costs are going to be in Berlin. As for firm 2, it produces x, in Berlin with cost cx. The inverse demand functions are pp(xp) = 1- Xp and pa(xg, X2) = 1- xg-X2. Each firm maximises profit. In particular, firm 1 maximises the total profit from its Paris and Berlin operations. (a) Consider first the case of simultaneous choice. Assume that firm 2 does not observe xp before making its production decision. This means that, although formally firm 1 chooses output xp first, this game should be anal- ysed as a simultaneous game between firm 1 and firm 2. What solution concept should we use here? ii. * Write down the profit functions for firm 1 and firm 2, and the maximisation programme each firm faces. iji , Find the first order condition for each firm with respect to each of their products. * Solve for the Nash equilibrium quantities of each product, iv. . xp, X, x V. rium quantities found in the previous part, determine how the equi- librium quantities change with a. Provide an intuition for this. By differentiating each of the expressions for the equilib- vi. Compute the profit of firm 2 in equilibrium. How does this profit level vary with a? Why are firm 2's profits affected by a even though the parameter a does not directly enter the cost function of Firm 2?
(b) Now consider the case of sequential choice. Assume that firm 2 observes
Xp before making its production decision x, making this a dynamic game
between firm 1 and firm 2.
i. :
What solution concept should we use here?
ii. :
Write down the maximisation programmes for firm 1 and
firm 2 for their Berlin operations in this set-up, i.e. for Xg and x, re-
spectively. Define clearly the profit function of each firm.
iii
Now focusing on period 2 only, find the first order condi-
tion with respect to xg for firm 1 and the first order condition with
respect to x, for firm 2.
iv.
rium values for x; and x; change with x;? Provide economic intuition
Solve for x; and x; as a function of x;. How do the equilib-
for this.
v. .. Express the Berlin profits of firm 1 as a function of x; and
use this to write the maximisation problem of firm 1 in the first period,
when it decides production in Paris.
Transcribed Image Text:(b) Now consider the case of sequential choice. Assume that firm 2 observes Xp before making its production decision x, making this a dynamic game between firm 1 and firm 2. i. : What solution concept should we use here? ii. : Write down the maximisation programmes for firm 1 and firm 2 for their Berlin operations in this set-up, i.e. for Xg and x, re- spectively. Define clearly the profit function of each firm. iii Now focusing on period 2 only, find the first order condi- tion with respect to xg for firm 1 and the first order condition with respect to x, for firm 2. iv. rium values for x; and x; change with x;? Provide economic intuition Solve for x; and x; as a function of x;. How do the equilib- for this. v. .. Express the Berlin profits of firm 1 as a function of x; and use this to write the maximisation problem of firm 1 in the first period, when it decides production in Paris.
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