A. [25 points] Suppose the market for semiconductors in the U.S. is characterize
ID: 1199321 • Letter: A
Question
A. [25 points] Suppose the market for semiconductors in the U.S. is characterized by: D = 200 – 40P [Demand]
S = 40 + 40P [Supply]
The market for semiconductors in the rest of the world is characterized by:
D = 160 – 40P [Demand] S = 80 + 40P [Supply]
Suppose the U.S. government imposes a quota of 32 units on its imports. Calculate the magnitude of the deadweight loss resulting from the quota under the assumption that the U.S. is a small open economy.
B. [25 points] Consider the following predation game involving an incumbent and a potential entrant. Payoffs are written with the potential entrant’s profits listed first and the incumbent’s listed second. The profit numbers represent discounted values over the life of the firms.
Stays Out (0, 10)
Enters
Predates (-5, 0)
Accommodates (4, 6)
Potential Entrant
Incumbent
i) What is the equilibrium of this game?
ii) Would the equilibrium be different if the (-5, 0) payoff were instead (-5, 8)?
Explanation / Answer
A)
US
D = 200 – 40P
S = 40 + 40P
Therefore, for equilibrium D = S
200 - 40P = 40 + 40P
160 = 80P
P = 2
Q = 200 - 40 * 2
Q = 120
World
D = 160 – 40P
S = 80 + 40P
Therefore, for equilibrium D = S
160 - 40P = 80 + 40P
80 = 80P
P = 1
Q = 160 - 40*1 = 120
Globally with trade:
D = 200 - 40P + 160 - 40P = 360 - 80P
S = 40 + 40P + 80 + 40P = 120 + 80P
Global Equilibrium:
360 - 80P = 120 + 80P
160P = 240
P = 1.5
Q = 360 - 80 * 1.5 = 240
US Equilibrium (with free trade) at P =1.5
Quantity Demanded: 200 - 40 * 1.5 = 140
Supplied by US: 40 + 40 * 1.5 = 100
Imported = 140 - 100 = 40
World equilibrium at P = 1.5
Quantity Demanded: 160 - 40 * 1.5 = 100
Supplied by World: 80 + 40 * 1.5 = 140
Exported = 140 - 100 = 40
US Market with quota = 32
Current supply = 40
Change in supply = 40 - 32 = 8
US domestic supply: S = 40 + 40P + 32
US equilibrium with quota:
40 + 40P + 32 = 200 - 40P
128 = 80P
P = 1.6
Quantity Demanded: 200 – 40 * 1.6 = 136
Supplied by US: 40 + 40 * 1.6 = 104
Imported = 134 - 104 = 32 (which is equivalent of the import quota)
Change in P: 1.6 - 1.5 = 0.1
Change in Q: 140 - 136 = 4
Deadweight loss in the US = 1/2 * Change in Price * Change in Quantity
Deadweight loss in the US = 1/2 * 0.1 * 4 = 0.2
World equilibrium with export quota=32
D = 160 – 40P + 32
S = 80 + 40P
160 - 40P + 32 = 80 + 40P
112 = 80P
P = 1.4
Quantity Supplied: 80 + 40 * 1.4 = 136
World local demand: 160 - 40 *1.4 = 104
Export = 136 - 104 = 32 (the exports to the US)
Change in Price = 1.5 - 1.4 = 0.1
Change in Q = 104 - 100 = 4
Deadweight loss in the World = 1/2 * Change in Price * Change in Quantity
Deadweight loss in the World = 1/2 * 0.1 * 4 = 0.2
Global deadweight loss = deadweight loss US + deadweight loss World = 0.2 + 0.2 = 0.4
Therefore, the import quota results in a total deadweight loss of 0.4.
B)
i)
The equilibrium of this game is (4,6), i.e. when the potential entrant enters the market and the incumbent accommodates. Potential entrants maximum payoff is 4, which is realized when it enters the market. Therefore, it will enter the market, and given its entry the incumbent will try and maximize its own returns. The incumbent can earn a maximum payoff of 6 when it decides to accommodate. If it would would have decided to predate its payoff would have been 0, which would leave him worse-off. Therefore the incumbent will decided to accommodate and thereby maximize its payoff. The equilibrium is therefore (4,6).
ii)
If the payoff would have been (-5,8) when potential entrant enters and incumbent predates, it would have changed the equilibrium point. This is because if the potential entrant would decide to enter the market, the incumbent would have predated and earned a payoff of 8, instead of 6 which would have been earned had it accommodated. Therefore, the equilibrium for this game will be (0,10) as the potential entrant will not enter the market. This is because if it enters the incumbent will maximize its payoff by predating and that would lead to a negative payoff for the potential entrant.
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