Question

Two countries, Algeria and Benin are trading with each other without tariffs. They know that once they raise tariffs, the other country responds by raising tariffs as well in the next period, which is costly in the long run. However, in the short run Algeria or Benin could gain by individually raising tariffs. If both players could commit to free trade, they would want to do so.

(Key: Algeria = Bold | Benin = Italicized)

	Free Trade	Tariffs
Free Trade	4, 5	1, 6
Tariffs	6, 1	2, 2

(a) In the payoff matrix yyou can see the payoffs are not symmetric. That is Benin benefits more from free trade than Algeria. Suppose that both countries ahve the same discount rate between 0 and 1. Show under which values Algeria is willing to choose free trade and not deviate to impose tariffs. Hint: x + xδ + xδ² + ... = x/(1 - δ)

(b) Similarly, show for which values of δ, Benin is willing to impose tariffs?

(c) For which values of δ can free be sustained? Explain what this means in terms of patience? Is it a good thing that Algeria and Benin care about the future or not, given that both want to cooperate and trade freely?

(d) The old president of Benin, Thomas Boni Yayi, who has a discount factor δ = 8/10 is replaced by a new president, Patrice Talon, who has a discount factor δ = 2/10. Before the election a trade agreement between Algeria and Benin was signed, which stipulates that both countries trade freely. Both countries agree that if one country breaks the agreement, the agreement is void, starting in the next period for an infinite number of periods. What would you expect Algeria and Benin do with this trade agreement after the election?

Answer 1

If they Both choose free trade then they will have higher payoff than that of NE

We have NE as (Tariffs,Tariffs) ini this case

Lets find δ for which Algeria is indifferent between Free trade and tariff

4+4δ+4δ^2+...=6+2δ+2δ^2+...=4+2+2δ+2δ^2+...

4/1-δ=4+2/1-δ

2/1-δ=4

δ=1/2

if δ >1/2 then algeria will choose to free trade otherwise he will impose tariff

Answer for b)

For Benin

similar representation will be

5+5δ+5δ^2+...=6+2δ+2δ^2+...

5/1-δ=4+2/1-δ

3/1-δ=4

3/4=1-δ

δ>1/4 for Benin to choose free trade over tariff

Answer for c)

if both have same δ then it will be sustained if δ>1/2 as δ increases to 1 it implies that both countries are patient enough and value future more than present.

Answer for d)

Now for new presidnet has δ=0.2 which is less than previous δ=.25 Benin has higher valuation if they impose tariff hence we can say that Benin will not go for free trade and will impose tariff and if Benin impose tariff then best response of Algeria is Tariff as well

Hence they will keep on playing (Tariff, Tariff) if new δ is 0.2 for Benin