Question

1. There are two oil producers, Saudi Arabia and Iran. The market price will be $60/barrel if the total volume of sales is 9 million barrels daily, $50 if the total volume of sales is 11 million barrels daily, and $35 if the total volume of sales is 13 million barrels daily. Saudi Arabia has two strategies; either produce 8 million barrels daily or 6 million. Iran has two strategies; either produce 3 million barrels daily or 5 million. Assume for simplicity that marginal cost of production is zero.
   1. What is the quantity the two countries wish to agree to produce to maximize the sum of profits?
   2. Write out the normal form representation of this game. For the payoffs, record the profits for each country.
   3. What is the Nash equilibrium in this game?
2. Why does sharecropping continue to exist as opposed to laborers renting land and paying for the rent with the proceeds of their harvest?

Sharecropping is a farming system in which owners of the land allow others to farm it and then the harvest is split, with some portion (let's say half) going to the laborer and some to the land owner. Renting land (the "English system") is an alternative in which laborers pay a fixed monetary rent and then keep all of the proceeds of their production. For hundreds of years commentators have pointed out that sharecropping lowers overall investment and effort and that renting both generates more revenue for owners and, on average, more revenue for laborers due to the harvest generally being much larger. However, when prices drop significantly for agricultural outputs, rents can exceed the total value of output under the English system. Given that in the English system rent returns more money to land owners and on average generates more income for laborers than sharecropping, why is sharecropping still so common? Note: The answer is not that the sharecroppers are poor.

Answer 1

GIVEN:

Market Price of each Barrel = $60/barrel when 9 million total barrels are sold daily. Total Revenue = Q*P = $540 million

MP = $50/barrel when 11 million total barrels are sold daily. Total Revenue = $550 million.

MP = $35/barrel when 13 million barrels are sold daily. Total Revenue = $455 million.

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a.

In order to maximise their profits, both the countries would want to gain the maximum revenue from their sales daily. And the maximum revenue that is earned in total of both the countries is when total of 11 million barrels are sold daily at $50 per barrel.

This will be possible when Saudi Arabia produces 8 million barrels and Iran produces 3 million barrels. Or Saudi Arabia produces 6 milliona and Iran produces 250 million barrels per day.

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b.

The payoffs of the countries will be in the form of the total revenue. The game in the following situation can be presented in normal form as :

	IRAN
SAUDI ARABIA		3 MILLION	5 MILLION
8 MILLION	(50*8M, 50*3M)	(35*8M, 35*5M)
6 MILLION	(60*6M, 60*3M)	(50*6M, 50*5M)

	IRAN
SAUDI ARABIA		3 MILLION	5 MILLION
8 MILLION	(400M, 150M)	(280M, 175M)
6 MILLION	(360M, 180M)	(300M, 250M)

Strategies of Saudi Arabia - Produce 8 million barrels or produce 6 million barrels.

Strategies of Iran - Produce 3 million barrels or produce 5 million barrels.

The first table shows the calculation of total revenue in each case as per the given prices and conditions.

The total barrel production in a day summing up to some quantities gives the prices to be considered in thst situation.

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c.

Starting with Iran, Iran would choose to produce 5 million barrels per day as his total payoff from producing 5 million barrels is more than that of 3 million.

So, when Iran chooses to produce 5 million barrels, Saudi Arabia will choose to produce 6 million barrels with higher payoff tahn that in 8 million barrels.

Thus, The Nash Equilibrium is (6million, 5million) with payoffs ($300million, $250million).

At this point both the countries will be better off and total revenue will be maximised as $550 million. But, still Saudi Arabia have better options and could deviate from the strategies.

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