please do all parks and show work Thank you 4 A cartel is a

please do all parks and show work. Thank you!!

4. A cartel is a group of firms who try to work together to behave like a monopoly. These firms attempt to share large monopoly profits by reducing output and raising prices. Perhaps the most famous cartel is OPEC (Organization of Petroleoum Exporting Countries). Let\'s consider the incentives faced by two members of OPEC, Saudi Arabia and Iran. Suppose the demand for oil is given by P- 40-Q, where Q is in millions of barrels of oil per day. Assume there is no cost for producing a single barrel of oil (the wells and infrastructure have already been built) The profit-maximizing quantity for a monopolist is 20 million barrels (check!). Saudi Arabia and Iran want to act like a monopolist and split the production and monopoly profits equally between them by reaching an agreement through OPEC. Finally, assume the countries can only choose from 2 strategies: low cartel production (10 million barrels) and high production (12 million barrels). Draw the normal form of this game and find the Nash equilibrium. Can the cartel agreement be sustained?

Solution

Normal form of the game

Iran

Low Cartel High Cartel

Low Cartel (10,10) (0,12)

S audi Arebia   

High Cartel *12,0) (12,12)

Then Nash Equilibrium is High cartel,High Cartel

As collectively output exceeds $20 mn Barrels hence cartel agreement wont be sustained