Answer to Question #264808 in Microeconomics for manuewrz

Question

a) Assume KBL Limited and Richet International are multinational firms that are weighing-in the option of simultaneously entering the Ghanaian market for the first time. If neither enters, both earn a payoff of zero. If both enter, they both lose 300. If one fim enters, it gains 150 while the other earns zero. i.) Set up the payoff matrix for this game and determine if any Nash equilibria exist. [5 marks] ii.) Can you predict the outcome of this game ? [3 marks] iii.) What is the outcome of game if KBL gets to decide first? Explain you answer. [5 marks]

b.) Suppose that market demand can be represented as P = 100 - 2Q. There are 10 identical firms producing an undifferentiated product, each with the total cost function TC = 50 + q2 (q square). i. Compare the competitive outcome with the cartel outcome in terms of price, output and profit [8marks]. ii. What is the individual firm's incentive to cheat on the cartel ?[4 marks]

Answer 1

(a)

(i)

The playoff matrix for the game:

There exists a nash equilibrium in mixed strategies.

(ii)

Outcome of this game:

$=\frac{-300}{-600}+\frac{150}{600}=\frac{3}{4}$

$=0.75$

(iii)

If the KBL decides first, the outcome would be$=\frac{-300}{-600}=\frac{1}{2}$

This is the outcome of Richet International not entering the market.

Richet International in this case will not enter into the market early. This will enable KBL Ltd. to enter into the market and make a profit earning of 150.

(b)

$P=100-2Q$

$TC=50+Q^2$

This means that each firm has $MC=2Q$

Setting $MC=P$ gives the individual firm's supply to the market:

$\implies 2Q=P$

$2Q=100-2Q$

$Q=25$