Week 8 Discussion Question
Question 1
Coca-Cola and Pepsi both advertise aggressively in a simultaneous decision making move, but would they be better off if they didn’t. Their commercials are not designed to convey new information about the products. Instead, they are designed to capture each other’s customers. Construct a payoff matrix using the following hypothetical information: If neither firm advertises: Coca-Cola and Pepsi both earn profits of US$750 million per year

If both firms advertise: Coca-Cola and Pepsi earn profits of US$500 million per year

If Coca-Cola advertises and Pepsi doesn’t: Coca-Cola earns profits of US$900 million per year and Pepsi earns profits of US$400 million.

If Pepsi advertises and Coca-Cola doesn’t: Pepsi earns profits of US$900 million per year and Coca-Cola earns profits of US$400 million.

Given the statement above in payoff matrix (in US$ million):
COCA - COLA

PEPSI

Advertise
Doesn’t Advertise

Advertise
(500, 500)
(900, 400)

Doesn’t Advertise
(400,900)
(750, 750)

a. If Coca-Cola wants to maximise profit, will it advertise? Briefly explain.
Based on the payoff matrix given above, the best outcome for Coca-Cola is to advertise in order to maximise its profit. Given that Pepsi doesn’t take the advertising move, this will give Coca-Cola the maximum profit possible which is US$900 million. However, if Pepsi did advertise, Coca-Cola will still at the advantage of having a US$ 500 million profit instead of US$ 400 million if they choose not to advertise. This is a dominant strategy where regardless of what Pepsi choose, Coca-Cola should choose to advertise to maximise their profit.

b. If Pepsi wants to maximise profit, will it advertise? Briefly explain.
Same application as mentioned above.

Based on the payoff matrix given above, the best outcome for Pepsi is to advertise in order to maximise its profit. Given that Coca-Cola doesn’t take the advertising move, this will give Pepsi the maximum profit possible which is US$900 million. However, if Coca-Cola did advertise, Pepsi will still at the advantage of having a US$ 500 million profit instead of US$ 400 million if they choose not to advertise. This is a dominant strategy where regardless of what Coca-Cola choose, Pepsi should choose to advertise to maximise their profit.

c. Is there a Nash equilibrium to this advertising game? If so, what is it? Is there a dominant strategy to this game?
Yes. The Nash equilibrium for this advertising game is US$ 500 million. The dominant strategy for both Coca-Cola and Pepsi is to advertise regardless of what the opponent choose.

d. What happens if Coca-Cola moves first and advertises?
If Coca-Cola moves first and choose to advertise, the best move for Pepsi remain the same which is to advertise as well and earn a profit of US$500 million.

Question 2
A large share of the world’s supply of diamonds comes from Russia and South Africa. Suppose that the marginal cost (assume MC=AVC=ATC for this case, i.e. a horizontal line) of mining diamonds is $1000 per diamond, and the demand for diamonds is described by the following schedule:

PRICE $
QUANTITY
8000
7000
6000
5000
4000
3000
2000
1000
6000
7000
8000
9000
10000
11000
12000
13000

a. If there were only one supplier of diamonds, what would be the price and quantity?

They should produce at a Q = 6000 and P = $8000. This gives a total profit of $42,000,000 = ($8000-$1000)*6000
b. If Russia and South Africa formed a cartel, and they split the market equally what would be the price and quantity, and profit?
If they split the Q = 6000 diamonds into 3000 diamonds each, assuming a cost of $1000 per diamond:
TC = $1000 * 3000 = $3,000,000
Q = 3000 diamonds
Price = $8000 (assumed)
Profit = ($8000-$1000)*3000 = $21,000,000 per supplier (half of before)

c. What would be South Africa’s profit if it increased its production by 1000 while Russia stuck to the cartel agreement?
If South Africa increased production by 1000, the price for a