Question

In an ongoing price war between Burger Haven (locally owned) and MacArches (a chain), both restaurant managers plan to change the price of a hamburger by 10e. If they both raise their prices, there will be no change in their market shares, but if they both lower their prices, the chain's netional advertising will ensure that MacArches gains 3% of the market. Again because of advertising, if Burger Haven lowers their price and MacArches raises their price, Burger Haven will gain only 2 % of the market, but if Burger Haven raises their price and MacArches lowers their price, MacArches will gain 7 % of the market. Use this information to decide what the managers should do MacArches L CC x % % Burger Haven % What does i represent? OL represents lowering the price by 10e OL represents raising the price by 10t. What does R represent?h R represents lowering the price by 10e. R represents raising the price by 10e. The saddle point is the in row and column What should the managers do Both restaurants should lower the price. O Burger Haven should lower its prices, while MacArches raises its prices. O MacArches should lower its prices, while Burger Haven raises its prices. Both restaurants should raise the price.

Answer 1

Lets construct a payoff matrix :

There are two players(restaurent managers) "MA" and "BH"

The choices for the manager are R(raising prices) and L(lowering prices)

Hence there are two choices for manager "BH" and for "MA"

So,the number of different situations to consider will be = 2.2 = 4

Now list the choices for the manager "MA" as rows and manager "BH" as columns

If both raise their prices, there will be no change in their market shares,so they will have neither an advantage

MacArches R L L Burger heaven R 0

if they both lower their prices, the chain's netional advertising will ensure that MacArches gains 3% of the market

MacArches R L L Burger heaven 3 R 0

if Burger Haven lowers their price and MacArches raises their price, Burger Haven will gain only 2 % of the market

MacArches R L L Burger heaven 3 2 R 0

if Burger Haven raises their price and MacArches lowers their price, MacArches will gain 7 % of the market.

MacArches R L L Burger heaven 3 2 7 R 0

Hence,the payoff matrix is:

  

MacArches R L L Burger heaven 3 2 7 R 0

L represents lowering the price by 10c

R represents raising the price by 10c

Saddle point:

Select the smallest value in each row

select the largest value in each column

The point which hovers both is saddle point

So saddle point = 2

As the saddle point is 2 in the row 1 and column 2,Burger haven should lower its prices and Masarches should raise its price

option B