The proprietor of Belvedere's is faced with the problem of deciding whether to expand his restaurant facilities now or to wait until some future date to do so. If he expands the facilities now and the economy experiences a period of growth during the coming year, he will make a net profit of $369,000; if he expands now and a period of zero growth follows, then he will make a net profit of $90,000; and if he expands now and an economic recession follows, he will suffer a net loss of $100,000. If he does not expand the restaurant now and the economy experiences a period of growth during the coming year, he will make a net profit of $257,000; if he does not expand now and a period of zero growth follows, he will make a net profit of $190,000. Finally, if he does not expand now and an economic recession follows, he will make a net profit of $160,000.
Represent this information in the form of a payoff matrix.

Hint: The row player is the proprietor of restaurant and the column player is the economy.

Question

The proprietor of Belvedere's is faced with the problem of deciding whether to expand his restaurant facilities now or to wait until some future date to do so. If he expands the facilities now and the economy experiences a period of growth during the coming year, he will make a net profit of $369,000; if he expands now and a period of zero growth follows, then he will make a net profit of $90,000; and if he expands now and an economic recession follows, he will suffer a net loss of $100,000. If he does not expand the restaurant now and the economy experiences a period of growth during the coming year, he will make a net profit of $257,000; if he does not expand now and a period of zero growth follows, he will make a net profit of $190,000. Finally, if he does not expand now and an economic recession follows, he will make a net profit of $160,000. ​
Represent this information in the form of a payoff matrix.
​
Hint: The row player is the proprietor of restaurant and the column player is the economy.
​

Quizplus · Accepted Answer

The payoff matrix can be represented as follows:

|             | Growth   | Zero Growth | Recession |
|-------------|----------|-------------|-----------|
| Expand      | 369,000  | 90,000      | -100,000  |
| Do not Expand | 257,000  | 190,000     | 160,000   |

To determine the best choice, we can use the maximin criterion. The maximin is the maximum of the minimum outcomes for each decision.

For the row player (proprietor of Belvedere's), the minimum outcomes for expansion are -100,000, 90,000, and 369,000 for recession, zero growth, and growth, respectively. The maximum of these minimum outcomes is 90,000.

For the row player if he does not expand, the minimum outcomes are 160,000, 190,000, and 257,000 for recession, zero growth, and growth, respectively. The maximum of these minimum outcomes is 190,000.

Comparing the two maximum of minimum outcomes, the proprietor should choose to not expand now and wait for a better opportunity in the future. Therefore, the best choice is D.

The Proprietor of Belvedere's Is Faced with the Problem of Deciding