Question

How does a firm make its decision to invest when there exists uncertainty? Explain using the maximin decision criterion and the minimax regret criterion.

Short answer

Answer: The maximin decision criterion, also known as the pessimistic approach, evaluates the worst possible outcome for each alternative and chooses the alternative with the highest minimum payoff. In other words, this criterion advises the decision-maker to select the investment option that ensures the best return in the worst-case scenario. The minimax regret criterion aims to minimize the maximum possible regret, which is the difference between an optimal decision and the chosen decision in hindsight. Regret is calculated by comparing the payoffs of each alternative under different scenarios. A firm can use the maximin decision criterion and the minimax regret criterion as tools to help make investment decisions under uncertainty. Each criterion highlights different aspects of uncertainty, allowing decision-makers to carefully consider options based on their risk tolerance and potential payoffs.

Step-by-step solution

Define uncertainty in investment decisions

Uncertainty in investment decisions refers to situations where the firm does not have complete information about the possible outcomes and their probabilities. In such cases, decision-makers must consider various scenarios, each with different possible outcomes and potential payoffs, and choose the best course of action.

Explain the maximin decision criterion

The maximin decision criterion, also known as the pessimistic approach, evaluates the worst possible outcome for each alternative and chooses the alternative with the highest minimum payoff. In other words, this criterion advises the decision-maker to select the investment option that ensures the best return in the worst-case scenario.

Explain the minimax regret criterion

The minimax regret criterion aims to minimize the maximum possible regret, which is the difference between an optimal decision and the chosen decision in hindsight. Regret is calculated by comparing the payoffs of each alternative under different scenarios. This approach provides a more balanced view as it considers not only the worst-case scenario, but also the potential regrets associated with each investment option.

Present an example with different investment alternatives

Let's say a firm is considering two investment alternatives: A and B, with uncertain payoffs in two possible scenarios (Scenario 1 and Scenario 2). | | Scenario 1 | Scenario 2 | |----------|------------|------------| | Option A | 1000 | 3000 | | Option B | 2000 | 2000 |

Apply the maximin decision criterion to the example

Using the maximin criterion, we will consider the worst outcomes for each option: - Option A: Worst outcome is a payoff of 1000 in Scenario 1. - Option B: Worst outcome is a payoff of 2000 in Scenario 2. Applying the maximin decision criterion, the firm should choose Option B, as it has the highest minimum payoff (2000).

Apply the minimax regret criterion to the example

Now, we will calculate the regret matrix by comparing the payoffs under each scenario: | | Scenario 1 | Scenario 2 | |----------|------------|------------| | Option A | 2000 - 1000 | 3000 - 3000 | | Option B | 2000 - 2000 | 3000 - 2000 | The regret matrix is: | | Scenario 1 | Scenario 2 | |----------|------------|------------| | Option A | 1000 | 0 | | Option B | 0 | 1000 | Applying the minimax regret criterion: - Option A: Maximum regret is 1000 in Scenario 1. - Option B: Maximum regret is 1000 in Scenario 2. In this case, both options have equal maximum regrets, and the firm can choose either option based on other non-quantitative factors or preferences. However, if one option exhibited a lower maximum regret, that option would be preferred according to the minimax regret criterion. In conclusion, the firm can use the maximin decision criterion and the minimax regret criterion as tools to help make investment decisions under uncertainty. Each criterion highlights different aspects of uncertainty, allowing decision-makers to carefully consider options based on their risk tolerance and potential payoffs.

Key concepts

Maximin Decision Criterion

Making sensible investment decisions when the future is a blur requires a robust strategy. The maximin decision criterion is like a guiding light for investors who'd rather play it safe. Imagine you're navigating through a dense fog, with various paths leading to different fortunes. The maximin criterion says, 'Choose the path with the least amount of risk; where even the worst outcome is something you can live with.' In practical terms, investors look at various investment options, investigate the gloomiest possible scenario for each, and then go for the one with the least dismal 'worst-case' financial return.

For instance, let's say you have to choose between investing in a start-up or buying government bonds. With the maximin approach, you'd compare the least favorable outcomes: the start-up could fail and yield nothing, while the worst for government bonds would be a small but guaranteed return. Bearing a cautious stance, the maximin rule would suggest going for the bonds, despite the higher potential upside of the start-up.

Minimax Regret Criterion

The minimax regret criterion, on the other hand, is about hindsight – that pesky 'shoulda, coulda, woulda' that haunts poor decisions. Instead of merely bracing for the worst as with maximin, this technique involves sizing up decisions based on what you might regret the most later on. In the investment world, it's like organizing a 'damage control' plan for your future self's potential facepalms. You line up your options side by side, imagine how each scenario could play out, and then measure each one's 'if only' quotient – essentially, the remorse you'd feel if you didn't choose the best possible outcome.

Using the previous example, if government bonds return consistently but modestly, while the start-up is a coin-toss between tanking and booming, the minimax regret criterion calculates the sorrow of missing out on that boom. It encourages a balanced approach, one that weighs the bliss of potential high returns against the agony of steep losses.

Uncertainty in Economics

Peering into the unknown can be daunting in the world of economics too – that's 'uncertainty' for you, a pesky cloud over every investor's head. It's like a meteor shower of 'what ifs' raining down on your parade of profits and plans. The uncertainty in economics is about not knowing the odds or the outcomes. It's dealing with a future that's as unpredictable as a plot twist in a mystery novel.

Economists and investors alike face a common challenge: decisions must be made without knowing the full script. Sure, you have historical data, market trends, and expert opinions, yet no crystal ball to reveal if the economy will soar like an eagle or nosedive like a faulty drone. Uncertainty forces investors to ponder 'What's the best move when the future's a jigsaw puzzle with missing pieces?' It’s the driving force behind the need for criteria like maximin and minimax regret, helping to illuminate the path even when the economic weather forecast is foggy at best.