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Expected Value and Uncertainty

I need some help in these 4 questions of expected value and uncertainty:
1. Global Expansion/Making Decisions with Uncertainty:
You're the manager of global opportunities for a U.S. manufacturer, who is considering expanding sales into Europe. Your market research has identified three potential market opportunities: England, France, and Germany. If you enter the English market, you have a 0.5 chance of a big success (selling 100,000 units at a per-unit profit of $8), a 0.3 chance of moderate success (selling 60,000 units at a per-unit profit of $6), and a 0.2 chance of failure (selling nothing). If you enter the French market, you have a 0.4 chance of big success (selling 120,000 units at a per-unit profit of $9), a 0.4 chance of moderate success (selling 50,000 units at a per-unit profit of $6), and a 0.2 chance of failure (selling nothing). If you enter the German market, you have a 0.2 chance of huge success (selling 150,000 units at a per-unit profit of $10), a 0.5 chance of moderate success (selling 70,000 units at a per-unit profit of $6), and a 0.3 chance of failure (selling nothing). If you can enter only one market, and the cost of entering market (regardless of which market you select) is $250,000, should you enter one of the European markets? If so, which one? If you enter, what is your expected profit?

2. Game Show Uncertainty:
In the final round of a TV game show, contestants have a chance to increase their current winnings of 1 million dollars to 10 million dollars. If they are wrong, their prize is decreased to $100,000. To win, they have to guess the exact percentage that answered a question a certain way, and the range has already been narrowed to an 11-point range. So, for example, the contestant knows that the correct answer is between 20% and 30% and he or she must guess the correct percentage in the range. So, let's say you have no idea what the right answer is and have to make a random guess. Should you play?

3. The Problem of Adverse Selection/Bicycle Insurance and Information Asymmetry:
You sell bicycle theft insurance. If bicycle owners do not know whether they are high- or low-risk consumers, is there an adverse selection problem?

4. The Problem of Moral Hazard/Locator Beacons for Lost Hikers:
Lightweight personal locator beacons are now available to hikers that make it easier for the Forest Service's rescue teams to locate those lost or in trouble in the wilderness. How will this affect the cost that the Forest Service incurs?

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Solution:
1. Expected Profit for Each Market needs to be calculated.

English Market:
0.5*(100,000*8) + 0.3*(60,000*6) + 0.2*(0) - 250,000 = 400,000 + 108,000 + 0 - 250,000 = $258,000

French Market:
0.4*(120,000*9) + 0.4*(50,000*6) + 0.2*(0) - 250,000 = 432,000 + 120,000 + 0 - 250,000 = $302,000

German Market:
0.2*(150,000*10) + 0.5*(70,000*6) + 0.3*(0) - 250,000 = 300,000 + 210,000 + 0 - 250,000 = $260,000

As French Market has the highest expected profit, it should be selected for entering with expected profit of $302,000.

2. The ...

Solution Summary

This solution explains the concept of moral hazard, adverse selection, risk reference and also explains the decision process based on expected value calculation in a step-by-step manner.

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