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What are the present value difference between an investment of $12,764 per year for 50 years and an investment of $12,784 per year in perpetuity at an interest rate of 12% per year?
What are the present value difference between an investment of $12,764 per year for 50 years and an investment of $12,784 per year in perpetuity at an interest rate of 12% per year?
Investment amount = $12,764
Interest rate = 12%
So for 50 years
Present Value = 12764 * (1- (1 / (1 + .12) ^ (50)) / .12 = 105998.6 USD
So for an infinite period,
Present Value = 12764 / .12 = $106,366.7
So, Difference = $106,366.7 - $105,998.6 = $368.048
1. Illustrate this using a normal form game.
2. Does either company have a dominant strategy? If yes, what are these strategies? Explain your answer.
3. What strategy will each firm adopt? Explain your answer.
4. Does this game have a Nash equilibrium? Explain your answer
5. Is collusion possible in this game? Explain your answer.
Answer 1. The normal form of the game can be illustrated below:
Clampett wide well Clampett narrow well
TEXplore wide well (1 M, 1 M) (16 M, -1 M)
TEXplor narrow well (-1 M, 16 M) (14 M, 14 M)
In the normal form above, each cell represents the payoffs/profits that can be earned by each firm. The strategies in this game consist of the choice of sinking a wide well or a narrow well.
Answer 2. Consider TEXplor first. If Clampett chooses to sink a wide well, TEXplor earns a higher payoff by sinking a wide well ( 1> -1). Similarly, if Clampett Chooses to sink a narrow well, TEXplor earns a higher payoff by sinking a wide well. Thus, irrespective of what Clampett chooses to do, TEXplor sinks a wide well, making it its dominant strategy.
Next, consider Clampett. Following the same argument as above, Clampett also always chooses to sink a wide well, irrespective of what TEXplor does. Thus, sinking a wide well is its dominant strategy.
Answer 3. Both firms will adopt the strategy of sinking a wide well since it yields a higher payoff irrespective of the strategy adopted by the other firm.
Answer 4. Yes, this game has a Nash equilibrium where both firms follow their dominant strategies, Thus, (wide well, wide well) is the Nash equilibrium of this game, yielding a payoff of GHC 1 million for each of the firms.
Answer 5. Collusion is possible in this game since it will bring a larger payoff to both the firms. If both the firms choose to collide and sink narrow wells, both Will get a payoff of GHC 14 Million, which is much larger than the equilibrium payoff of GHC 1 Million. Thus, if there's a high probability of future interaction Between the two firms, collusion can be sustained.
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