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What is the difference in present value between an investment of $ 12,764 per year for 50 years and an investment of $ 12,784 per year in perpetuity at 12% interest per year
Question: What is the difference in present value between an investment of $ 12,764 per year for 50 years and an investment of $ 12,784 per year in perpetuity at 12% interest per year
Answer:
Here,
Investment amount = $ 12,764
Interest rate = 12%
So for 50 years
Present Value = 12.764 * (1- (1 / (1 + .12) ^ (50)) / .12 = 105,998.6 USD
So for an infinite period,
Present Value = 12764 / .12 = $ 106,366.7
So, difference = $ 106,366.7 - $ 105,998.6 = $ 368.048
1. Demonstrate this using a game in the normal way.
2. Does any firm have a rigidly dominant strategy? If so, what (are) these strategies? Explain your answer.
3. What is the strategy that each company will adopt? Explain your answer.
4. Does this game have a nash balance? Explain your answer
5. Is collusion possible in this game? Explain your answer.
Answer 1. The normal game format can be illustrated below:
Clampett wide well tight Clampett well
Wide TEXplor well (1 m, 1 m) (16 m, -1 m)
Narrow well TEXplor (-1 m, 16 m) (14 m, 14 m)
In the normal figure above, each cell represents the payments/profits each company can generate. The strategies in this game consist of choosing to sink a large pot or a narrow bowl.
Answer 2. Think about TEXplor first. If Clampett chooses to sink a large bowl, TEXplor gets a higher reward for sinking a large bowl (1> -1). Likewise, if Clampett chooses to sink a narrow pot, TEXplor gets a higher reward for sinking a large bowl. So, no matter what Clampett chooses to do, TEXplor drowns out a great deal, which makes it his dominant strategy.
Next, look at Clampett. Following the same argument above, Clampett also always chooses to sink a wide well, regardless of what TEXplor does. So sinking a great deal is your overriding strategy.
Answer 3. Both companies adopt a strategy of drilling a large well, as it achieves higher profitability regardless of the strategy adopted by the other company.
Answer 4. Yes, this game contains a nash equilibrium as both companies follow their dominant strategies. So, (very broad, very broad) is the Nash equilibrium for this game, which results in a payment of 1 million GHC per company.
Answer 5. There could be collusion in this game because it would generate a higher reward for both companies. If both companies chose to collide and flood the narrow wells, they would each receive a reward of 14 million GHC, which is much higher than the equilibrium reward of 1 million GHC. Therefore, if there is a high probability of future interaction between the two companies, collusion can be preserved.
If you like my article, then you can also watch my previous articles on other web pages.
Here,
Investment amount = $ 12,764
Interest rate = 12%
So for 50 years
Present Value = 12.764 * (1- (1 / (1 + .12) ^ (50)) / .12 = 105,998.6 USD
So for an infinite period,
Present Value = 12764 / .12 = $ 106,366.7
So, difference = $ 106,366.7 - $ 105,998.6 = $ 368.048
1. Demonstrate this using a game in the normal way.
2. Does any firm have a rigidly dominant strategy? If so, what (are) these strategies? Explain your answer.
3. What is the strategy that each company will adopt? Explain your answer.
4. Does this game have a nash balance? Explain your answer
5. Is collusion possible in this game? Explain your answer.
Answer 1. The normal game format can be illustrated below:
Clampett wide well tight Clampett well
Wide TEXplor well (1 m, 1 m) (16 m, -1 m)
Narrow well TEXplor (-1 m, 16 m) (14 m, 14 m)
In the normal figure above, each cell represents the payments/profits each company can generate. The strategies in this game consist of choosing to sink a large pot or a narrow bowl.
Answer 2. Think about TEXplor first. If Clampett chooses to sink a large bowl, TEXplor gets a higher reward for sinking a large bowl (1> -1). Likewise, if Clampett chooses to sink a narrow pot, TEXplor gets a higher reward for sinking a large bowl. So, no matter what Clampett chooses to do, TEXplor drowns out a great deal, which makes it his dominant strategy.
Next, look at Clampett. Following the same argument above, Clampett also always chooses to sink a wide well, regardless of what TEXplor does. So sinking a great deal is your overriding strategy.
Answer 3. Both companies adopt a strategy of drilling a large well, as it achieves higher profitability regardless of the strategy adopted by the other company.
Answer 4. Yes, this game contains a nash equilibrium as both companies follow their dominant strategies. So, (very broad, very broad) is the Nash equilibrium for this game, which results in a payment of 1 million GHC per company.
Answer 5. There could be collusion in this game because it would generate a higher reward for both companies. If both companies chose to collide and flood the narrow wells, they would each receive a reward of 14 million GHC, which is much higher than the equilibrium reward of 1 million GHC. Therefore, if there is a high probability of future interaction between the two companies, collusion can be preserved.
If you like my article, then you can also watch my previous articles on other web pages.
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