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Assignment Submission and Questions

## Relations in Transitivity and Completeness

By submitting this assignment I declare that this assignment has been prepared by me and represents my own work.

If the universe is the set of all living people, are the following relations complete and/or transitive? Explain your answers.

1. ‘lives at a higher elevation than’ [4 points]
2. ‘lives on the same floor as’ [4 points]
1. If the universe is all people living in New Zealand, is the relation transitive? Is it complete? Explain your answers. [4 points]
2. If the universe is a religious cult whose members must love each another and themselves, is the relation transitive and or complete? Explain your answers. [4 points]

Describe a situation when you ignored opportunity costs when making a decision. Explain how taking opportunity costs into account when making the decision would have resulted in a better outcome (Word limit: 150 words.) [10 points]

Ocean Spirit manufactures a sailboat, called The Sprint, that scores 9 out of 10 for speed and 4 out of 10 for safety. Another firm manufactures a boat called The Tub, that scores 4 out of 10 for speed and 9 out of 10 for safety. Both the Sprint and The Tub have the same price.

Draw a graph with speed on the horizontal axis and safety on the vertical axis and mark the location of The Sprint with an and the location of The Tub with a .[2 points]

Market research suggests that a typical consumer prefers The Tub to The Sprint. On your graph, draw an indifference curve that goes through and draw an indifference curve that goes through .Make sure your indifference curves are consistent with the market research evidence. [3 points]

1. Ocean Spirit decides to use a decoy to steer customers toward The Sprint. On your graph, shade the region where the decoy should be placed. [4 points]
2. Assuming the decoy works as anticipated, use dashed lines to show what the typical consumer's indifference curves might look like after the introduction of the decoy. [3 points]

Jane and Tuiara both work for the same marketing company, Sales Plus, and have the value function  for gains and  for losses.

Graph the value function for the following values: -400, -200, -100, +100, +200, +400. Measure  on the horizontal axis and  on the vertical axis. [4 points]

Sales Plus is having a great month and announces that it will give each employee a \$200 bonus at the end of the month. If neither Jane or Tuiara were expecting a bonus prior to the announcement, in terms of value, how much do they each gain following the announcement? [2 points]

1. At the end of the month, Sales Plus’s profit is less than expected so it only gives each employee a \$100 bonus.
2. Jane incorporated the \$200 bonus into her endowment when it was announced. In terms of value, how much does she lose when the bonus is reduced to \$100? [2 points]
3. Tuiara did not incorporate the \$200 bonus into her endowment when it was announced. In terms of value, how much does she lose when the bonus is reduced to \$100? [2 points]

In terms of value, what is Jane’s net gain from the announcement of the \$200 bonus and subsequent awarding of a \$100 bonus? What is Tuiara’s net gain from the same sequence of events? [2 points]

Who is happiest at the end of the month? Explain your answer using the concept of loss aversion. [4 points]

Quickmart has a large stock of canned soup that it wishes to sell before the end of the month. To increase sales, it trials two sales strategies.  In Strategy 1, it discounts the price from \$2 to \$1.50 per can. In Strategy 2, the price is also reduced from \$2 to \$1.50  per can, and Quickmart limits the number of cans of soup that people can buy at the \$1.50 sale price to 12 per customer

According to rational choice theory, relative to Strategy 1, what impact will the maximum limit on cans per custom in Strategy 2 have on the average number of cans sold per customer? [5 points]

Suppose that each customer buys, on average, two cans of soup under Strategy 1 and five cans under Strategy 2. What heuristics-and-biases strategy is the larger number of sales per custom under Strategy 2 relative to Strategy 1 consistent with? Explain your answer. [5 points]

Suppose you have a 20-sided die. One side is labelled 1, one side is labelled 2, one side is labelled 3, and so on, all the way up to 20.

1. If you roll the die once, what is the probability that you roll a 17? [2 points]
2. If you roll the die once, what is the probability that you roll a number less than 17? [2 points]
3. If you roll the die twice, what is the probability that you roll a 17 twice? [2 points]
4. If the die is rolled twice, what is the probability of not rolling a 17? [3 points]
5. If the die is rolled twice, what is the probability of rolling at least one 17? [3 points]

Robert has been fishing at Sandpit Pier since dawn. All fish at Sandpit Pier are either small, medium, or large. Each time Robert catches a fish the probability that it is a small is 1/3, the probability that it is medium is 1/3, and the probability that it is large is 1/3. Robert has caught two fish.

What is the outcome space for the fish that Robert has caught? Use S to denote a small fish, M to denote a medium fish, and L to denote a large fish.[4 points]

1. What is the probability that Robert has caught two large fish? [2 points]
2. Suppose you know that at least one fish caught by Robert is large
3. What is the new outcome space? [2 points]
4. What is the probability that Robert has caught two large fish? [2 points]
5. Suppose you know that the first Robert caught was large.
6. What is the new outcome space? [2 points]
7. What is the probability that Robert has caught two large fish? [2 points]

Evaluate the following statement. ‘The US men’s basketball team is expected to beat all other men’s basketball teams that qualify for the Olympic Games, so if they don’t win a gold medal it will be huge surprise.’