Assignment:
Do All Problems
1) Wanda's will power is 25% in convincing people to vote for her. She needs 50% of the vote to win. Assuming everyone votes, in order for Wanda to win what percentage of people must already be planning on voting for her?
2) Paula wants to help plan for environmental protection for the next hundred years. Her financial expert is currently using a discount rate of 10% to determine the present value of several different projects. Relative to today, what must the environment be worth in 100 years to be counted of equal value ? Discuss how realistic this would be. What would the discount rate have to be so that so that an environment worth twice as much as today, would be counted as of equal value?
3) Take the (correct) answers from problem 4 of Homework 8/9, and answer the following:
i) Assume M = 500, Pf = 25, Pt = 100, and the person starts with no training: What is the optimal quantity of food, morsel size, number of bites, training, and savoring factor?
ii) What are the optimal amounts if the person started with 4 hours of training?
iii) Assume that training (when not used) atrophies at 2 units of year. Given the answer for i) and ii) how much would utility decline after one year of atrophy? Does this change optimal behavior?
iv) Describe and explain what might be missing from the model used.
v) Attempt to use formulas to represent your answer for iv)
4) Consider two-person households, which run on the principle each should experience the same utility from consumption. Let C1 = Person 1's consumption, and C2 = Person 2's consumption. They have $90/day to spend on consumption for the whole household.
a) Assume the individual's utility equals how much they consume. Determine how much each will consume, and what their utility levels will be
b) In this case the first person feels competitive with the second, but the second feels compersion for the first. Their respective utility functions are as follows:
U1 (C1,C2) = C1 * ( C1/C2), U2(C1,C2) = C1 * C2
Determine how much each will consume, and what their utility levels will be.
c) Let the household be as if in part b. However, person 1 can increase the second person's sense of compersion by giving a small gift that costs k. When they do utility functions become:
U1 (C1,C2) = (C1 - k) * [ (C1 - k) / (C2 + k) ] , U2(C1,C2) = (C1 - k) 2 * (C2 + k)
Determine the formulas for C1 and C2. If k = .5, determine how much each consumes and their utility levels.
d) Describe how the gift changed their relationship and shares of consumption.
e) Assume that a person must consume at least $5/day to sustain the household. Which of the above scenarios are sustainable as they are. Are there any where the gift givin becomes problematic ? What endogenous constraints would be required to make it sustainable (determine the new consumptions levels and utilities be, can the household still run by the equal utility principle?)
Imagine the following: A new social media platform "Space2Pace" has an architecture where messages are delayed by m minutes before being sent. The sender can cancel the message within those m minutes. Researchers show that the fraction of regrettable messages cancelled by users (r) based on the following formula:
r = .10 * m 1/2
the users utility was based on the formula:
U = n - x2
Where n = number of messages they write an hour ,
x = number of messages they wish they hadn't sent per hour.
When expressing physically, messages take 1 minute to write, but 50% are regrettable.
When expressing emotionally, messages take 3 minutes to write, and 20% are regrettable
When expressing rationally, messages take 11 minutes to write, and 5% are regrettable p = probability of message being regrettable, g = number of regrettable messages written Users can work (or wait) on only one message a time (hint: how are g and x related?)
i) Fill in the following table:
|
Mindset
|
m
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t
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p
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n
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g
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r
|
x
|
Utility
|
|
Physical
|
0
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|
|
|
|
|
|
|
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Emotional
|
0
|
|
|
|
|
|
|
|
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Rational
|
0
|
|
|
|
|
|
|
|
|
Physical
|
1
|
|
|
|
|
|
|
|
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Emotional
|
1
|
|
|
|
|
|
|
|
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Rational
|
1
|
|
|
|
|
|
|
|
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Physical
|
4
|
|
|
|
|
|
|
|
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Emotional
|
4
|
|
|
|
|
|
|
|
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Rational
|
4
|
|
|
|
|
|
|
|
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Physical
|
9
|
|
|
|
|
|
|
|
|
Emotional
|
9
|
|
|
|
|
|
|
|
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Rational
|
9
|
|
|
|
|
|
|
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ii) For each mindset state the optimal available delay time.
iii) For each delay time, state the optimal mindset
iv) Given this information, how would you market "Space2Pace"?
Keep in mind that m =0 implies it is the same as regular email.