ECON240 Final Exam Fall 2019 –

Do All Problems (note there are 110 points, you will be graded out of 100)

1) 5 pt 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) 10pt 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) 25pt 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) 40 pt 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 giving

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?)

5) 30 pt 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 |
t |
p |
n |
g |
r |
x |
Utility |

Physical |
0 |

Emotional |
0 |

Rational |
0 |

Physical |
1 |

Emotional |
1 |

Rational |
1 |

Physical |
4 |

Emotional |
4 |

Rational |
4 |

Physical |
9 |

Emotional |
9 |

Rational |
9 |

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.