# Spectrumecons 7 Week Challenge – Challenge 4: Make Me Happy

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Hi Everyone,

Welcome to the Spectrumecons 7 Week Challenge. During the months of July and August, I will be running an economics challenge series. This series will consist of 7 challenges. Some of these challenges will be familiar to my followers, while others will be completely different to any previous challenges or contests I have run.

Each challenge will reward winners with as much as 60 Hive. The value of the prize will depend on the level of participation. For each new participant, the prize will increase by 5 Hive. This will continue until 60 Hive is reached (12 participants). The first 12 participants will also receive a 50% upvote from this account. In addition to the prize money, the top few participants will be given points. These points will be used to determine the overall challenge series winner. This winner may receive as much as 80 Hive. The value of the prize will equal the sum of the number of participants across all challenges. This will continue until 80 Hive is reached.

For more information on the challenge series and the upcoming challenges, read my post Spectrumecons Seven-Week Challenge (Coming Soon).

## How to Play?

Utility is one of the fundamental concepts in economics. It is an essential determent of behaviour and driver of demand. In this challenge, participants are required to maximise the utility of one of the characters described in this question. Participants will be given a timeframe of 7 days (168 hours) to allocate to activities that yield their selected character utility. These activities are as follows:

• Working
• Sleeping
• Eating out
• Watching TV
• Painting
• Going to the pub
• Social media
• Gardening
• Exercising
• Playing sport
• Camping
• Playing video games

The character’s utility will be calculated using a formula described later in the question.

All entries must be made in the comments section of this post.

Each account is only permitted one entry.

## Objectives of the game

The objective of the game is to obtain the highest utility for your selected character using the activities described within the 7-day (168 hours) timeframe. If two or more participants obtain the exact same utility for their characters, the participant who entered first wins.

## Game Assumptions

• Characters utility is determined by a utility function, parameters and the participants choice of activities for their character.
• Characters are only allowed to spend money they have earned during the 168 hours of the game (i.e. characters do not bring money into the game).
• Participants are not allowed to spend more than their character earns in that week.
• Participants can only allocate a maximum of 60 hours of work to their character.
• Participants cannot exceed the 168 hour limit for their character but they may choose to leave some time unallocated.
• All characters require at least a minimum income stream to pay for basic expenditure (see Table 1 for costs of basic expenditure).
• Participants can select any character even if another participant has already selected that character (e.g., we could have 4 players using Velma).
• Time can only by allocated in whole hours.
• Participants must allocate at least 42 hours (6 hours a day) of sleep to their character.
• Travelling between locations and mundane daily activities not described in this challenge are not assumed to consume any time.

## What information is provided?

• Characters names and characteristics are provided.
• Utility function applied to characters is provided.
• All costs for each characters activities are provided (i.e. costs for activities and a basic expense that needs to be covered).
• Rates of diminishing marginal utility are provided.
• Exact utility values (utils) are not provided for each activity. Instead, maximum and minimum values are provided. A model will be used to determine the utility values using a uniform distribution.

## Utility Function

The utility function to be applied all characters activities is expressed in Figure 1.

## How are the results of the game determined?

A Microsoft Excel Model is used to determine the exact utility values for each activity for each character. These utility values will be applied to the formulae described in the previous section to determine the total utility for each participants’ character. Utility will be determined based on each participant’s allocation of time to his or her character. The results post will contain a video of the generation of all of the above. The winner will be announced in both the video and written post.

## Contest Prizes

The account with the winning entry may receive up to 60 Hive. The number of participants determines the value of the prize. For every entry, the prize is increased by 5 Hive until a value of 60 Hive is reached. The first 12 entries will be given upvotes. The winner of this challenge will be given 30 points, second place 20 points, and third place 10 points. These points will be tallied at the end of the challenge series to determine the overall winner.

## Let the challenge begin

Participants can choose between 5 hypothetical characters. These characters are as follows:

• Charlene
• Jonah
• Randall
• Velma
• Patty

Below are some statements from these characters so that you can get to know them better.

Activities have costs. These costs vary for different characters as they visit different places to conduct their activities. These costs can be as low as zero for activities such as sleeping and reading a book. The work activity is the only activity that can earn a character money. At some point, time needs to be dedicated to work, as money is required to at least cover a character’s basic expenses. Money is also needed for most activities. Table 1 contains the costs of activities for each character.

### Table 1: Costs of activities

Each activity yields utility to the characters. Table 2 contains the minimum and maximum utility each activity provides each character.

### Table 2: Utility obtained from activities

Activities generally produce diminishing marginal utility. It varies depending on the activity and the person. Table 3 contains the powers used to diminish utility in the function described in Figure 1.

### Entry format

For this challenge, I expect to see entries made in the following format:

Name of Character:
Number of hours working:
Number of hours sleeping:
Number of hours eating out:
Number of hours watching TV:
Number of hours reading a book:
Number of hours painting:
Number of hours going to the pub:
Number of hours on social media:
Number of hours gardening:
Number of hours exercising:
Number of hours playing sport:
Number of hours camping:
Number of hours playing video games:

Note: It is not necessary to allocate time to all activities.

### Example of entry

Name of Character: Jonah
Number of hours working: 38
Number of hours sleeping: 42
Number of hours eating out: 0
Number of hours watching TV: 32
Number of hours reading a book: 12
Number of hours painting: 0
Number of hours going to the pub: 0
Number of hours on social media: 12
Number of hours gardening: 0
Number of hours exercising: 0
Number of hours playing sport: 0
Number of hours camping: 0
Number of hours playing video games: 32

The closing date and time for this challenge is 6PM coordinated universal time (UTC) 23/07/2021. Responses after this time will not be accepted. The answers will be provided in the results post along with the video containing the generation of utility values for each activity for each character and the total utility obtained for each participant’s character.

I hope everyone has fun and enjoys this fourth challenge. I look forward to your participation in the fifth challenge.