# Maximizing Income in Evony: A Mathematical Analysis

• Mentallic
In summary, the problem is that the player wants to figure out an ideal tax rate in order to achieve maximum income. If the player takes: \frac{dI}{dT}=2.10^{-4}PT=0, then T=0, and they are doing something wrong.
Mentallic
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## Homework Statement

I derived this problem from back when I used to play Evony. I do not endorse this game whatsoever, and I think it has made enough of a mockery for itself with its plentiful supply of false and explicit advertisements such that I don't need to add to its shame.

Anyway, my problem was that I wanted to figure out a means to achieving maximum income through the game's population-tax policy. This is how it works:

You build houses to make room for your population. The more houses, the higher your maximum population potential (denoted P) will be. The actual population you can have will be between 0 and P. This population is dependant on the tax rate (denoted T), and it follows a simple inversely proportional function. With 100% T, you will have 0 population. With 0% T you will have P population. Of course, in both these cases you will have a 0 income so they are the extreme minimums. At, say, 50% T, you will have P/2 population so you will then make P/4 gold/hour (each population gives 1 gold/hour when taxed at 100%, so 2 people give 1 gold/hour at 50% T).

## The Attempt at a Solution

The people, x, is defined by: $$x=P\left(\frac{T}{100}\right)$$ where $0\leq T\leq 100$

The income, I, is defined by: $$I=x\left(\frac{T}{100}\right)$$

Therefore by combining both equations we get: $$I=\frac{PT^2}{100^2}$$

Now, P is a constant since the max pop is defined and not going to change (for this calculation at least) and I want to find the ideal tax rate, T, in order to get maximum income.

If I take: $$\frac{dI}{dT}=2.10^{-4}PT=0$$
I get $T=0$ since $P\neq 0$

So what am I doing wrong? Since I already established that the extremities of the tax rate, $T=0,100$ result in 0 income.

And if you don't understand or need clarification in something, don't hesitate to ask
Thanks for helping me satisfy my curiosity.

Actually I just noticed that my derived equation is wrong. $$I\neq \frac{PT^2}{100^2}$$ since for $T=100$ the income, I, should be 0 but from this equation it would be P.
I guess I need help setting up the right equation.

Never mind, I solved it.

## What is Evony and why is it relevant to maximizing income?

Evony is an online strategy game where players build and manage their own virtual city. Maximizing income is important in Evony because it allows players to grow their city and army faster, making them more competitive in the game.

## How does income in Evony work?

Income in Evony is generated through resources such as food, wood, stone, and iron. These resources are produced by buildings in the city and can also be obtained through attacking other players or completing quests.

## What is the best strategy for maximizing income in Evony?

The best strategy for maximizing income in Evony is to focus on building resource-producing buildings, upgrading them, and completing quests for additional resources. It is also important to maintain a balance between the different types of resources.

## How does mathematics play a role in maximizing income in Evony?

Mathematics is crucial in maximizing income in Evony as it helps players calculate the most efficient use of resources and buildings. It also helps players determine the most profitable quests to complete and the best strategy for attacking other players.

## Are there any tips or tricks for maximizing income in Evony?

Yes, there are various tips and tricks for maximizing income in Evony. These include focusing on resource-producing buildings, upgrading them strategically, completing quests, and joining alliances for resource trading. It is also important to regularly check and adjust resource production based on city population and needs.

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