# Individualistic Economics Formalism

[](https://hackmd.io/yDlYsfMeRy-z7TfqqveC1Q)

> "The only real power comes out of a long rifle." -- Joseph Stalin

Let's take some notes.

1. Initial conditions: Population, resources.
2. Evolutionary traits: Population, resources, trade, demand and supply, currency.

---

### **Local**

Data structures:

abstract type AbstractGovernment end

struct Resource <: AbstractGovernment
    name :: String 
end

abstract type Entity <: AbstractGovernment end

struct Person <: Entity
    resources :: Dict{Resource, Real} # resource => amount?
    bundles :: Real # Money?
end

struct Contract <: Entity
    parties :: Array{Person}
    resources :: Dict{Resource, Real} 
    # This addresses shared ownership (resource => ownership?)
    bundles :: Real
end

How to query ownership?

function ownership(bank :: Contract, money :: Resource, johnny :: Person)
    if johnny in bank.parties 
        if money in bank.resources
            bank.resources(money) # bundles saved, but how?
        else
            println("$(johnny) doesn't own this resource.")
    else
        println("$(johnny) isn't in this contract.")
    end
end

# Constraint on ownership
# sum(ownership.(drugs, characters)) == 1

---
## Demand-Supply Economics

In the following, the first person is the client, and the second person is the vendor.

$$Demand :: Resource \times Person \times Person \to \mathbb R$$

function demand(dress :: Resource, lisa :: Person, johnny :: Person)
    ???
    Profit.
end

$$Supply :: Resource \times Person \times Person \to \mathbb R$$

function supply(drugs :: Resource, chris_r :: Person, denny :: Person)
    ???
    Jail.
end

$$Price :: Resource \times Person \times Person \to \mathbb R$$

function price(drugs :: Resource, chris_r :: Person, denny :: Person)
    dem = demand(drugs, chris_r, denny)
    sup = supply(drugs, chris_r, denny)
    
    func(dem, sup)
end

func(demand, supply) = ...

Data analytics:

Datum = (Demand, Supply, Price)
data :: [Datum]

Cases: $(+/-, +/-, +/-)$

_e.g._
Trash ≈ (-, -, +)\
Vendor-Vendor

Consider `r :: Resource, p1 :: Person, p2 :: Person`, where `p1` is a client and `p2` is a vendor.

datum res p1 p2 = ( demand res p1 p2,
		     supply res p1 p2,
		     price res p1 p2 )

datum(r, p1, p2) == (+dem, +sup, +prc)
# ⇒ p1 wants to buy r and pay for what p2 is selling.

datum(r, p1, p2) == (-dem, -sup, -prc)
# ⇒ p2 wants to buy r and pay for what p1 is selling.

datum(r, p1, p2) == (-dem, +sup, 0) | (+dem, -sup, 0)
# ⇒ either both want to sell or both want to buy

datum(r, p1, p2) == (-dem, -sup, +prc)
# ⇒ p1 wants to get rid of r and p2 is willing to take it,
# for a positive price (to be paid by p1)

datum(r, p1, p2) == (+dem, +sup, -prc)
# ⇒ p1 wants to buy r, which p2 is supplying, but expects p2 to pay.

# Skew-symmetry
datum(r, p1, p2) == ( dem,  sup,  prc) ⇔ 
datum(r, p2, p1) == (-dem, -sup, -prc)

Seems like $\mathbb Z_2^3 / \mathbb Z$.

---

### **Global**

$$Demand :: Resource \to \mathbb R$$

function macro_demand(dress :: Resource)
    ¿ sum(demand(dress, lisa, johnny)
            for lisa in population, johnny in population) ?
end

$$Supply :: Resource \to \mathbb R$$

function macro_supply(drugs :: Resource)
    ¿ sum(supply(drugs, chris_r, denny)
            for chris_r in population, denny in population) ?
end

$$Price :: Resource \to \mathbb R?$$

Consider $Price :: Resource \times [Person] \to \mathbb R$?

persons :: [Person]
persons = ???
function macro_price(football) 
	couples = product(persons, persons)
end

price r persons = sum [p * min d s | (d, s, p) <- date] / 
	   	  sum [min d s | (d, s, _) <- date]
		where
			allpairs = distinctPairs persons
			date = filter (\(_, _, p) -> p > 0) $ [ datum r p1 p2 | (p1, p2) <- allpairs ]