A presentation by Dr. Robin Upton. Available for download at www.altruists.org/ae6Attribution – NonCommercial - ShareAlike

Altruistic Economics

. Personal Exchange Rates

www.altruists.org

AE6: Exchange Rates v1.0

Recommended Pre-requisite: AE2 or AE5

Introduction to Exchange Rates

. ‘Goods are Good’

• Exchange rates are personal, not system-wide

• They are statements of preference/possibility . that inter-relate different resources

• People have different exchange rates

• They are all published in a standard format01 0101

? Uncertain outcomes

?

?

Wanted outcomes

Unwanted outcomes

X

Y

Less X

More Y

More X

Less Y

More X

More Y

Less X

Less Y

‘Goods are Good’

. Traditional (Linear) Exchange Rate

For clarity, axes in this presentation are

normalized so that moves upwards or rightwards

(typically increases) correspond to desired

outcomes.

More D

Less C

More C

Less D

More D

More C

Less D

Less C

Traditional (Linear) Exchange Rate

. Exchange Rate Notation

• Dollars and Cents can be exchanged at a Rate of 1:100

Strict loss

C:D Equivalence

Dollars

Cents

1

-1

100-100

Exchange Rate Notation

. Asymmetric Exchanges

D

C

1

-1

100-100

C->D (nD, -100nC)

Denote the rate:

D->C (100nC, -nD)

The symmetric case is important, so let’s give it a shorthand form:

D=100C

n means any amount can be exchanged

• There are actually 2 possible conversions here:

1. Swapping Dollars for Cents:

2. Swapping Cents for Dollars:

Asymmetric Exchanges

. Convexity of Strict Loss Region

• We record these 2 rates separately, in case they are different.

e.g. 1 Dollar buys 50 Taka, but 60 Taka buys 1 Dollar

D->T (50nT, -nD)

Less D, More T

Denote this:

More D, Less T

T->D (nD, -60nT)Taka

Dollars

50

-1

1

50

Strict Loss

Convexity of Strict Loss Region

The strict loss region tends to be convex…

Dollars

Taka-50 50

-1

1

…because repeated exchanges usually mean a strict loss. .

. Limited Exchanges

Limited Exchanges• Fish may be swapped for rice or vice versa, but only up to 2 units

More Rice, Less FishLess Rice, More Fish

Notional Exchange Rate

Rice

Fish

R->F (2F, -2R)F->R (2R, -2F)

Denote this:

. Whole Number Exchanges

Whole Number Exchanges• Laptops can be bought for $25 each, in whole numbers only

Notional Exchange Rate

Laptops

Dollars1

23

-25-50-75

Feasible Exchanges

Denote this:

D->L (1niL, -25niD)

i stands for ‘integer’

. Non-linear Exchanges

Non-Linear Exchanges

F->R Exchange Rate

• Up to 5 units of Fish may be swapped for an equal amount of Rice, but after that the exchange rate changes

Denote this:

F->R 5R, -5F nR, -2nF

Rice

Fish

5

-5

-

. Production as Resource Exchange

1st line applies to first 5 units2nd applies to all subsequent units

• The format below is a slight revision of that used for

sympathy in AE5 & earlier

Production as Resource Exchange• Exchange rates can be used to express capability to produce goods

ChairsWoodInput Output

Alternatively, if a chair buyer supplies him with wood:

Chairs

Wood

e.g. A carpenter may have an exchange rate Wood -> Chairs

. Multi-Dimensional Exchange Rates

Multi-Dimensional Exchange Rates

. Presenting 3-D Exchange Rates

• 1 Egg and 15 Minutes can be exchanged for 1 Omelette!

To graph this, we need 3 dimensions:

Eggs, Time & Omelettes

Denote the exchange:(+niO, -niE, -15niT )

Eggs

Omelettes

Time /minutes

15

1

-1

-1

-15

1

Presenting 3-D Exchange Rates

. Multiple In-/Out-puts

3-D graphs are unsatisfactory, so we can display this transformation as:

• A transformation with 2 inputs and 1 output needs a 2+1 = 3-Dimensional exchange rate

Inputs Outputs

Eggs Time /minutes Omelettes

-1 -15 +1

(-niE, -15niT, +niO)

Eggs

Time

Omelettes-1

-15

+1

Multiple In/Outputs

This information can be summarised as :

Inputs Outputs

Eggs Time /minutes Yolks Shells Whites

-1 -2 +1 +1 +1

• Breaking and separating an egg takes 2 minutes, & has multiple inputs and outputs.

. Sympathy as Resource Exchange

(-niE, -2niT, +niY, +niS, +niW)Would need a 5D graph!

Yolks

Whites

Eggs

Time

Shells

-1

-2

+1

+1

+1

Sympathy as Resource Exchange

My sympathy for my friend

My friend’s sympathy for me

Friend’s Resource

My Resource

1

23

-1-2-3-1

-2

1

• A crucial application of exchange rates is expressing preference relationships between identical resources of different people.

. Capability as Resource Exchange

• Willingness to give up ones own resources to increase someone

else’s is sympathy [AE1].

Capability as Resource Exchange• Exchange rates can be used to express capability to carry out services

Computer Fixing Time

My Time1

23

-1-2-3 1

• In AE5 & earlier, this was assumed linear

People express capabilities by

stating an ability to swap their time for a specialist skill.

. Requests as Resource Exchange

Requests as Resource Exchange

. Exchange Rates - Summary

• Exchange rates can be used to express requests for services

• In AE5 & earlier, this was assumed linear

Computer Fixing Time

My Time-1

1

-1 1 2 3

-2

-3

4People express

requests by stating an ability to swap a specialist skill for

their time.

Summary of Exchange Rates• Personal exchange rates are a flexible tool to express

complicated relationships between commodities

Recommended Further Reading: AE7: Multiple Currencies

http://www.altruists.org/ae7.

• Requests for/ability to provide particular goods & services can be easily expressed by publishing exchange

rates

• Sympathy statements can also be regarded as publication of personal exchange rates