A presentation by Dr. Robin Upton. Available for download at Attribution – NonCommercial - ShareAlike Altruistic Economics. Personal Exchange Rates 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 format 01

? 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

Exchange Rate Notation. Asymmetric Exchanges D C 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

Strict Loss Convexity of Strict Loss Region The strict loss region tends to be convex… Dollars Taka …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 Fish Less 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 Dollars Feasible Exchanges Denote this: D->L (1n i L, -25n i D) 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 Production as Resource Exchange 1 st line applies to first 5 units 2 nd 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 Chairs Wood Input Output Alternatively, if a chair buyer supplies him with wood: Chairs Wood e.g. A carpenter may have an exchange rate W ood -> C hairs. 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: E ggs, T ime & O melettes Denote the exchange: (+n i O, -n i E, -15n i T ) E ggs O melettes T ime /minutes

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 InputsOutputs Eggs Time /minutes Omelettes (-n i E, -15n i T, +n i O) E ggs T ime O melettes

Multiple In/Outputs This information can be summarised as : InputsOutputs Eggs Time /minutes YolksShellsWhites -2+1 Breaking and separating an egg takes 2 minutes, & has multiple inputs and outputs.. Sympathy as Resource Exchange (-n i E, -2n i T, +n i Y, +n i S, +n i W) Would need a 5D graph! Y olks W hites E ggs T ime S hells -2 +1

Sympathy as Resource Exchange My sympathy for my friend My friend’s sympathy for me Friend’s Resource My Resource 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 Time 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 People 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 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