View source for Emergence of Money and Liquidity

== Project objective==
The best way to think about money is not to think about money.  Do not want to assume what we are trying to explain (i.e., we do not want to code "money" into the model!).  With these caveats in mind, the objective of this project is to build an ABM demonstrating the emergence of money that builds off of the previous models of [http://en.wikipedia.org/wiki/Nobuhiro_Kiyotaki Nobu Kiyotaki], [http://en.wikipedia.org/wiki/John_Hardman_Moore John Moore], and [http://en.wikipedia.org/wiki/Randall_Wright Randall Wright].  All of these models take a broad view of money: "money" is any asset which is widely accepted as a medium of exchange (i.e., is highly "liquid"). 

== Motivating example == 
The following is taken from Kiyotaki and Moore (2001). Suppose I need to get my teeth cleaned.  To get my teeth cleaned, I can just go to a dentist who will clean my teeth in exchange for payment. Assume that both the dentist and I have bank accounts, and for simplicity assume that both account balances are initially zero.  When I pay for my teeth cleaning using a debit card, funds are immediately transferred from my account to the dentist's.  Now my account has a negative balance (i.e., I have issued an IOU to the bank); and the dentist's account has a positive balance (i.e., the bank has issued an IOU to the dentist).  

* Question: Instead of using my debit card, why didn't I simply issue one of my own IOUs to the dentist as payment?  In other words, why does the bank need to intermediate the transaction between myself and the dentist?  Simple answer is that the dentist doesn't trust me enough to repay the debt.  In other words my ability to credibly commit to repaying the debt is imperfect. Let 0 &lt; &theta; &le; 1 be a measure of my ability to commit with a particular agent (i.e., &theta; is a measure of ''bilateral commitment'').  There is a more subtle answer.  The dentist may trust me to repay (particularly as she could threaten to do something nasty to my teeth the next time I needed them cleaned), but perhaps no one ''else'' trusts me (i.e., the dentist is unable to use my IOU for her own purchases).  Let 0 &lt; &phi; &le; 1 be a measure of my ability to commit with all other agents (i.e., &phi; is a measure of ''multilateral commitment'').

Note that if the dentist has the ability to perfectly commit with a particular agent (i.e., the dentist's &theta;=1), then my general lack of trustworthiness (i.e., the fact that both my &theta; and &phi; < 1) wouldn't matter.  The dentist would be willing to accept my less than perfect IOU because she can simply issue her own IOUs anytime she wants to purchase something.  

Suppose that no one else trusts the dentist either. In this case, the dentist can not issue her own IOUs (nor can she endorse my IOUs).  Thus the only way the dentist can make purchases before the maturity date of my IOU is if she is paid with a bank IOU (and also, in return, the bank holds my IOU).  The dentist gets more benefit from being paid with a bank IOU compared with my IOU.  In the language of economics: my debt and bank debt are imperfect substitutes.    

The bank’s IOU is used by me and the dentist to lubricate our transaction.  Why? Because the bank’s IOU can freely circulate around the economy. Like blood, it is liquid. In fact, the bank's IOU is functionally equivalent to cash. But, unlike cash, it doesn’t come from outside the private system, it comes from inside. For this reason, bank debt is called "inside money". Quantitatively, "inside" money dwarfs "outside" (i.e., cash/coin or currency) money by more than almost 2 orders of magnitude.

The degree of trust between agents in an economy is hugely important in determining the level of investment activity that a given economy can sustain.  Unfortunately, trust is a fundamentally scarce resource in economic systems.  Why? To borrow from Arthur Eddington (and John Moore), the reason trust is fundamentally scarce resource in economics is because "[http://en.wikipedia.org/wiki/Arrow_of_time time's arrow] cannot fly backwards."  Investment is not time-reversible (if it were, then trust would be irrelevant).  

In broad terms, the degree of bilateral commitment in an economy places a bound on the entire stock of private paper, whereas the degree of multilateral
commitment determines how much of this paper can circulate.

== What is money? ==
Wikipedia's entry for [http://en.wikipedia.org/wiki/Money money] is a pretty good place to start.

'''Distinction between "inside" and "outside" money:'''  When most people think of money, they have in mind cash/coin (i.e., currency) issued by the government.  Currency is called "outside" money precisely because it is issued by the government which is by definition "outside" the private economic system.  However, there can be many other forms of money that are created within the private economic system, such forms of money are called "inside" money.  Richard Lagos from the Minneapolis FED has a nice short [http://www.minneapolisfed.org/research/sr/sr374.pdf paper] on the distinction between the two.

'''==First paper money in the world== by Jianfeng Xu'''
The first paper money “jiaozi” appeared in Sichuan province of China at 10th century. Facing the problem of limited supply of copper to make coins, varies of paper certificates issued by private businesses were circulating in the market. Local official regulated these “IOU” by limiting the issuers to 16 richest families and setting a 2 year limit to cash out or renew these “jiaozi”. (This is inside money). Finally government could not resist stepping in and printing state-issued paper money. Inflation happened when government printed money to cover over spending. Therefore, paper money lose credit and never been widely used until early 1900s. (This is outside money).

== What does money do? ==
I think of a market economy as being a (quite sophisticated) de-centralized optimization algorithm that maximizes the size of the "economic pie" (think output, GDP, etc) subject to resource constraints.  Because agents in the economy have only local information about their economic environment, in order for the "algorithm" to work there needs to exist some mechanism for passing information about the relative scarcity of resources between agents.  In market economies, prices are the mechanism for transmitting such information.  In a way, prices are like the economy's central nervous system in that prices signal the needs of various parts of the economic body.  Flow of money and private securities through the economy is analogous to the flow of blood: "money" dispatches resources to different parts of the economic body in response to price signals.   


== The model ==  
''' Consumption rule:''' Turtles are assumed to consume a fixed fraction, 1 - &beta; (where 0 &lt; &beta; &lt; 1 is a turtle's discount factor), of their start of period net-worth each period.

'''Movement rule:''' Movement is sequential across agents (the order of movement is randomized each period in order to eliminate any type of "first mover" advantage).  If the entrepreneur sees available investment project(s) within his field of vision, he will move to the patch containing the project with the highest amount of resources (i.e., collateral).  If there are no available investment projects within an entrepreneur's neighborhood, entrepreneurs are assumed to move to the un-occupied patch within their neighborhood that contains the maximal amount of resources.     

''' Investment opportunities:''' Investment projects are created on a given patch in period t=0 with some exogenous probability, &pi (investment opportunities are what generate potential demand for borrowing).  Investment projects are assumed to require an entrepreneur in order to become active.    Basic idea: from time to time, entrepreneurs will encounter an investment opportunity  (i.e., they will move to a patch that houses an investment opportunity); investment projects require some fixed number of periods, say T, to complete and once started the entrepreneur managing the project is required to remain fixed on his patch (implicitly we assume that the project cannot continue without the entrepreneur's specific supervision). 

'''Production Technology:'''  Each agent is assumed to have access to an identical constant returns to scale production technology.  Specifically model assumes that output is a function of the amount of grain invested: 

y<sub>t + T</sub> = (x<sub>t</sub> / a(1 - &lambda;))<sup>1 - &lambda;</sup> where 0 < &lamdba; < 1

Note that output takes T periods to produce!  Useful to characterize the cost of producing a level of output y<sub>t + T</sub>:

G(y) = x<sub>t</sub> =  a(1 - &lambda;)y<sub>t + T</sub><sup>1 / (1 - &lambda;)</sup>  


'''Finance:'''  The scale of the project (i.e., the amount of ''y'' produced) will depend on the amount of capital available at the time the project is started, and the amount of capital depends on the amount of finance that the turtle can raise.  A turtle with an investment opportunity has several options for finance:
* Self-finance: the turtle may invest his own funds in the project.  If turtle has been a lender in the past, he may have assets (i.e., IOUs from other turtles) that he could sell.  Additionally, turtle will also have savings (i.e., grain that has been collected but not consumed).
* Borrowed funds: the turtle may borrow funds from any other turtle (within his vision!) that does not have an investment project.  Borrowing is subject to a collateral constraint which depends on the turtle's ability to commit bilaterally (i.e., turtle's &theta;) and on the inherent quality of the patch on which the project is being undertaken.  Specifically, suppose that the patch has a ''max-grain-here'' =''G,'' then the turtle can borrow at most ''&theta;G''.  

When deciding whether or not to borrow, the turtle ''i'' compares his marginal benefit from borrowing an additional unit with the marginal cost of borrowing from turtle ''j'' and will want to borrow iff:

&beta;<sub>i</sub><sup>T</sup>(1 - &theta;<sub>i</sub>)a &ge; R<sub>j</sub>    

The lending turtle ''j'' meanwhile will only be willing to lend iff the marginal benefit from lending exceeds his opportunity cost:

&beta;<sub>j</sub><sup>T</sup>&theta;<sub>i</sub>R<sub>j</sub> &ge; max{1, R<sub>k</sub>}

Note that the lender's opportunity cost allows for the possibility that he may have other turtles wishing to borrow funds from him!  These two inequalities will pin down an interval in which the interest rate must fall if a bi-lateral agreement can be struck between turtle's ''i'' and ''j.''  Also, although a turtle who is managing a project must remained fixed on his patch, a lending turtle can move freely.

== Background reading ==
* [http://www.princeton.edu/~kiyotaki/papers/Evilistherootofallmoney.pdf Evil is the Root of all Money]: 2001 Clarendon Lecture given on money emerging as a solution to a bi-lateral and multi-lateral contracting problem. Origins of the &theta; - &phi; model of money.
* [http://www.princeton.edu/~kiyotaki/papers/Financial-Deepening.pdf Financial Deepening]: Gives a more succinct treatment of the &theta; - &phi; model of money.
* [https://pantherfile.uwm.edu/vesely/www/831/Kiyotaki%201989%20JPE.pdf On Money as a Medium of Exchange:] Another well known model of model in the economics literature that uses a [http://en.wikipedia.org/wiki/Search_theory search-theoretic] framework.
* Add a relevant paper...