1. Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague JEM027 Monetary Economics The role of money Tomáš Holub Tomas.Holub@cnb.cz October 5, 2015

2. JEM027 – Monetary Economics 1 Basic question Why does money exist?

3. JEM027 – Monetary Economics 2 Three basic roles Medium of account 1 Medium of exchange (payments) 2 Store of value 3

4. JEM027 – Monetary Economics 3 Walrasian economy ▪ No transaction costs, perfect information, perfect enforcement of contracts ▪ Money as a unit of account (numeraire) ▪ It can be any type of good ▪ Not needed, just convenient Agent 7Agent 3 Agent 2 Agent 4 Agent ∞ Agent 6 Agent 1 Agent 5 Divine auctioneer

5. JEM027 – Monetary Economics 4 ▪ Transactions are costly (in terms of time and resources) ▪ Information asymmetries ▪ Imperfect enforcement of contracts Real world

6. JEM027 – Monetary Economics 5 Classical approach ▪ Why money, rather than barter? ▪ Lack of double coincidence of wants (Jevons, 1875) ▪ High transaction costs of multilateral barter

7. JEM027 – Monetary Economics 6 Agent 1Agent 2 Agent 1Agent 2 Agent 3 Money helps Agent 1Agent 2 Agent 3 Double coincidence of wants

8. JEM027 – Monetary Economics 7 Advances in transaction technology ▪ Organized markets ▪ Indirect barter ▪ Commodity money ▪ Fiat money ▪ Inside money ▪ Electronic money ▪ …. (Virtual currencies?) Resources Time Another illustration Transaction technology Indiference curve

9. JEM027 – Monetary Economics 8 Storability A Divisibility B Easy manipulation C Acceptability (Menger, 1892) D Minimizing transaction costs Desirable characteristics

10. JEM027 – Monetary Economics 9 Divisibility?

11. JEM027 – Monetary Economics 10 JEM027 – Monetary Economics Easy manipulation? Yap stone money (Micronesia)

12. JEM027 – Monetary Economics 11 JEM027 – Monetary Economics ” According to local legend, two or three generations before Furness's arrival a large stone in transit was lost at sea during a storm. The claim to this stone continued to have value, even though the stone itself was unrecoverable. “ Yap stone money (Micronesia) … or acceptability? Source: http://jpkoning.blogspot.cz/2013/01/yap-stones-and-myth-of-fiat-money.html

13. JEM027 – Monetary Economics 12 JEM027 – Monetary Economics ▪ Why money, rather than credit? ▪ Asymmetric information and imperfect contracts ▪ Emphasis on acceptability of money, rather than physical properties Modern approach

14. JEM027 – Monetary Economics 13 JEM027 – Monetary Economics Money helps Agent 1Agent 2 Agent 3 Credit may help Agent 1Agent 2 Agent 3... if someone does not run away Money vs. credit

15. JEM027 – Monetary Economics 14 JEM027 – Monetary Economics OLG model of money (e.g. Wallace, 1980) (1/3) ▪ Money as a store of value (improves consumption smoothing) ▪ Money circulates, only if all future generations will accept it (multiple equilibria) ▪ But: rate-of-return-dominance puzzle (money will stop circulating if there is a store of value with – even marginally – higher return)

16. JEM027 – Monetary Economics 15 JEM027 – Monetary Economics OLG model of money (2/3) ▪ Economy exists forever, but people live for two periods (Y,O) only ▪ Single non-storable good ▪ People get income y only when young, it falls down from heaven ▪ People maximize their lifetime utility ⇒ want to smooth consumption ⇒ want to trade between young and old ▪ With no store of value (money), U=u(y), no consumption smoothing is achieved (no double coincidence of wants)

17. JEM027 – Monetary Economics 16 JEM027 – Monetary Economics OLG model of money (3/3) c0c0 cYcY y (P t /P t+1 )*y ▪ If generation 0 gets money and if all future generations are expected to accept it, it can start circulating, thus improving welfare

18. JEM027 – Monetary Economics 17 JEM027 – Monetary Economics ▪ „Acceptability, Means of Payment and Media of Exchange“ ▪ Simple theoretical model that determines acceptability of money endogenously ▪ Money as a means of transactions ▪ Economy - assumptions: – large number of infinitely lived agents, meet bilaterally once each period and trade only if it is mutually advantageous – large number of perfectly storable consumption goods, – each agent consumes a fraction x of goods – each good is consumed by a fraction x of agents. Random matching model (e.g. Kyiotaki, Wright, 1991-1992)

19. JEM027 – Monetary Economics 18 JEM027 – Monetary Economics Assumptions – goods and utility ▪ All goods produced by an equal number of agents, but agents don’t produce goods that they consume themselves. ▪ Goods, money - indivisible (units of size 1; no issue of price determination). ▪ Consumption of the good provides utility u, ▪ Immediately a new good is produced → cost c (disutility) ▪ Note: agents cannot produce without first consuming ▪ Transaction cost ε (in terms of disutility) carried by the receiver of the consumption good from the trade (no transaction cost for accepting money) ▪ Net utility from consumption: U=u-c-ε > 0

20. JEM027 – Monetary Economics 19 JEM027 – Monetary Economics Assumptions – endownments ▪ Initial endowment of some agents (randomly chosen) with consumption goods and the rest with money (people cannot hold both money and goods at the same time). ▪ M … fraction of agents endowed with money (only 1 unit of money per agent, units indivisible) ▪ 1-M … fraction of agents endowed with their commodity

21. JEM027 – Monetary Economics 20 JEM027 – Monetary Economics Determination of Acceptability of Money (i): ▪ π... own probability of accepting money (by a representative economic agent) ▪ Π... average probability of accepting money by the others ▪ V(c)... value of having a commodity at the end of each period ▪ V(m)... value of having money at the end of each period ▪ β... discount factor between periods condition for the acceptability of money: V(m)  V(c)

22. JEM027 – Monetary Economics 21 JEM027 – Monetary Economics Determination of Acceptability of Money (ii): Determination of agent’s payoff (for commodity/money) agent with a commodity: V(c) =  {(1-M)x 2 U + Mx  V(m) + (1-Mx  )V(c)} agent with money: V(m) =  {(1-M)x  (U+V(c)) + [1-(1-M)x  ] V(m)}

23. JEM027 – Monetary Economics 22 JEM027 – Monetary Economics Determination of Acceptability of Money (iii): From V(c) and V(m): if  < x, then V(m) < V(c) (i.e. when money is less acceptable than the commodity, the payoff from trading with money is less than from barter) result:  = 0 (never trade commodity for money) if  > x, then V(m) > V(c) (i.e. when money is more acceptable than the commodity, the payoff from trading with money is more than from barter) result:  = 1 (always trade commodity for money)

24. JEM027 – Monetary Economics 23 JEM027 – Monetary Economics Determination of Acceptability of Money (iv): if  = x, then V(m) = V(c) (i.e. when money is just as acceptable as the commodity, the payoffs from trading with money and from barter are equal) result: any  between 0 and 1  3 equilibria in the model:  = 0, when money not acceptable  = 1, money generally acceptable  = x, money partially acceptable

25. JEM027 – Monetary Economics 24 JEM027 – Monetary Economics Graphical Illustration ▪ Multiple equilibria – the system is potentially fragile. ▪ Money circulates if acceptability exceeds the critical level x.

26. JEM027 – Monetary Economics 25 JEM027 – Monetary Economics Graphical Illustration – with opportunity cost ▪ Opportunity cost of holding money implies that money must be more acceptable than goods to start circulating. ▪ But it may still circulate, i.e. there is no rate-of- return-dominance puzzle. ▪ Only if the OC exceeds some critical level, monetary equilibrium breaks down (e.g. due to hyperinflation).

27. JEM027 – Monetary Economics 26 JEM027 – Monetary Economics Kyiotaki, Wright: Conclusions ▪ Acceptability is key for circulation of money ▪ It is determined endogenously in the model ▪ Money improves welfare (higher frequency of trade) ▪ Money may circulate even with some opportunity costs (no rate-or-return dominance puzzle) ▪ But the monetary equilibrium may collapse with too high opportunity costs (e.g. hyperinflation) ▪ Multiple equilibria – the monetary system is potentially fragile, based on trust

28. JEM027 – Monetary Economics 27 JEM027 – Monetary Economics Random Matching Model vs. OLG OLGRM GoodsNon-storableStorable People2 periodsInfinitely-lived Function of moneyStore of valueMedium of exchange May improve welfareYes (consumption smoothing) Yes (higher frequency of trade) Acceptability crucialYes Endogenous acceptabilityYes Multiple equilibriaYes Rate-of-return dominance puzzle YesNo

29. JEM027 – Monetary Economics 28 JEM027 – Monetary Economics Money improves welfare by reducing transaction costs and addressing information asymmetries 1 The system might be fragile, acceptability (credibility) is key 2 Policy implications: build credible monetary institutions, avoid hyperinflations 3 Conclusions