The monetary and fiscal control of a simple economy without outside randomness is studied here from the micro-economic basis of a strategic market game. The government’s bureaucracy is treated as a public good that provides services at a cost. A conventional public good is also considered.
The classical Fisher equation asserts that in a nonstochastic economy, the inflation rate must equal the difference between the nominal and real interest rates. We extend this equation to a representative agent economy with real uncertainty in which the central bank sets the nominal rate of interest. The Fisher equation still holds, but with the rate of inflation replaced by the harmonic mean of the growth rate of money. Except for logarithmic utility, we show that on almost every path the long-run rate of inflation is strictly higher than it would be in the nonstochastic world obtained by replacing output with expected output in every period. If the central bank sets the nominal interest rate equal to the discount rate of the representative agent, then the long-run rate of inflation is positive (and the same) on almost every path. By contrast, the classical Fisher equation asserts that inflation should then be zero. In fact, no constant interest rate will stabilize prices, even if the economy is stationary with bounded i.d.d. shocks. The central bank must actively manage interest rates if it wants to keep prices bounded forever. However, not even an active central bank can keep prices exactly constant.
Keywords: Inflation, Equilibrium, Control, Interest rate, Central bank, Harmonic Fisher equation
Arrow’s original proof of his impossibility theorem proceeded in two steps: showing the existence of a decisive voter, and then showing that a decisive voter is a dictator. Barbera replaced the decisive voter with the weaker notion of a pivotal voter, thereby shortening the first step, but complicating the second step. I give three brief proofs, all of which turn on replacing the decisive/pivotal voter with an extremely pivotal voter (a voter who by unilaterally changing his vote can move some alternative from the bottom of the social ranking to the top), thereby simplifying both steps in Arrow’s proof.
My first proof is the most straightforward, and the second uses Condorcet preferences (which are transformed into each other by moving the bottom alternative to the top). The third (and shortest) proof proceeds by reinterpreting Step 1 of the first proof as saying that all social decisions are made the same way (neutrality).
We construct explicit equilibria for strategic market games used to model an economy with fiat money, one nondurable commodity, countably many time- periods, and a continuum of agents. The total production of the commodity is a random variable that fluctuates from period to period. In each period, the agents receive equal endowments of the commodity, and sell them for cash in a market; their spending determines, endogenously, the price of the commodity. All agents have a common utility function, and seek to maximize their expected total discounted utility from consumption.
Suppose an outside bank sets an interest rate rho for loans and deposits. If 1+rho is the reciprocal of the discount factor, and if agents must bid for consumption in each period before knowing their income, then there is no inflation. However, there is an inflationary trend if agents know their income before bidding.
We also consider a model with an active central bank, which is both accurately informed and flexible in its ability to change interest rates. This, however, may not be sufficient to control inflation.
Keywords: Inflation, strategic market games, control, interest rate, central bank, equilibrium
An overlapping generations model of an exchange economy is considered, with individuals having a finite expected life-span. Conditions concerning birth, death, inheritance and bequests are fully specified. Under such conditions, the existence of stationary Markov equilibrium is established in some generality, and several explicitly solvable examples are treated in detail.
Keywords: Overlapping generations, inheritance, stochastic process, life span
We describe conditions for the existence of a stationary Markovian equilibrium when total production or total endowment is a random variable. Apart from regularity assumptions, there are two crucial conditions: (i) low information — agents are ignorant of both total endowment and their own endowments when they make decisions in a given period, and (ii) proportional endowments — the endowment of each agent is in proportion, possibly a random proportion, to the total endowment. When these conditions hold, there is a stationary equilibrium. When they do not hold, such equilibrium need not exist.
Keywords: Information, stochastic process, money, and disequilibrium
Modeling problems for a monetary economy are discussed and some examples are presented in the context of an infinite-horizon economy with one or two types of traders, who use fiat money to buy a single perishable consumption good. Three instances are considered, all with transactions in fiat money. The first model has no borrowing or lending. The second model permits both borrowing and lending, but all loans are secured. The third model has borrowing and unsecured lending, and takes into account the presence of debtors who are unable to honor their debts and go bankrupt. Borrowing and depositing take place through an outside bank, although in some circumstances a money market could be used instead. Conditions for different forms of lending are discussed. This is a survey of three technical papers, where the mathematical models are developed in detail and the proofs are supplied.
We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money market, and a continuum of agents. These use fiat money in order to offset random fluctuations in their endowments of the commodity, are not allowed to borrow more than they can pay back (secured lending), and maximize expected discounted utility from consumption of the commodity. Their aggregate optimal actions determine dynamically prices and/or interest rates for borrowing and lending, in each period of play. In equilibrium, random fluctuations in endowment- and wealth-levels offset each other, and prices and interest rates remain constant.
As in our related recent work, KSS (1994), we study in detail the individual agents’ dynamic optimization problems, and the invariance measures for the associated, optimally controlled Markov chains. By appropriate aggregation, these individual problems lead to the construction of stationary Markov competitive equilibrium for the economy as a whole.
Several examples are studied in detail, fairly general existence theorems are established, and open questions are indicated for further research.
This paper studies stationary noncooperative equilibria in an economy with fiat money, one nondurable commodity, countably many time periods, no credit or futures market, and a measure space of agents — who may differ in their preferences and in the distributions of their (random) endowments. These agents are immortal, and hold fiat money as a means of hedging against the random fluctuations in their endowments of the commodity. In the aggregate, these fluctuations offset each other, and equilibrium prices are constant.
We carry out an equilibrium analysis that focuses on distribution of wealth, on consumption, and on price formation. A careful analysis of the one-agent, infinite-horizon optimization problem, and of the invariant measure for the associated optimally controlled Markov chain, leads by aggregation to a stationary noncooperative or competitive equilibrium. This consists of a price for the commodity and of a distribution of wealth across agents which, under appropriate simple strategies for the agents, stay fixed from period to period and preserve the basic quantities of the model.
We hope that, in future work, we shall be able to address additional features of the model treated here, such as borrowing and lending at appropriate (endogenously determined) interest rates, the endogenous production of the commodity, overlapping generations of agents, and bankruptcy and treatment of creditors.