{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

palgrave-wright - Search-and-Matching Models of Monetary...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Search-and-Matching Models of Monetary Exchange Prepared for The New Palgrave by Randall Wright University of Pennsylvania 1 Introduction In this article we review a class of equilibrium search (matching) models that can be used to study the trading process, and in particular to develop a formal theory of money as a medium of exchange . Developing such a theory is one of the longest-standing issues in economics, but it met with at best limited success prior to the development of search-based models, which provide a natural frame- work in which to formalize venerable stories about money helping to facilitate exchange. 1 2 Background Diamond (1982) introduced a framework that, although it cannot used directly, can be extended naturally to build microfoundations for monetary economics. In his model, a [0 , 1] continuum of in fi nitely-lived agents interact in an economy where activity takes place in two distinct sectors: one for production and one 1 These stories, going back to Smith, Jevons, Menger, Wicksell, and others (many of which are reprinted in Starr 1990) concern a double coincidence of wants problem in bilateral ex- change, as discussed below. Overlapping generations models (e.g. Wallace 1980) provide an alternative approach. Ostroy and Starr (1990) survey earlier attempts to develop microfoun- dations for monetary theory, including Jones (1976), which is similar in spirit if not detail to modern search models. There is not space here to discuss pros and cons of the various approaches, but it seems fair to say search and matching models now dominate the area. 1
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
for exchange. In the fi rst sector, agents encounter potential production oppor- tunities randomly over time according to a Poisson process with arrival rate α . Each opportunity yields a unit of output at cost c 0 , where c is random with CDF F ( c ) . Since c is observed before a production decision is made, given an opportunity, there is a reservation cost k such that agents produce i ff c k . For now, these goods are indivisible, and agents can store at most one at a time. All goods yield utility of consumption u > 0 , except by assumption agents cannot consume their own output; hence they must trade. Traders with goods meet bilaterally in the exchange sector according to a Poisson process with arrival rate γ . Upon meeting they trade, consume, and return to production. Since all goods are the same, and indivisible, every meeting yields trade, and every trade is a one-for-one swap. Generally, γ = γ ( N ) depends on the measure of agents in the exchange sector N . This is based on a matching technology that gives the number of agents who meet a partner per unit time as m ( N ) , with m 0 ( N ) > 0 , implying γ ( N ) = m ( N ) /N for all N > 0 . Let V 0 and V 1 be the value functions for producers and traders. The fl ow Bellman equation for a producer is 2 rV 0 = αE max { V 1 V 0 c, 0 } = α Z k 0 ( k c ) dF ( c ) , where k = V 1 V 0 . Similarly, for a trader rV 1 = γ ( N )( u + V 0 V 1 ) = γ ( N )( u k ) .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern