Subject : New Monetarist Economics / Micro
Credit and Liquidity
Consider a typical Lagos-Wright environment with a centralized market (CM) and a decentralized market (DM). Tere are two consumption goods, the CM good and the DM good. There is no money but a fixed supply of trees. The stock of trees is â ≤ 1. Each tree gives a dividend δ > 0 in the CM. Assume that δ is "not too big". Each tree trade in the CM at a price of Φ. In the CM, agents can work and they consume the CM good. Their utility from working l hours and consuming X units of the CM good is
U(X, l) = log(X) - Al
where A > 0. Also in the CM, a continuum of firms operate a technology F(l) that transforms labor into the CM good. Assume that F(l)=2√p. Firms hire workers on a competitive labor market and pay the market (real) wage w. Firms maximize profit.
In the DM, agents meet bilaterally and, depending on their match, they can either be producers or consumers. They are consumers or producers with probability α and with probability 1 - 2α they do not trade. The utility from consuming the DM good is u(q) while the disutility of producing it is c(q). Te bargaining protocol implies that consuming q units of the DM good requires a (real) payment of z(q) units of the CM good (for example, with "buyer takes all", z(q) = c(q)). By being "not too big" we mean that z(q*) > Φ + δ where q* satisfies u'(q*) = c'(q*) - this implies that buyers will be constrained.
Question 1: Characterize the steady state equilibrium.
Question 2: Show that the asset trades above its fundamental value. What happens to this apparent "bubble" when a decreases.
Some background information on the framework can be found here:
https://qed.econ.queensu.ca/pub/students/phds/liuqian/MRG/Fall_2007/Lagos_Wright2005.pdf
https://wwz.unibas.ch/fileadmin/wwz/redaktion/witheo/personen/aleks/Teaching/Monetary_Economics/chapter_1.pdf
https://wwz.unibas.ch/fileadmin/wwz/redaktion/witheo/personen/aleks/Teaching/Monetary_Economics/chapter_4.pdf