Stochastic Equilibrium Economy with Irreversible Investment (with M.
A stochastic continuous-time economy on a finite time interval consists of
(i) a commodity producing firm which must decide on cash holdings,
employment levels and investment for capacity expansion, (ii) agents who
maximize expected total utility of consumption, of money holding and of leisure,
some of whom are employed by the firm, some facilitate capacity expansion
(“construction”) and some who are retired or on welfare. All agents
participate in a financial market. The money supply (in real terms) is
determined exogenously by the monetary authorities. We show how to
construct an equilibrium where prices (and other parameters) are set so
that both the agents and the firm can achieve their optimal choices and
the markets clear.