This paper establishes an algorithm for the equilibrium in a stochastic continuous time economy model, on a finite time interval, including a representative agent maximizing her expected total utility of consumption, leisure, and money, and a single firm that optimally produces the consumption good and maximizes its expected total profits based on employment rate and money held. First, under the assumption of equilibrium, a link between the firm’s control problem and the representative agent’s optimal expected total utility is obtained. Then such link is exploited to establish an algorithm for equilibrium.
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