By de Croix D.l., Michel P.
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19). 1). The shaded region is the one where the equilibrium is not unique. Non-uniqueness thus arises for low values of both elasticities. 19), which is plotted with a solid line. The interest of this latter condition is that it does not depend on the other parameters A, α, β, and n. We should note that the uniqueness of the equilibrium is a fundamental property for interpreting the perfect foresight assumption in a non-ad-hoc way. Only when the equilibrium is unique can it be analyzed as an equilibrium with rational perfect foresight.
10). Hence, the equilibrium wage equalizing supply and demand is wt = ω Kt Nt = ω(kt ). 11) kt = Kt /Nt is the stock of capital per young person, or the equilibrium capital–labor ratio. 2. Equality between realized and distributed profits: By assumption, the effective profits are distributed to the owners of capital. Given the equilibrium on the labor market, we have πt = f (kt )Kt . The old households receive πt = Nt−1 Rt st−1 = Rt Kt , as Kt = Nt−1 st−1 . The equality between effective profits and distributed profits implies that the rate of return on the savings made at time t − 1 is equal to the marginal productivity of capital: Rt = f (kt ).
19), which is plotted with a solid line. The interest of this latter condition is that it does not depend on the other parameters A, α, β, and n. We should note that the uniqueness of the equilibrium is a fundamental property for interpreting the perfect foresight assumption in a non-ad-hoc way. Only when the equilibrium is unique can it be analyzed as an equilibrium with rational perfect foresight. In the case of uniqueness, there is no exogenous problem of coordinating expectations, as each agent can solve the model as we did and calculate the next period equilibrium kt+1 , which is necessary to obtain the rate of return Ret+1 = f (kt+1 ).