A System of Renewal Equations
R. K. Miller
Source abstract
Chipman [1] formulated a renewal model of a macroscopic one-commodity economic system. Here a continuous version of his renewal model is studied, that is, the asymptotic behavior of certain Volterra integral equations is studied. When constant returns to scale are assumed, the equations are linear. When diminishing returns to scale are assumed, the equations become nonlinear. For the linear case we show that comparison by the overtaking principle can be reduced to comparison of asymptotic rates of growth of a related linear system. This result is used to improve a result of Chipman [1, Thm. 11]. For the nonlinear case we show that in certain cases comparison by the overtaking principle can be reduced to comparison of the asymptotic growth rates of some related linear systems. Moreover, we analyze some situations in which the model breaks down.
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