Overlapping Research On Overlapping Generations Models

I've recently read Saverio Fratini's "Reswitching of Techniques in an Intertemporal Equilibrium Model with Overlapping Generations" (Contributions to Political Economy V. 26, N. 1 (2007): 43-59).

Mainstream economists responded to the Cambridge Capital Controversy by claiming that disaggregated models of intertemporal and temporary equilibrium are unaffected. So the question arises whether Cambridge capital-theory “paradoxes” can tell us anything interesting about such models. It is known that multiple equilibria can arise in overlapping generations, single-good, models. So pointing out multiple equilibria is not enough. Fratini addresses this issue. He constructs a reswitching example in which reswitching is necessary for multiple equilibriua to arise at an interest rate in a region where a higher interest rate is associated with more savings.

Here’s the abstract of Fratini’s paper:

"We study an overlapping generation model of Diamond's type. In contrast to Diamond, we do not assume that the technology can be represented by an aggregate neoclassical production function. Rather, we study the case in which (i) the technology consists of a finite number of constant coefficient productive activities, (ii) there are capital goods physically heterogeneous with respect to each other and to the economy's only consumption good and (iii) there are two alternative production methods for obtaining the consumption good. We explore the possible linkage between reswitching of techniques and the multiplicity of stationary state equilibria of the model."

Fratini’s research is quite close to some of my own research. Let me compare and contrast:

• Fratini considers a structure of production in which in each technique, the single consumption good is produced with a different capital good. This approach resembles this example I take from Garegnani, except in Garegnani’s example a continuum of capital goods is available. In Fratini’s model, only two techniques are available.
• Fratini imposes some constraints on his model that I do not consider. For example, roughly, he assumes that in each technique the production of the consumption good is more capital-intensive than the production of the capital good for that technique.
• Fratini is better on the economic intutition. For example, he explains his savings schedule as combining income and well-behaved substitution effects.
• I have described a wider range of overlapping generation models. In particular, I wonder if my needing to include a labor-leisure trade-off in the agents’ utility function (as compared to Section 3 here) to get multiple equilibria associated with the “perverse” switch is a challenge to Fratini’s results. (Keep in mind that I do not impose any restriction on the direction of price Wicksell effects.)
• Fratini briefly analyzes the stability of stationary states, drawing on past results in the economic literature.
• I think I am better on visualization of results. This is probably only because I was willing to do more tedious work within a spreadsheet that is needed to generate Fratini’s Figures 1 and 2 and Table 1.
• Fratini has gone through the labor of writing up his results in a coherent whole and seeing the article through the refereeing and publishing process.