Recursive Prefereces

I'm working on it. Reading Brackus, Routledge, and Zin. And Koopmans

The idea is to define the relative substitutability of good over time, a vector of utility functions of the goods, and see how it evolves over time toward an equilibrium value. They construct a Marginal Rate of Substition Matrix [MRS], which is the array of partial elasticities over time. The ask how that array converges after perturbations from a starting point, as each agent incrementally adjusts the relative consumption of goods.

Under what conditions cn the final Utility Function be constructed from a Polynomial of the MRS matrix.

If all goes well, the utility of consuming some good at a point of time in the future will converge, and the path toward convergence can be computed accurately as long as the time step reduces. Generally, one likes to get a set of polynomials int time in which to constructes the final versionj of Ut(c), for some t, and for each c, consumption preference with a discount rate. Whew!

So, the assumption is infinite certaint in the converged position. What happend if the discount rate us uncertain, or beter, if the period t, is unsertain to a constand 15%, NIID uncertainty? Then when construction the motion of Ut out of polynomials, the set of polynomils becomes finite. To see this, imagine an agent buying houses and cars. He buys a house every 10 years, a car every 5. Why ten and five? Because he cannot predict axactly when the next house comes, but it is 7 to 13 years; and he buys a car every 4-6 years. Thus his car buying period and uncertainty does not overlap his house buying process. So, constant uncertainty in time or i measurement results in a finite, restricted set of polynomials to construct Ut.


Any way, HT Arnold Kling