Introduction to Modern Economic Growth at time t, where a0 (t) is the quality of the technique he has available for production.2 At t = 0, the entrepreneur starts with a (0) = From then on, at each date, he can either engage in production using one of the techniques he has already discovered, or spend that period searching for a new technique Let us assume that each period in which he engages in such a search, he gets an independent draw from a timeinvariant distribution function H (a) defined over a bounded interval [0, a¯] Therefore, the decision of the entrepreneur at each date is whether to search for a new technique or to produce If he decides to produce, he has to use the technique he has just discovered (this assumption is relaxed in Exercise 6.17) The consumption decision of the entrepreneur is trivial, since there is no saving or borrowing, and he has to consume his current income, c (t) = y (t) The reason why this problem already introduces some of the ideas we will discuss later in the book is that the entrepreneur has a choice of technology Rather than technology being given as mana from heaven as in the models we have seen so far, the entrepreneur has a non-trivial choice which affects the technology available to him In particular, by searching more, which is a costly activity in terms of foregone production, he can potentially improve the set of techniques available to him Moreover, this economic decision is similar to the trade-offs faced by other economic agents; whether to produce with what he has available today or make an “investment” in one more round of search with the hope of discovering something better This type of economic trade-off will feature prominently in models of endogenous technology later in the book For now, our main objective is to demonstrate how dynamic programming techniques can be used to analyze this problem Let us first try to write the maximization problem facing the entrepreneur as a sequence problem We begin with the class of ¯]t be a sequence of techniques decision rules of the agent In particular, let at ∈ [0, a observed by the entrepreneur over the past t periods, with a (s) = 0, if at time s, the entrepreneur engaged in production We write at = (a (0) , , a (t)) Then a decision rule for this individual would be q (t) : At → {at } ∪ {search} , 2The use of a here for the quality of ideas, rather than as asset holdings of individual before, should cause no confusion 300