@@ -29,13 +29,14 @@ kernelspec:
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29 | 29 | This lecture and {doc}`Cass-Koopmans Competitive Equilibrium <cass_koopmans_2>` describe a model that Tjalling Koopmans {cite}`Koopmans` |
30 | 30 | and David Cass {cite}`Cass` used to analyze optimal growth. |
31 | 31 | |
32 | | -The model can be viewed as an extension of the model of Robert Solow |
33 | | -described in [an earlier lecture](https://python-programming.quantecon.org/python_oop.html) |
34 | | -but adapted to make the saving rate be a choice. |
| 32 | +The model extends the model of Robert Solow |
| 33 | +described in [an earlier lecture](https://python-programming.quantecon.org/python_oop.html). |
| 34 | + |
| 35 | +It does so by making the saving rate be a choice, instead of a hard-wired fixed number. |
35 | 36 | |
36 | 37 | (Solow assumed a constant saving rate determined outside the model.) |
37 | 38 | |
38 | | -We describe two versions of the model, one in this lecture and the other in {doc}`Cass-Koopmans Competitive Equilibrium <cass_koopmans_2>`. |
| 39 | +We describe two versions of the model, a planning problem without prices in this lecture, and a competitive equilibrium with prices in this lecture {doc}`Cass-Koopmans Competitive Equilibrium <cass_koopmans_2>`. |
39 | 40 | |
40 | 41 | Together, the two lectures illustrate what is, in fact, a |
41 | 42 | more general connection between a **planned economy** and a decentralized economy |
@@ -59,7 +60,7 @@ The lecture uses important ideas including
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59 | 60 | - A min-max problem for solving a planning problem. |
60 | 61 | - A **shooting algorithm** for solving difference equations subject |
61 | 62 | to initial and terminal conditions. |
62 | | -- A **turnpike** property that describes optimal paths for |
| 63 | +- A **turnpike** property of optimal paths for |
63 | 64 | long but finite-horizon economies. |
64 | 65 | |
65 | 66 | Let's start with some standard imports: |
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