John W. Dawson Department of Economics Appalachian State University Boone, NC 28608

1. Catching Up vs. The Cutting Edge: A New Approach to Teaching Economic Growth in the Principles Course John W. Dawson Department of Economics Appalachian State University Boone, NC 28608

2. Background • 1956: Solow’s “Contribution” to growth (QJE) • Late 1980s undergraduate: no growth at all • 1986: Romer’s “endogenous” growth model (JPE) • 1987: Solow wins Nobel Prize • Early 1990s graduate student: First exposure to Solow Model in core PhD courses • 1990s-mid 2000s: Explosion of research on growth in the economics literature

3. Economic Growth in the Undergraduate Classroom • First appears in the intermediate texts • Routinely appears before business cycles • Solow model appears in intermediate texts • Discussions of growth eventually appear in the principles texts • Most treatments rely on storytelling and discussions of what determines productivity, with no formal modeling • What model to use, if any?

4. Advantages? Models help simplify complicated processes Better understanding of different types of growth Better understanding of the sources of growth Better understanding of the various parts of the growth “process” Disadvantages? Too complicated Too mathematical Too graphically rigorous Not accessible to a wide range of students at various skill levels Requires too much time in class The Solow Model in the Principles Course?

5. Teaching the Solow Model • Overall objective: • Explaining how economic growth results from capital accumulation and the creation of new ideas.

6. Teaching the Solow Model (cont’d) • Four Simple Steps: • Introduce production functions and the law of diminishing marginal returns. • Explain the process of capital accumulation and define the concept of a “steady state.” • Demonstrate the growth that results from capital accumulation—called “catching-up” growth—and explain its characteristics. • Demonstrate the growth that results from new ideas—called “cutting-edge” growth—and explain its characteristics.

7. Teaching the Solow Model (cont’d) • General Theme: • If you can teach these four steps, you can teach the Solow Model. • You can teach these four steps to most Principles students.

8. Step 1: The Production Function • The basic idea of the production function is simple: factors of production → output

9. The Production Function (cont’d) • In mathematical terms: Y = F(A, K, eL) • Ignoring changes in A and eL for now: Y = F(K) = √K

10. The Production Function (cont’d)

11. The Production Function (cont’d) • The law of diminishing marginal returns • Many students already familiar • Represented by the concave shape of the production function (i.e., the slope of the function declines a higher values of K) • Changes in Y greater for the first units of K than for later units. • A crucially important concept in the Solow model.

12. Step 2: Capital Accumulation • The production function provides the first clue about the story of growth: increases in K cause increases in Y. • But what drives increases in K? This is the process of capital accumulation. • Capital accumulation results from: • Investment: additions to the existing K stock • Depreciation: subtractions from the existing K

13. Capital Accumulation (cont’d) • Thus, capital accumulation depends on the difference between investment (I) and depreciation (d): ΔK = I − d. • In summary: • If I > d, then K will grow. • If I < d, then K will decline. • If I = d, then K will remain constant.

14. Capital Accumulation (cont’d) • A steady state is said to occur when K is neither growing nor declining (i.e., when I = d). • Graphically: • Investment (saving) is assumed to be a constant share (30%) of output. • Depreciation is assumed to be a constant fraction (2%) of the existing capital stock. • Since both investment and depreciation depend on K, both curves can be graphed on the same graph with K on the horizontal axis. • The steady state occurs where the two curves intersect… much like the concept of “equilibrium” which students are already familiar with.

15. Capital Accumulation (cont’d)

16. Step 3: “Catching-Up” Growth • Definition: increases in output that occur as a result of capital accumulation as an economy moves toward its steady state (a.k.a. “transitional” growth). • Key Characteristics: • Must eventually fizzle out (because of DMR) • Cannot explain growth in the very long run • Implies convergence (again, because of DMR) • Explains growth in modern-day China and in post-WWII Germany, Japan, and the U.S.

17. Step 4: “Cutting-Edge” Growth • New Ideas: • Re-introducing “A” in the production function • Y = A√K • Increases in A represent new ideas (a.k.a. technology) • New ideas shift the entire production function • New ideas increase the productivity of all factors of production • No increase in K required

18. Cutting-Edge Growth (Cont’d)

19. Cutting-Edge Growth (Cont’d) • Cutting-Edge Growth: increases in output resulting from the continuous flow of new ideas. • Key Characteristics: • Can explain growth in the very long-run • Does not require capital accumulation • Fundamentally different from catching-up growth—results from a different source • Generates more catching-up growth, too

20. Cutting-Edge Growth (Cont’d)

21. Conclusions • Benefits of using the Solow model: • Formalizes the production process and puts it on center-stage • Illuminates macro implications of micro concepts (production, DMR, innovation) • Highlights the role of investment and capital accumulation in the growth process • Distinguishes between “catching-up” and “cutting-edge” growth—and their sources

22. Conclusions (Cont’d) • Potential Challenges: • Mathematical rigor: Really not an issue • Graphical rigor: Similar to other areas of the principles course • Time requirements: Presentation of the model should follow a more general introduction to growth and discussion of the growth process (e.g., institutions → incentives → investment, education, R&D → factors of production → growth)