How Does The Solow Model Explain Technological Change?

Model of long-run economic growth

The Solow–Swan model or exogenous growth model is an economic model of long-run economic growth. It attempts to explain long-run economic growth by looking at capital letter accumulation, labor or population growth, and increases in productivity largely driven by technological progress. At its core, information technology is an amass production function, oft specified to be of Cobb–Douglas type, which enables the model "to brand contact with microeconomics".^{[ane] : 26} The model was adult independently by Robert Solow and Trevor Swan in 1956,^{[ii] [3] [note 1]} and superseded the Keynesian Harrod–Domar model.

Mathematically, the Solow–Swan model is a nonlinear system consisting of a single ordinary differential equation that models the development of the per capita stock of capital. Due to its particularly bonny mathematical characteristics, Solow–Swan proved to be a convenient starting point for various extensions. For instance, in 1965, David Cass and Tjalling Koopmans integrated Frank Ramsey's analysis of consumer optimization, thereby endogenizing^{[ clarification needed ]} the saving rate, to create what is now known equally the Ramsey–Cass–Koopmans model.

Background [edit]

The Solow-Swan model was an extension to the 1946 Harrod–Domar model that dropped the restrictive assumption that only capital contributes to growth (so long equally there is sufficient labor to use all capital). Of import contributions to the model came from the work done past Solow and by Swan in 1956, who independently developed relatively unproblematic growth models.^{[2] [three]} Solow's model fitted available data on US economical growth with some success.^[four] In 1987 Solow was awarded the Nobel Prize in Economics for his work. Today, economists use Solow's sources-of-growth bookkeeping to judge the separate effects on economic growth of technological change, capital, and labor.^[v]

Solow model is also i of the most widely used models in economics to explain economical growth.^[half-dozen] Basically, it asserts that outcomes on the "total factor productivity (TFP) can lead to limitless increases in the standard of living in a state."^[half-dozen]

Extension to the Harrod–Domar model [edit]

Solow extended the Harrod–Domar model by adding labor as a factor of production and capital-output ratios that are not fixed as they are in the Harrod–Domar model. These refinements allow increasing capital intensity to be distinguished from technological progress. Solow sees the stock-still proportions product part equally a "crucial assumption" to the instability results in the Harrod-Domar model. His own work expands upon this by exploring the implications of alternative specifications, namely the Cobb–Douglas and the more general constant elasticity of substitution (CES).^[ii] Although this has become the canonical and celebrated story^[7] in the history of economics, featured in many economic textbooks,^[8] recent reappraisal of Harrod's work has contested it. I central criticism is that Harrod'southward original piece^[nine] was neither mainly concerned with economic growth nor did he explicitly use a stock-still proportions production part.^{[8] [10]}

Long-run implications [edit]

A standard Solow model predicts that in the long run, economies converge to their steady state equilibrium and that permanent growth is achievable but through technological progress. Both shifts in saving and in populational growth crusade only level effects in the long-run (i.e. in the accented value of existent income per capita). An interesting implication of Solow'south model is that poor countries should grow faster and eventually catch-upwards to richer countries. This convergence could be explained by:^[11]

• Lags in the diffusion on cognition. Differences in existent income might shrink every bit poor countries receive better engineering science and data;
• Efficient allocation of international capital flows, since the charge per unit of render on upper-case letter should be college in poorer countries. In practice, this is seldom observed and is known as Lucas' paradox;
• A mathematical implication of the model (assuming poor countries have not even so reached their steady country).

Baumol attempted to verify this empirically and found a very strong correlation betwixt a countries' output growth over a long period of fourth dimension (1870 to 1979) and its initial wealth.^[12] His findings were later contested by DeLong who claimed that both the non-randomness of the sampled countries, and potential for significant measurement errors for estimates of real income per capita in 1870, biased Baumol's findings. DeLong concludes that in that location is little evidence to support the convergence theory.

Assumptions [edit]

The key assumption of the Solow-Swan growth model is that capital is subject area to diminishing returns in a closed economy.

• Given a fixed stock of labor, the affect on output of the terminal unit of capital accumulated will always be less than the one before.
• Bold for simplicity no technological progress or labor force growth, diminishing returns implies that at some indicate the amount of new majuscule produced is merely just enough to make upwardly for the amount of existing uppercase lost due to depreciation.^[ane] At this point, because of the assumptions of no technological progress or labor force growth, we can see the economy ceases to abound.
• Assuming not-zero rates of labor growth complicate matters somewhat, but the bones logic still applies^[2] – in the short-run, the charge per unit of growth slows equally diminishing returns take effect and the economy converges to a abiding "steady-state" rate of growth (that is, no economic growth per-capita).
• Including non-cipher technological progress is very similar to the supposition of not-zero workforce growth, in terms of "effective labor": a new steady land is reached with abiding output per worker-hour required for a unit of output. However, in this case, per-capita output grows at the charge per unit of technological progress in the "steady-state"^[iii] (that is, the rate of productivity growth).

Variations in the effects of productivity [edit]

In the Solow–Swan model the unexplained change in the growth of output after accounting for the effect of upper-case letter accumulation is called the Solow residual. This residual measures the exogenous increase in total factor productivity (TFP) during a particular time period. The increase in TFP is oft attributed entirely to technological progress, merely it likewise includes any permanent comeback in the efficiency with which factors of product are combined over time. Implicitly TFP growth includes any permanent productivity improvements that event from improved management practices in the private or public sectors of the economic system. Paradoxically, even though TFP growth is exogenous in the model, information technology cannot be observed, and so information technology tin only be estimated in conjunction with the simultaneous estimate of the issue of capital accumulation on growth during a detail time period.

The model tin be reformulated in slightly different ways using unlike productivity assumptions, or different measurement metrics:

• Average Labor Productivity (ALP) is economic output per labor hour.
• Multifactor productivity (MFP) is output divided by a weighted average of capital and labor inputs. The weights used are ordinarily based on the aggregate input shares either gene earns. This ratio is often quoted as: 33% return to upper-case letter and 67% return to labor (in Western nations).

In a growing economic system, uppercase is accumulated faster than people are built-in, so the denominator in the growth function nether the MFP calculation is growing faster than in the ALP adding. Hence, MFP growth is almost always lower than ALP growth. (Therefore, measuring in ALP terms increases the credible capital deepening result.) MFP is measured past the "Solow residual", not ALP.

Mathematics of the model [edit]

The textbook Solow–Swan model is set in continuous-fourth dimension globe with no regime or international trade. A unmarried good (output) is produced using two factors of production, labor ( ${\displaystyle L}$ ) and capital ( ${\displaystyle Grand}$ ) in an aggregate production function that satisfies the Inada conditions, which imply that the elasticity of substitution must be asymptotically equal to i.^{[13] [14]}

${\displaystyle Y(t)=M(t)^{\blastoff }(A(t)50(t))^{1-\alpha }\,}$

where ${\displaystyle t}$ denotes time, ${\displaystyle 0<\alpha <1}$ is the elasticity of output with respect to majuscule, and ${\displaystyle Y(t)}$ represents total production. ${\displaystyle A}$ refers to labor-augmenting technology or "knowledge", thus ${\displaystyle AL}$ represents effective labor. All factors of production are fully employed, and initial values ${\displaystyle A(0)}$ , ${\displaystyle Chiliad(0)}$ , and ${\displaystyle Fifty(0)}$ are given. The number of workers, i.due east. labor, equally well as the level of technology grow exogenously at rates ${\displaystyle northward}$ and ${\displaystyle one thousand}$ , respectively:

${\displaystyle L(t)=L(0)e^{nt}}$

${\displaystyle A(t)=A(0)eastward^{gt}}$

The number of effective units of labor, ${\displaystyle A(t)L(t)}$ , therefore grows at rate ${\displaystyle (northward+g)}$ . Meanwhile, the stock of capital depreciates over time at a constant charge per unit ${\displaystyle \delta }$ . Yet, only a fraction of the output ( ${\displaystyle cY(t)}$ with ${\displaystyle 0<c<one}$ ) is consumed, leaving a saved share ${\displaystyle southward=1-c}$ for investment. This dynamic is expressed through the following differential equation:

${\displaystyle {\dot {M}}(t)=s\cdot Y(t)-\delta \cdot K(t)\,}$

where ${\displaystyle {\dot {K}}}$ is shorthand for ${\displaystyle {\frac {dK(t)}{dt}}}$ , the derivative with respect to fourth dimension. Derivative with respect to time means that it is the alter in capital stock—output that is neither consumed nor used to replace worn-out old uppercase goods is net investment.

Since the production function ${\displaystyle Y(M,AL)}$ has constant returns to scale, it can be written as output per effective unit of labour ${\displaystyle y}$ , which is a measure for wealth creation:^{[note 2]}

${\displaystyle y(t)={\frac {Y(t)}{A(t)L(t)}}=one thousand(t)^{\alpha }}$

The main involvement of the model is the dynamics of upper-case letter intensity ${\displaystyle k}$ , the capital stock per unit of effective labour. Its behaviour over time is given by the cardinal equation of the Solow–Swan model:^{[note three]}

${\displaystyle {\dot {m}}(t)=sk(t)^{\alpha }-(north+g+\delta )k(t)}$

The first term, ${\displaystyle sk(t)^{\blastoff }=sy(t)}$ , is the actual investment per unit of constructive labour: the fraction ${\displaystyle s}$ of the output per unit of constructive labour ${\displaystyle y(t)}$ that is saved and invested. The 2nd term, ${\displaystyle (north+chiliad+\delta )k(t)}$ , is the "break-even investment": the corporeality of investment that must be invested to prevent ${\displaystyle k}$ from falling.^{[15] : 16} The equation implies that ${\displaystyle k(t)}$ converges to a steady-state value of ${\displaystyle k^{*}}$ , defined past ${\displaystyle sk(t)^{\alpha }=(n+grand+\delta )k(t)}$ , at which at that place is neither an increment nor a subtract of upper-case letter intensity:

${\displaystyle k^{*}=\left({\frac {s}{n+g+\delta }}\right)^{ane/(1-\alpha )}\,}$

at which the stock of capital ${\displaystyle K}$ and effective labour ${\displaystyle AL}$ are growing at rate ${\displaystyle (n+yard)}$ . Likewise, it is possible to summate the steady-state of created wealth ${\displaystyle y^{*}}$ that corresponds with ${\displaystyle yard^{*}}$ :

${\displaystyle y^{*}=\left({\frac {due south}{northward+m+\delta }}\right)^{\blastoff /(1-\alpha )}\,}$

By assumption of constant returns, output ${\displaystyle Y}$ is also growing at that rate. In essence, the Solow–Swan model predicts that an economy will converge to a balanced-growth equilibrium, regardless of its starting point. In this situation, the growth of output per worker is determined solely by the rate of technological progress.^{[15] : eighteen}

Since, by definition, ${\displaystyle {\frac {One thousand(t)}{Y(t)}}=k(t)^{one-\alpha }}$ , at the equilibrium ${\displaystyle yard^{*}}$ we take

${\displaystyle {\frac {K(t)}{Y(t)}}={\frac {s}{northward+grand+\delta }}}$

Therefore, at the equilibrium, the majuscule/output ratio depends only on the saving, growth, and depreciation rates. This is the Solow–Swan model'southward version of the golden rule saving charge per unit.

Since ${\displaystyle {\alpha }<ane}$ , at any fourth dimension ${\displaystyle t}$ the marginal product of capital letter ${\displaystyle K(t)}$ in the Solow–Swan model is inversely related to the majuscule/labor ratio.

${\displaystyle MPK={\frac {\partial Y}{\fractional 1000}}={\frac {\alpha A^{1-\alpha }}{(Chiliad/50)^{1-\blastoff }}}}$

If productivity ${\displaystyle A}$ is the same across countries, so countries with less capital per worker ${\displaystyle K/50}$ have a college marginal product, which would provide a higher render on capital investment. Equally a issue, the model predicts that in a world of open marketplace economies and global financial capital, investment volition menstruum from rich countries to poor countries, until capital/worker ${\displaystyle One thousand/L}$ and income/worker ${\displaystyle Y/L}$ equalize across countries.

Since the marginal product of physical capital is non higher in poor countries than in rich countries,^[16] the implication is that productivity is lower in poor countries. The basic Solow model cannot explain why productivity is lower in these countries. Lucas suggested that lower levels of human capital in poor countries could explain the lower productivity.^[17]

Because the marginal production of majuscule ${\displaystyle {\frac {\partial Y}{\partial G}}}$ equals the rate of return ${\displaystyle r}$

${\displaystyle \alpha ={\frac {K{\frac {\fractional Y}{\partial K}}}{Y}}={\frac {rK}{Y}}\,}$

then that ${\displaystyle \alpha }$ is the fraction of income appropriated past upper-case letter. Thus, the Solow–Swan model assumes from the beginning that the labor-capital split of income is constant.

Mankiw–Romer–Weil version of model [edit]

Addition of human capital [edit]

Northward. Gregory Mankiw, David Romer, and David Weil created a human capital augmented version of the Solow–Swan model that tin can explicate the failure of international investment to menses to poor countries.^[18] In this model output and the marginal product of upper-case letter (1000) are lower in poor countries because they have less human capital than rich countries.

Similar to the textbook Solow–Swan model, the production function is of Cobb–Douglas type:

${\displaystyle Y(t)=K(t)^{\alpha }H(t)^{\beta }(A(t)Fifty(t))^{1-\blastoff -\beta },}$

where ${\displaystyle H(t)}$ is the stock of human capital, which depreciates at the same charge per unit ${\displaystyle \delta }$ every bit physical capital. For simplicity, they presume the same part of accumulation for both types of uppercase. Like in Solow–Swan, a fraction of the upshot, ${\displaystyle sY(t)}$ , is saved each period, simply in this case split up upwards and invested partly in concrete and partly in human upper-case letter, such that ${\displaystyle s=s_{K}+s_{H}}$ . Therefore, there are ii fundamental dynamic equations in this model:

${\displaystyle {\dot {1000}}=s_{K}k^{\blastoff }h^{\beta }-(n+g+\delta )k}$

${\displaystyle {\dot {h}}=s_{H}k^{\alpha }h^{\beta }-(n+chiliad+\delta )h}$

The balanced (or steady-country) equilibrium growth path is adamant by ${\displaystyle {\dot {k}}={\dot {h}}=0}$ , which ways ${\displaystyle s_{K}g^{\alpha }h^{\beta }-(due north+thousand+\delta )k=0}$ and ${\displaystyle s_{H}thousand^{\blastoff }h^{\beta }-(n+m+\delta )h=0}$ . Solving for the steady-state level of ${\displaystyle g}$ and ${\displaystyle h}$ yields:

${\displaystyle thousand^{*}=\left({\frac {s_{K}^{1-\beta }s_{H}^{\beta }}{n+g+\delta }}\right)^{\frac {one}{1-\alpha -\beta }}}$

${\displaystyle h^{*}=\left({\frac {s_{G}^{\alpha }s_{H}^{1-\alpha }}{n+one thousand+\delta }}\right)^{\frac {one}{ane-\alpha -\beta }}}$

In the steady state, ${\displaystyle y^{*}=(k^{*})^{\alpha }(h^{*})^{\beta }}$ .

Econometric estimates [edit]

Klenow and Rodriguez-Clare cast doubt on the validity of the augmented model considering Mankiw, Romer, and Weil's estimates of ${\displaystyle {\beta }}$ did not seem consistent with accepted estimates of the effect of increases in schooling on workers' salaries. Though the estimated model explained 78% of variation in income across countries, the estimates of ${\displaystyle {\beta }}$ implied that human uppercase's external furnishings on national income are greater than its direct effect on workers' salaries.^[19]

Accounting for external furnishings [edit]

Theodore Breton provided an insight that reconciled the large outcome of human capital from schooling in the Mankiw, Romer and Weil model with the smaller event of schooling on workers' salaries. He demonstrated that the mathematical properties of the model include meaning external furnishings between the factors of product, because human uppercase and physical capital are multiplicative factors of product.^[20] The external upshot of man capital on the productivity of physical capital is evident in the marginal product of physical capital:

${\displaystyle MPK={\frac {\partial Y}{\partial Thou}}={\frac {\alpha A^{1-\alpha }(H/L)^{\beta }}{(K/50)^{1-\alpha }}}}$

He showed that the large estimates of the result of human capital letter in cantankerous-state estimates of the model are consistent with the smaller effect typically constitute on workers' salaries when the external effects of human capital on physical capital and labor are taken into account. This insight significantly strengthens the case for the Mankiw, Romer, and Weil version of the Solow–Swan model. Near analyses criticizing this model neglect to account for the pecuniary external effects of both types of upper-case letter inherent in the model.^[20]

Total cistron productivity [edit]

The exogenous rate of TFP (full cistron productivity) growth in the Solow–Swan model is the residual subsequently bookkeeping for capital letter accumulation. The Mankiw, Romer, and Weil model provide a lower estimate of the TFP (remainder) than the bones Solow–Swan model because the improver of man capital letter to the model enables capital accumulation to explain more of the variation in income across countries. In the basic model, the TFP remainder includes the effect of human majuscule because human capital is not included as a factor of product.

Conditional convergence [edit]

The Solow–Swan model augmented with homo capital predicts that the income levels of poor countries will tend to catch up with or converge towards the income levels of rich countries if the poor countries take like savings rates for both concrete capital and human capital as a share of output, a process known every bit conditional convergence. Even so, savings rates vary widely across countries. In item, since considerable financing constraints exist for investment in schooling, savings rates for human uppercase are likely to vary as a office of cultural and ideological characteristics in each country.^[21]

Since the 1950s, output/worker in rich and poor countries generally has not converged, but those poor countries that accept greatly raised their savings rates have experienced the income convergence predicted by the Solow–Swan model. As an example, output/worker in Japan, a country which was once relatively poor, has converged to the level of the rich countries. Japan experienced high growth rates after it raised its savings rates in the 1950s and 1960s, and it has experienced slowing growth of output/worker since its savings rates stabilized around 1970, every bit predicted by the model.

The per-capita income levels of the southern states of the Us have tended to converge to the levels in the Northern states. The observed convergence in these states is too consistent with the conditional convergence concept. Whether absolute convergence between countries or regions occurs depends on whether they have similar characteristics, such as:

• Teaching policy
• Institutional arrangements
• Free markets internally, and trade policy with other countries.^[22]

Additional evidence for conditional convergence comes from multivariate, cross-country regressions.^[23]

Econometric analysis on Singapore and the other "Due east Asian Tigers" has produced the surprising effect that although output per worker has been rising, almost none of their rapid growth had been due to ascent per-capita productivity (they take a depression "Solow remainder").^[v]

Encounter also [edit]

• Economic growth
• Endogenous growth theory

Notes [edit]

References [edit]

1. ^ Acemoglu, Daron (2009). "The Solow Growth Model". Introduction to Modern Economic Growth . Princeton: Princeton University Press. pp. 26–76. ISBN978-0-691-13292-1.
2. ^ ^{a b c} Solow, Robert M. (February 1956). "A contribution to the theory of economic growth". Quarterly Journal of Economics. 70 (1): 65–94. doi:10.2307/1884513. hdl:10338.dmlcz/143862. JSTOR 1884513. Pdf.
3. ^ ^{a b} Swan, Trevor Due west. (November 1956). "Economic growth and capital letter aggregating". Economic Tape. 32 (ii): 334–361. doi:x.1111/j.1475-4932.1956.tb00434.ten.
4. ^ Solow, Robert M. (1957). "Technical change and the aggregate production function". Review of Economic science and Statistics. 39 (iii): 312–320. doi:10.2307/1926047. JSTOR 1926047. Pdf.
5. ^ ^{a b} Haines, Joel D.; Sharif, Nawaz M. (2006). "A framework for managing the sophistication of the components of technology for global competition". Competitiveness Review: An International Business organization Periodical. 16 (2): 106–121. doi:10.1108/cr.2006.xvi.2.106.
6. ^ ^{a b} Eric Frey (2017). "The Solow Model and Standard of Living". Undergraduate Journal of Mathematical Modeling: One + Two. 7 (two (Commodity 5)): Abstract. doi:10.5038/2326-3652.seven.2.4879. ISSN 2326-3652. OCLC 7046600490. Archived from the original on September 22, 2017.
7. ^ Blume, Lawrence E.; Sargent, Thomas J. (2015-03-01). "Harrod 1939". The Economic Journal. 125 (583): 350–377. doi:ten.1111/ecoj.12224. ISSN 1468-0297.
8. ^ ^{a b} Besomi, Daniele (2001). "Harrod's dynamics and the theory of growth: the story of a mistaken attribution". Cambridge Journal of Economics. 25 (1): 79–96. doi:x.1093/cje/25.1.79. JSTOR 23599721.
9. ^ Harrod, R. F. (1939). "An Essay in Dynamic Theory". The Economical Journal. 49 (193): 14–33. doi:10.2307/2225181. JSTOR 2225181.
10. ^ Halsmayer, Verena; Hoover, Kevin D. (2016-07-03). "Solow's Harrod: Transforming macroeconomic dynamics into a model of long-run growth". The European Periodical of the History of Economical Thought. 23 (4): 561–596. doi:10.1080/09672567.2014.1001763. ISSN 0967-2567. S2CID 153351897.
11. ^ Romer, David (2006). Avant-garde Macroeconomics. McGraw-Hill. pp. 31–35. ISBN9780072877304.
12. ^ Baumol, William J. (1986). "Productivity Growth, Convergence, and Welfare: What the Long-Run Data Show". The American Economic Review. 76 (five): 1072–1085. JSTOR 1816469.
13. ^ Barelli, Paulo; Pessôa, Samuel de Abreu (2003). "Inada conditions imply that production function must be asymptotically Cobb–Douglas" (PDF). Economics Messages. 81 (three): 361–363. doi:10.1016/S0165-1765(03)00218-0. hdl:10438/1012.
14. ^ Litina, Anastasia; Palivos, Theodore (2008). "Exercise Inada weather imply that production function must exist asymptotically Cobb–Douglas? A annotate". Economics Letters. 99 (3): 498–499. doi:10.1016/j.econlet.2007.09.035.
15. ^ ^{a b} Romer, David (2011). "The Solow Growth Model". Advanced Macroeconomics (Fourth ed.). New York: McGraw-Hill. pp. 6–48. ISBN978-0-07-351137-five.
16. ^ Caselli, F.; Feyrer, J. (2007). "The Marginal Production of Upper-case letter". The Quarterly Journal of Economics. 122 (2): 535–68. CiteSeerX10.1.ane.706.3505. doi:x.1162/qjec.122.2.535. S2CID 9329404.
17. ^ Lucas, Robert (1990). "Why doesn't Capital letter Flow from Rich to Poor Countries?". American Economic Review. 80 (2): 92–96.
18. ^ Mankiw, N. Gregory; Romer, David; Weil, David Due north. (May 1992). "A Contribution to the Empirics of Economical Growth". The Quarterly Journal of Economics. 107 (two): 407–437. CiteSeerX10.1.1.335.6159. doi:10.2307/2118477. JSTOR 2118477. S2CID 1369978.
19. ^ Klenow, Peter J.; Rodriguez-Clare, Andres (January 1997). "The Neoclassical Revival in Growth Economics: Has Information technology Gone Too Far?". In Bernanke, Ben S.; Rotemberg, Julio (eds.). NBER Macroeconomics Annual 1997, Volume 12. National Bureau of Economic Inquiry. pp. 73–114. ISBN978-0-262-02435-8.
20. ^ ^{a b} Breton, T. R. (2013). "Were Mankiw, Romer, and Weil Right? A Reconciliation of the Micro and Macro Effects of Schooling on Income" (PDF). Macroeconomic Dynamics. 17 (5): 1023–1054. doi:ten.1017/S1365100511000824. hdl:10784/578. S2CID 154355849.
21. ^ Breton, T. R. (2013). "The role of teaching in economic growth: Theory, history and current returns". Educational Enquiry. 55 (2): 121–138. doi:ten.1080/00131881.2013.801241. S2CID 154380029.
22. ^ Barro, Robert J.; Sala-i-Martin, Xavier (2004). "Growth Models with Exogenous Saving Rates". Economical Growth (Second ed.). New York: McGraw-Hill. pp. 37–51. ISBN978-0-262-02553-ix.
23. ^ Barro, Robert J.; Sala-i-Martin, Xavier (2004). "Growth Models with Exogenous Saving Rates". Economic Growth (Second ed.). New York: McGraw-Colina. pp. 461–509. ISBN978-0-262-02553-nine.

Further reading [edit]

• Agénor, Pierre-Richard (2004). "Growth and Technological Progress: The Solow–Swan Model". The Economic science of Aligning and Growth (2nd ed.). Cambridge: Harvard University Press. pp. 439–462. ISBN978-0-674-01578-4.
• Barro, Robert J.; Sala-i-Martin, Xavier (2004). "Growth Models with Exogenous Saving Rates". Economical Growth (Second ed.). New York: McGraw-Hill. pp. 23–84. ISBN978-0-262-02553-9.
• Burmeister, Edwin; Dobell, A. Rodney (1970). "1-Sector Growth Models". Mathematical Theories of Economical Growth. New York: Macmillan. pp. xx–64.
• Dornbusch, Rüdiger; Fischer, Stanley; Startz, Richard (2004). "Growth Theory: The Neoclassical Model". Macroeconomics (Ninth ed.). New York: McGraw-Hill Irwin. pp. 61–75. ISBN978-0-07-282340-0.
• Farmer, Roger East. A. (1999). "Neoclassical Growth Theory". Macroeconomics (Second ed.). Cincinnati: South-Western. pp. 333–355. ISBN978-0-324-12058-5.
• Ferguson, Brian S.; Lim, G. C. (1998). Introduction to Dynamic Economic Models. Manchester: Manchester University Press. pp. 42–48. ISBN978-0-7190-4996-5.
• Gandolfo, Giancarlo (1996). "The Neoclassical Growth Model". Economical Dynamics (Third ed.). Berlin: Springer. pp. 175–189. ISBN978-3-540-60988-9.
• Halsmayer, Verena (2014). "From Exploratory Modeling to Technical Expertise: Solow'south Growth Model as a Multipurpose Design". History of Political Economic system. 46 (Supplement one, MIT and the Transformation of American Economic science): 229–251. doi:10.1215/00182702-2716181. Retrieved 2017-11-29 .
• Intriligator, Michael D. (1971). Mathematical Optimalization and Economic Theory. Englewood Cliffs: Prentice-Hall. pp. 398–416. ISBN978-0-xiii-561753-3.
• van Rijckeghem Willy (1963) : The Structure of Some Macro-Economic Growth Models : a Comparison. Weltwirtschaftliches Archiv book 91 pp. 84–100

External links [edit]

• Solow Model Videos - 20+ videos walking through derivation of the Solow Growth Model's Conclusions
• Java applet where you tin can experiment with parameters and acquire near Solow model
• Solow Growth Model by Fiona Maclachlan, The Wolfram Demonstrations Project.
• A stride-by-step caption of how to understand the Solow Model
• Professor José-Víctor Ríos-Rull'south form at University of Minnesota

Source: https://en.wikipedia.org/wiki/Solow%E2%80%93Swan_model

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