Introduction to Romer and Solow models of sustainable growth
The long-term growth is explained by the Romer and Solow models. The growth rate in the long-run is zero as per the Romer model. Nevertheless, the growth rate in the long-run is modest and positive as per the Solow model. Altogether, these two indicate that the growth rate in the long-run is positive and fast. The Solow model describes the economic phenomenon that the population size is expanding day by day, and that the amount of output should rise in accordance with population expansion, but with the desires of people. It emphasizes the pace of growth, the rate of savings, and the rate of technological advancement. It is presumed that the savings rates and population growth are constant, and that the output quantity follows a constant return to scale. The Romer model, on the other hand, overlooks the microeconomic elements that influence the growth rate. This focuses solely on macro factors. The Romer model is a former economic model, whereas the Solow model is an exogenous model. This concept illustrates how technological improvements are the result of research and entrepreneurs who backed economic development incentives.
The Solow Model explains why impoverished nations with less capital expand faster than affluent ones with more capital (transition dynamics). 2) Increasing an economy’s saving/investment rate raises GDP per capita. The Solow Model cannot explain 1) why there is long-run consistent growth. 2) Income disparities across countries. TFP is still required to account for variances (Boyko et al., 2019). A is an exogenous model, which means that external variables are included while determining economic growth. Economic development cannot be achieved without technical innovation as per Solow model. In contrast, the Solow model was unable to describe the significance of human capital in determining economic growth. If the savings rate is high, the economy will have a big capital stock and consequently a high level of output; conversely, if the saves rate is low, the economy will have a low level of output. Changes in capital stock, in turn, can contribute to economic development. According to the Solow model, countries with good population increase will have lower levels of production per person.
The main economic phenomena explained by Romer Model is Sustained Growth in the long run (Etro, 2019). The essential economic phenomena behind the Romer model are that the ratio of capital goods to population serves to promote long-run economic development. The Romer model of endogenous growth theory demonstrates that technical innovation via the development of new ideas is what drives long-run sustainable growth. As a result, it is understandable why the fact of technological progress is so important to the legitimacy of endogenous growth theory. If technical innovation does not rise despite an increase in the number of personnel working in R&D, the Romer model loses credibility since it says that the expansion of technology (ideas) will always result in consistent growth in production over time. However, it is important to consider whether the Romer model’s forecast of constant rates of growth will be realized in practice.
The Solow Model of sustainable growth
There are two equations in a basic Romer Model, that is ideas production and goods production
Goods Production: Yt = AtLy, t (1)
Ideas Production: ?At+1 = AtLa, t (2)
Total labor available in the economy is given by = Ly + La, t and La, t = γ is used in the ideas sector. Hence, ideas production and goods production equation can be rewritten as:
Goods production: Yt = At(1-γ)
Ideas Production: ?At+1 = Atγ
We wish to explain GDP per capita as the aggregate variable of interest with this model. We should first write GDP per capita in terms of model parameters (A0, γ, , t) in order to solve the model which is our main goal (Leon-Ledesma, & Moro, 2020).
Yt = At(1-γ)
And placing it into per Capita form
We can now turn to ideas production function to remove At term. The function for ideas Production is:
?At+1 = Atγ
Remember that ?At+1/ At is the expression for rate of change. Hence;
Since, we know the growth rate will enable us to write At as
At = A0(1+gA) t
Ultimately, we can substitute the expression back to equation (3)
yt = A0(1 + gA)t(1-γ)
A graph of effect of a decrease in proportion of labor
The reallocation of labor will affect both growth rate gA = and GDP level yt = A0(1 + gA)t(1-γ). The intuition is that if there are more workers who builds actual goods, and so, we will have fewer workers who will be creating new ideas. The more workers who build goods will cause an increase in the amount goods due to the one-time shift labor, this is known as the level effect. Whilst fewer workers who create ideas is going to lower the general growth rate of ideas as well as GDP permanently, this is known as the growth effect.
The economic interpretation is that when individuals are still in school, they are in a position to supply either market. Nevertheless, they might give contribution to the stock of ideas. The labor that has taught these students might give contribution to the stock of ideas as well (Meijerink & Keegan, 2019).
The above question is identical to 2a) only the fact that a substitution for Ht should occur first.
?At+1 = AtHtLa, t. (4)
Ht = Ls,t (5)
?At+1 = AtL8, tLa, t (6)
We can substitute in Ls,t = 0.25 and La,t = 0.25L produces
?At+1 = At(0.25)2 (7)
?At+1 = ¯zAt0.06252 (8)
The growth rate of the economy becomes gA = 0.06252 = 625 while the GDP per capita becomes:
Yes, the growth rate of the economy is larger in this particular economy compared to that of the basic model. The basic model predicts that gA = γ100. Since 0 < γ < 1, it should be the case of the economy with human capital assumption grows faster (Saydaliyev et al., 2020).The Bathub Model and inverse Say’s Law
The Romer Model of sustainable growth
Et + Ut =
?Ut+1 = sEt − fUt
Steady state level of unemployment (?Ut+1 = 0)
?Ut+1 = 0
sEt − fUt = 0
sEt = fUt
s( − Ut) = fUt
s = (f + s)Ut
this is the steady state of unemployment
Supposing separation rate rises s will increase given steady state level of employment and findings r numerator will increase and steady state level of unemployment will increase (Jin, 2020). An aid of a calculus can helps to illustrate this;
Hence, if separation rate increases, ceteris paribus then steady state of unemployment increases.
Suppose the jobseeker program is decided and providing subsidies to firms to pass on their employees finding rate will be more because if the firm hires the employees, then those who unemployed would get work and as a result the finding rate will increase that’s why f will rise and the whole of right-hand side will fall then steady state of unemployment will fall (Williams & Lück-Vogel, 2020).
Hence, as finding rate increases then steady state of unemployment will fall.
Now, the jobseeker program is implemented then subsidies are given to those who are currently working. Hence, it will directly affect the separation rate s since it doesn’t aid to find a job instead it aids those people who are losing their jobs. Hence, it increases the separation rate and so the steady state of unemployment would rise as I have illustrated above.
The statement is false. It depends on the level of the minimum wage and whether it is indexed to inflation. Suppose the minimum wage is set below the equilibrium real wage it has no effect on the natural state (11) (Bonin et al., 2020). If it set above the natural rate, but not indexed to inflation, then it only has a temporary effect on the unemployment wage over time and leave the natural rate unchanged. The only case where it has an effect on the natural rate of unemployment is case 1 when it is assumed that the nominal wage is indexed to inflation so that it holds its real value (Lavecchia, 2020).
Conclusion
To summarize, taking cognizance of technical growth is critical for the legitimacy of endogenous growth theory, because the theory is intrinsically dependent on technological growth. At the crux of the issue, the essential question is whether huge resources put in product development are often a positive idea. The Romer model would indicate that this is often the case, but we cannot draw those inferences without a greater knowledge of the nature of scientific advance.
References
Bonin, H., Isphording, I. E., Krause-Pilatus, A., Lichter, A., Pestel, N., & Rinne, U. (2020). The German statutory minimum wage and its effects on regional employment and unemployment. Jahrbücher Für Nationalökonomie Und Statistik, 240(2-3), 295-319.
Boyko, A. A., Kukartsev, V. V., Tynchenko, V. S., Eremeev, D. V., Kukartsev, A. V., & Tynchenko, S. V. (2019, November). Simulation-dynamic model of long-term economic growth using Solow model. In Journal of Physics: Conference Series (Vol. 1353, No. 1, p. 012138). IOP Publishing.
Etro, F. (2019). The Romer model with monopolistic competition and general technologies. Economics Letters, 181, 1-6.
Jin, W. L. (2020). Generalized bathtub model of network trip flows. Transportation Research Part B: Methodological, 136, 138-157.
Lavecchia, Adam M. “Minimum wage policy with optimal taxes and unemployment.” Journal of Public Economics 190 (2020): 104228.
Leon-Ledesma, M., & Moro, A. (2020). The rise of services and balanced growth in theory and data. American Economic Journal: Macroeconomics, 12(4), 109-46.
Meijerink, J., & Keegan, A. (2019). Conceptualizing human resource management in the gig economy: Toward a platform ecosystem perspective. Journal of managerial psychology.
Williams, L. L., & Lück-Vogel, M. (2020). Comparative assessment of the GIS based bathtub model and an enhanced bathtub model for coastal inundation. Journal of Coastal Conservation, 24(2), 1-15.
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