Decentralized Decisions and Technological Progress: A Formal Proof

This paper provides attempts to formalize Hayek’s theory of knowledge. It has been theoretically shown that exponential income distribution is a spontaneous order of the well-functioning market economy. We show that this theoretical result is supported by the empirical evidence from the United Kingdom and China. In particular, we empirically show how the income structure of China evolved towards an exponential distribution after the market-oriented economic reformation. Furthermore, we strictly prove that, if the income structure of an economy obeys an exponential distribution, the income summation over all households leads to an aggregate production function with Hicks-neutral-like technical progress, in which the technology factor is exactly equal to society’s information stock that is a result of combining all of decentralized decisions.

Technology factor as society’s information stock: An elegant proof

It has been empirically observed that the income structure of the vast majority of populations in market-economy countries follows an exponential distribution. The empirical evidence has covered more than 66 countries, ranging from Europe to Latin America, North America, and Asia. Here, to further support exponential income distribution as a signature of the well-functioning market economy, we empirically show how the income structure of China evolved towards an exponential distribution after the market-oriented economic reformation. In particular, we strictly prove that, if the income structure of an economy obeys an exponential distribution, the income summation over all households leads to a neoclassical aggregate production function, in which the technology factor is exactly equal to society’s information stock. This finding provides an insight into understanding the underlying implication of technological progress.JEL Classification: O33; D31; D83; C46

Produkční funkce jako nástroj zobrazení ekonomické reality

The monograph develops the theory of production functions and their systematic typology. It looks at the relationship between inputs and outputs as a universal relationship that is used not only in economics but also in other disciplines. In addition to the static production function, special attention is paid to the dynamization of individual quantities and the issue of expressing the effect of changes in these quantities on the change in production. It is explained why in the aggregate production function expressed through aggregate factor input and aggregate factor productivity it is necessary to use a multiplicative relationship, why the multiplicative link is also suitable in terms of total input factor and why the share of weights in labor and capital should be the same. The use of the production function is demonstrated on the development of the economies of the USA, China and India and on the ten largest economies of the world in terms of absolute GDP, on cryptocurrencies and on the so-called farming role.In addition to a comprehensive overview of production functions, the monograph also enriches new ideas that arose during long-term computational and analytical activities of economic and business. Particularly innovative is the generalization of the production function to any system with variable inputs and outputs. The production function can thus be recognized in many identities. The original intention of the research was to examine the intensity of economic development, but it turned out that it is closely related to production functions. The impetus for this research comes from Prof. Ing. František Brabec, DrSc. a genius mathematician, designer, economist and manager, former general director of Škoda in Pilsen and later rector of ČVÚT.The presented typology of production functions is not limited to one area of economics, but goes beyond it. The monograph respects the definition of the static production function as the maximum amount of production that can be produced with a given number of production factors. On this function, which can be effectively displayed using polynomial functions of different orders,significant points can be systematically defined, ie the inflection point, the point of maximum efficiency, the point of maximum profit and the point of maximum production. The purpose is to optimize the number of inserted production factors. The text is preferred the point with the greatest effectiveness. If this quantity does not correspond, for example, to demand, it is possible to choose another technology, which will be reflected in a shift in the static production function. At the same time, the important points of these functions describe the trajectory, which has the nature of a dynamic production function. For a dynamic production function, the crucial question is how the change in individual factors contributes to the overall change in output. If the production function is expressed through inputs and their efficiency, dynamic parameters of extensibility and intensity can be defined, which exactly express the effect of changes in inputs and the effect of changes in efficiency on changes in outputs for all possible situations. Special attention is paid to the aggregate production function. It explains why it should be expressed as the product of the aggregate input factor (TIF) and aggregate factor productivity (TFP), or why the term TIF should be expressed as a weighted product of labor and capital, in which the value of labor and capital weights could be and identical. The monograph here surpasses the traditional additive view of the multi-factor production function by proposing a multiplicative link, which also allows the derivation of growth accounting, but with a new interpretation of weights and (1-), which do not need to be calculated for each subject and each year.The time production function is used to forecast the GDP development of the US, China and India economies until 2030 and 2050, respectively. It is also predicted an increase in the absolute GDP of Indonesia, a stable position of Russia and the loss of the elite position of Japan and Germany.The monograph also deals with the hitherto unresolved question of whether, even in economics, it is also necessary in certain circumstances to take into account a phenomenon called quantization in physics. It turns out that quantization is a common thing in economics, which is documented on specific forms of production functions that respect quantization in economics.The monograph also deals with the relationship between the efficiency of an individual given the use of a certain point on a specific static production function and common efficiency, ie all actors together. These examples assume limited resources. The sum of the outputs of all actors depends on how the actors share these limited resources. It can be expected that there will be at least one method of distribution that will bring the highest sum of outputs (products, crops) of all actors. This result, however, also depends on the shape of the production functions. This is investigated using EDM, i.e.elementary distribution models. EDM for polynomial production functions of the 2nd to 5th order are not yet published in summary. Of the new findings, they are the most interesting. When using two polynomial production functions, the EDM boundary becomes linear if the inflection point is used for both production functions. If we are above the inflection point, the EDM is properly concave. It turned out that the "bending" of the production function in the region of the inflection point can be modeled using a quantity of the order of the respective polynomial. The higher the order of the polynomial, the higher the deflection can be achieved. This proved to be a very important finding in modeling specific production functions. This effect cannot be achieved by combining other parameters.

Effect of economic sectors on employment in Sub-Saharan Africa.

The motif of this study was to determine the effect of economic sectors on employment in Sub-Saharan Africa, given that the Sub-Saharan African region had had about two decades of sustained economic growth. Thirty Sub-Saharan African countries were used in this study, their data that was obtained and used spanning from the year 1990 to the year 2015. The study made use of the traditional neo-classical aggregate production function in the estimation of the regression results. The software program that was used in data analysis was STATA. Hausman test was undertaken and it determined that fixed effects estimations were preferred to random effect and as a result fixed effects were utilized in the study in carrying out regression analysis. On effect of economic sectors on employment, foreign direct investment was found to negatively influence employment though the influence was not statistically significant. The export and agriculture variables negatively and statistically significantly influenced employment. All the other variables in the study were found to positively and statistically significantly influence employment. Empirical results established that the gender gap in employment was maintained in the whole period of the study with more men being employed than women.

Method for assessing the results of hierarchical socio-economic systems’ functioning based on the aggregated production function

The article presents a method that develops a methodology for assessing the functioning of hierarchical socio-economic systems. The methodology includes formalized description of the object of research and the construction of partial and integral performance indicators. Performance indicators are calculated using production functions. The method is based on an algorithm for constructing an aggregated production function, which is used to calculate the normative (expected) value of the result of the functioning of the object of research. Using the example of the regions in Central Federal District and data for 2007–2016 testing and comparative analysis of four algorithms for estimating the parameters of the aggregate production function in the construction of the integral indicator are carried out. The gross regional product for the NACE sections (C, D and E) was chosen as effective indicators. The scientific novelty of the study is as follows. Three algorithms for constructing the distribution density of an aggregated random variable, which is a combination of residuals from econometric equations that describe the particular results of the functioning of elements of a hierarchical socio-economic system, are proposed and tested. The distribution density is used to find the parameters of the aggregated production function. For the two-dimensional case, analytical expression of the corresponding probability distribution density is obtained. The conclusion about the possibility of using the method to evaluate the results of the functioning of hierarchical socio-economic systems is substantiated.

Modeling Trade Tensions

In this paper, we investigate the mechanisms through which import tariffs impact the macroeconomy in two large scale workhorse models used for quantitative policy analysis: a computational general equilibrium (CGE) model (Purdue University GTAP model) and a multi-country dynamic stochastic general equilibrium (DSGE) model (IMF GIMF model). The quantitative effects of an increase in tariffs reflect different mechanisms at work. Like other models in the trade literature, in GTAP higher tariffs generate a loss in terms of output arising from an inefficient reallocation of resources between sectors. In GIMF instead, as in other DSGE models, tariffs act as a disincentive to factor utilization. We show that the two models/channels can be broadly interpreted as capturing the impact of tariffs on different components of a country’s aggregate production function: aggregate productivity (GTAP) and factor supply/utilization (GIMF). We discuss ways to combine the estimates from these two models to provide a more complete assessment of the macro effects of tariffs.

Equilibrium and -efficient fertility with increasing returns to population and endogenous mortality

A general equilibrium model that characterizes the gap between optimal and equilibrium fertility and investment in human capital is developed. The aggregate production function exhibits increasing returns to population arising from specialization, but households face a quantity–quality trade-off when choosing their fertility and how much education these children receive. We show that equilibrium fertility is too low and investment per child is too high, in contrast to a current planner who internalizes the externality of current fertility on the next generation's productivity. We next introduce mortality of young adults in the model and assume that households have a precautionary demand for children. Human capital investment lowers next generation mortality. This model endogenously generates a demographic transition but, since households do not internalize the negative effects of human capital on mortality, the equilibrium demographic transition takes place many years later than the efficient solution. We show that ${\rm {\cal A}}$-efficient fertility and human capital investment pair can switch; in high-mortality regimes, ${\rm {\cal A}}$-efficient fertility is lower than equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is higher than equilibrium investment. In the zero mortality regime, however, ${\rm {\cal A}}$-efficient fertility exceeds equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is lower than the equilibrium choice.

Human Capital and Macroeconomic Development: A Review of the Evidence

The role of human capital in facilitating macroeconomic development is at the center of both academic and policy debates. Through the lens of a simple aggregate production function, human capital might increase output per capita by directly entering in the production process, incentivizing the accumulation of complementary inputs, and facilitating the adoption of new technologies. This paper discusses the advantages and limitations of three approaches that have been used to evaluate the empirical importance of these channels: cross-country regressions, development accounting, and quantitative models. The key findings in the literature are reviewed and some of them are replicated using updated data. The bulk of the evidence suggests that human capital is an important determinant of cross-country income gaps, especially when its measurement is broadened to go beyond simple proxies of educational attainment. The paper concludes by highlighting policy implications and promising avenues for future work.

Corruption and Economic Growth: The Case of Portugal

In this paper we investigate the impact of corruption on economic growth in Portugal over the period 1980-2018. The empirical approach makes use of a VAR model inspired by the standard Cobb-Douglas aggregate production function. The VAR model includes the capital stock, hours worked, total factor productivity and the corruption perceptions index (CPI) of Transparency International. The CPI combines several sources of information on the level of corruption in each country. The scale of this index goes from 0, the highest level of corruption, to 10, the lowest level. The magnitude of the estimated effect of corruption on economic growth in the unrestricted VAR model is large (and positive), but statistically not significantly different from zero. However, the results from the estimation of a structural VAR model with economically plausible long-run restrictions indicate modest gains from reducing corruption.