Two-sector Economy Research Articles

Optimal Control in the Resource Allocation Problem for a Two-Sector Economy with a CES Production Function

We consider the resource allocation problem in a two-sector economy with a Constant Elasticity of Substitution (CES) production function on a given sufficiently long finite planning horizon. The performance criterion being optimized is one of the phase coordinates at the terminal time. The scalar control u satisfies the geometrical constraint u ∈ [0, 1]. The optimal control contains a singular section. Analyzing the Pontryagin maximum principle boundary-value problem we find the extremal triple and prove its optimality using a special representation of the functional increment (the theorem of sufficient conditions of optimality in terms of maximum-principle constructs). The solution is constructed with the aid of a Lambert special function y = W(x), that solves the equation ye y = x. The optimal control consists of three sections: the initial section that involves motion toward the singular ray L sng = {x 1 = x 2 > 0} , the singular section that involves motion along the singular ray, and terminal section that involves motion under zero control. When the initial state is on the singular ray, the optimal control consists of two sections — singular and terminal. The article is related to a number of the authors’ publications using other production function.

The effect of economic cycles on job satisfaction in a two-sector economy

Economic growth improves the material well-being of all workers. However, when remuneration in the public sector is less sensitive to economic cycles than in the private sector, as is typically the case, economic growth will worsen the position of workers in the public sector relative to workers in the private sector, even though their income improves in absolute terms. As a result, job satisfaction may be countercyclical in the public sector. We test this counterintuitive hypothesis in a real-effort laboratory experiment that simulates an economy with two sectors differing only in their remuneration scheme. Economic cycles are introduced in order to test for their effect on job satisfaction and productivity in each sector. We find that job satisfaction in the “public” sector is negatively correlated with the state of the economy. This effect, however, does not carry over to productivity: even though an increase in a worker's productivity in the public sector reduces his relative income, in comparison to a similar private sector worker, we find that this does not have a negative effect on job satisfaction.

Discounted Agricultural Growth in South Africa

This paper examines impacts of appropriate resource allocation on subsistence level output. This study uses a stylized Coase Bargaining model and data from the South African Reserve bank to support the second welfare theorem. Back of the envelope calculations indicate the opportunity cost of manufacturing output has been the 20% discount in agricultural output in South Africa since 1968. This paper offers an exercise that can be implemented in developing nations having institutions resulting in two-sector economies. Moreover, the methods used here will help policy makers to estimate an appropriate value for wealth transfers.

Market participation in a two-sector Diamond-Dybvig economy

Purpose This paper aims to reconsider the role of asset-market participation in Diamond-Dybvig economies, to reconcile the existence of asset markets as a channel for financial integration with the distortions that they might impose on the banking system. Design/methodology/approach The paper is a two-sector Diamond-Dybvig model of financial intermediation, with comparative advantages in the investment technologies, and introduces the possibility for the depositors to participate in an economy-wide asset market, when they can trade a bond without being observed by their banks. Findings The two-sector competitive banking equilibrium with hidden trades is not equivalent to autarky, is the unique Nash equilibrium of a “participation game” and is a constrained efficient. Originality/value This paper is the first to characterize the equilibrium of a two-sector Diamond-Dybvig economy with hidden trading in the asset market, and produces novel results, in contrast to the existing literature, with respect to the rationale for the existence of a financial system, its coexistence with asset markets and its efficiency. These conclusions also have important implications in terms of policy, in particular, regarding the case for the introduction of financial regulation.

Energy Transition Under Irreversibility: A Two-Sector Approach

This paper analyses the optimal energy transition of a two-sector economy (energy and final goods) under irreversible environmental catastrophe. First, it proposes a general appraisal of optimal switching problems related to energy transition showing: (1) the possibility of a catastrophe due to accumulation of pollution; and (2) technological regimes with the adoption of renewable energy. Second, it numerically shows that for given baseline parameter values, the most profitable energy transition path may correspond to the one in which the economy starts using both resources, crosses the pollution threshold by losing a part of its capital, and never adopts only clean energy. Third, it extends the model to allow for additional investment in energy saving technologies. We then find that this additional investment favours full transition to the sole use of renewable energy. It is then profitable to take advantage of these synergies by jointly promoting deployment of clean energy and providing incentives for investment in energy saving technologies.

A short-run model of a two-sector economy with tourism and unemployment

The article develops a Keynesian style short-run model of a two-sector economy, comprising an industrial sector and a tourism sector. Industrial goods can be consumed, invested, exported, and imported. Tourism services produced in the tourism sector are consumed by foreigners and domestic residents. The two sectors are linked via consumption of domestic residents, which, in the Keynesian tradition, depends positively on disposable income, and via investment. An increase in sectoral production (industrial and tourism sector) stimulates consumption and investment expenditures. Output is completely demand determined, and resulting in unemployment in case of a lack of demand is Keynesian. Via the production function, changes in sectoral outputs translate into changes in unemployment. Focusing on the short run, prices are held constant. The article provides a graphical apparatus to analyze different types of sectoral demand shocks. We investigate an increase in foreigners’ demand for domestically produced tourism services (inbound tourism). Depending on the exchange rate regime or monetary policy, sectoral outputs and unemployment rates may move in tandem or in opposite directions. Our results support the popular view that tourism can reduce unemployment.

Net energy ratio, EROEI and the macroeconomy

In an input–output model of a two-sector economy (energy and manufacturing), we analyse the macroeconomic implications of the quality of secondary energy production. We measure it by the net energy ratio (NER for short), i.e. the fraction of produced energy available for net final production. NER is shown to be related to the EROEI concept encountered in energy science and to affect (a) the energy intensiveness of final output, (b) the capital requirements of the two sectors of the economy and the aggregate capital–output ratio, and (c) the rate of capital accumulation and the growth rate of the economy at given saving rate. As a consequence, an energy transition characterized by a decreasing NER would exert a drag on economic growth.

VOTING ONESELF INTO A CRISIS

We suggest that voters' lack of recognition of complex economic links may give rise to economic policies that eventually lead to a crisis. We consider a two-sector economy in which a majoritarian political process determines governmental regulation in one sector: a minimum nominal wage. If voters recognize general equilibrium feedbacks, workers favoring market-clearing wages will form a majority across sectors. If voters take into account only direct effects in the regulated sector, not only workers that enjoy minimum wages but also workers in the other sector are willing to vote for wage rises in each period. The reason is that they expect higher real wages for themselves, too. The political process leads to constantly rising unemployment and tax rates. The resulting crisis may trigger new insights into economic relationships on the part of the voters and may reverse bad times.

The political economy of deforestation when distributional interests matter - a dynamic approach

Market and political forces are analysed in a two-sector political economy model as main determinants of deforestation and land conversion decisions. User groups involve in lobby and pressure activities to influence the decision maker to release land towards their specific sectors. The interaction is modelled as a cooperative bargaining process and the Nash solution corresponds to the political organisational equilibrium where the interests of all parties, including that of the decision maker are maximised. Using dynamic theory, the steady-state demand for forest land is derived, and the conclusion is that deforestation and land conversions are adjustment processes based on distributional interests, lobbying and the decision maker's self-interest motive, mainly to enhance the welfare of user groups.

Special modes in a two-sector economy model with an integral utility function

In this work, we study a two-sector economic model with the Cobb–Douglas production function on an infinite planning horizon where the utility function is a functional of an integral form and a Lagrangian of a logarithmic type. A one-dimensional equation is obtained that depends only on the coefficients of elasticity and amortization, and determines the possible special modes. The special modes are described in analytical form.

Boundary value problem of Pontryagin’s maximum principle in a two-sector economy model with an integral utility function

An infinite-horizon two-sector economy model with a Cobb–Douglas production function and a utility function that is an integral functional with discounting and a logarithmic integrand is investigated. The application of Pontryagin’s maximum principle yields a boundary value problem with special conditions at infinity. The search for the solution of the maximum-principle boundary value problem is complicated by singular modes in its optimal solution. In the construction of the solution to the problem, they are described in analytical form. Additionally, a special version of the sweep method in continuous form is proposed, which is of interest from theoretical and computational points of view. An important result is the proof of the optimality of the extremal solution obtained by applying the maximum-principle boundary value problem.

Burdett–Mortensen model of on-the-job search with two sectors

The focus of this paper is on the steady state of a two-sector economy with undirected search where employed and unemployed workers can search for jobs, both within a sector and between the sectors. As in the one-sector model, on-the-job search generates wage dispersion among homogeneous workers. The analysis of the two-sector model uncovers a property called constant tension that is responsible for analytical tractability. We characterize the steady state in all cases with constant tension. When time discounting vanishes, constant tension yields the endogenous separation rate in each sector as a linear function of the present value for a worker. The one-sector economy automatically satisfies constant tension, in which case the linear separation rate implies that equilibrium offers of the worker value are uniformly distributed. Constant tension also has strong predictions for worker transitions and value/wage dispersion, both within a sector and between the two sectors. When constant tension does not hold, we compute the steady state numerically and illustrate its properties.

Burdett-Mortensen Model of On-the-Job Search with Two Sectors

The focus of this paper is on the steady state of a two-sector economy with undirected search where employed and unemployed workers can search for jobs, both within a sector and between the sectors. As in the one-sector model, on-the-job search generates wage dispersion among homogeneous workers. The analysis of the two-sector model uncovers a property called constant tension that is responsible for analytical tractability. We characterize the steady state in all cases with constant tension. When time discounting vanishes, constant tension yields the endogenous separation rate in each sector as a linear function of the present value for a worker. The one-sector economy automatically satisfies constant tension, in which case the linear separation rate implies that equilibrium offers of the worker value are uniformly distributed. Constant tension also has strong predictions for worker transitions and value/wage dispersion, both within a sector and between the two sectors. When constant tension does not hold, we compute the steady state numerically and illustrate its properties.

Sectoral Imbalance in Two-Sector Economy with Mobility Constraint and Firm Migration

We consider a two-sector economy with a low-technology agriculture sector (sector A) and a high-technology manufacture sector (sector M). We investigate the scenario with mobility constraint that worker in sector A, when unemployed, has to afford the migration cost in order to move to sector M. By developing an agent-based two-sector model with computational simulation, we show that productivity growth localized at agriculture sector with mobility constraint leads to a decrease of agricultural market price, sectoral imbalance that workers are trapped unemployed in agriculture sector, and the overall economy experiencing economic downturn. In particular, localized productivity growth leads to both sectors bearing with high unemployment, low level of aggregate output, and low level of aggregate real wage income. Regarding remedy for the economic downturn under this scenario, we investigate the policy of firm migration such that agriculture firms can migrate to manufacture sector together with their employed workers. Agent-based study shows that this policy restores employment in both sectors, with a side effect of an increase of agricultural market price.

Structural change and inter-sectoral mobility in a two-sector economy

This paper studies the dynamics of a two-sector economy (with a natural resource-dependent sector and an industrial sector) characterized by free inter-sectoral labor mobility and heterogeneity of agents (workers and entrepreneurs). In such a context, we analyze the effects of the deterioration of natural resources, caused by the production activity of both sectors, on inter-sectoral movements of the labor force (structural changes), on ecological dynamics and on the revenues of workers and entrepreneurs. As in the seminal work by Matsuyama (1992), we obtain that a low productivity of labor in the resource-dependent sector can fuel the industrialization process. However, differently from Matsuyama, in our model the industrialization process may give rise to a reduction in workers’ revenues if the contribution to environmental depletion of the industrial sector, per unit of product, is higher than that of the resource-dependent one.

Влияние размера рынка на формирование предпринимательского сектора и уровень неравенства среди индивидов при неэластичном выпуске каждой фирмы

This paper is addressed to explanation of impact of market size on selection into entrepreneurship and inequality within two-sector economy with secluded good, populated by individuals with additively-separable preferences, defined by power specification of utility function. Individuals are differentiated by two characteristics: productivity and type of variety, which can be potentially produced by given individual if he or she chooses entrepreneurial activity instead of salaried work. Each entrepreneur can produce only one unit of givenindividual characteristics specific variety. The specific variety are produced not unique producer, but for any type of entrepreneurial ability there are individuals with given ability, who produce the same variety. Number of such producers is defined by distribution of entrepreneurial abilities. Anyone of entrepreneurs producing the given type of variety has no market power and sells the variety by market price. From the other side, under giventype of entrepreneurial abilitywhole range of varieties are produced by different entrepreneurs with given entrepreneurial ability. As far cost of production depends on entreprenurial ability, the prices charged by entrepreneurs with the same ability are equal. Such specification of market structure allows consider symmetric equilibrium in terms of prices. The main result oathe model is nontrivial impact of market size on outcome: the bigger number of population, the less share of salaried workers, the hire prices and the economy is more unequal.

Post-Malthusian Population Model of the British Industrial Revolution in a Lewis Unlimited Supply of Labor Model

To explain the population equilibrium of the British Industrial Revolution, this study proposes a two-sector economy that produces both agricultural foods and manufacturing goods. A Lewis model is used to discuss the interrelations among population increase, capital accumulation, and structural change of the British economy in the 19th century. We place capital accumulation at the center of the model to explain the growth in population size. Structural changes in the economy that are induced by capital accumulation favor the employment of labor in the manufacturing sector and trigger population increase. We examine this hypothesis by applying Granger causality tests to such variables as population size, capital accumulation, trade volume, and structural change in the British economy during the Industrial Revolution.Keywords: Britain's Industrial Revolution, Lewis's model, Capital accumulation, Population increaseJEL Classification: J11, N10(ProQuest: ... denotes formulae omitted.)I. IntroductionThe growth of population size is essential to the transition from a post- Malthusian regime to a modern economy regime. The post-Malthusian implies the stage after the escape from the Malthusian trap. This argument is rooted in the Boserupian viewpoint (1981) on the positive effects of population size on technical progress. Large-scale economies, which result from the increased demand caused by the increase in population size, generate technical progress. The unified growth model of Galor and Weil (1980) demonstrates that large-scale economies lead to economic conditions in which investments on human capital are favored. However, a gap remains between a gpost-Malthusian population economyh and a gmodern economyh with respect to determining population size. How the increase in population is achieved remains unclear, and how such an increase provides economic environments that are conducive for human capital investments is poorly understood.This study employs capital accumulation to determine the gpost- Malthusian population equilibrium,h which can fill the gap in the research on the population equilibrium between the gMalthusian stationary stateh and the gModern neo-classical population equilibriumh of family size choice. The function of capital goods in the context of the British Industrial Revolution as a growth model is rarely discussed. The function of capital goods in the transitional growth path of a unified growth model remains uncertain. Voigtla.nder and Voth (2006) presented a growth model of the British Industrial Revolution. This model considered capital goods. Their study indicated that an Ashton gwave of gadgetsh in the Industrial Revolution generated the growth of the British economy. The endogenous growth model of a gvarietyh kind did not determine the population size.We employ the gUnlimited Supply of Labor modelh of Lewis to discuss the function of capital accumulation during the British Industrial Revolution and relate it to the determination of population size. Yang and Kim (2013) suggested a population equilibrium for the Malthusian economy of a one-sector agricultural economy. Their study emphasized the improvement of the marginal physical productivity of the agricultural worker in escaping the Malthusian trap. The present work retains the biophysical wage rate hypothesis of Fogel. Thus, the post-Malthusian model implies that income significantly affects the choice of family size.The three factors of economic production are land, labor, and capital. Land is specific to the agricultural sector, whereas labor and capital move between the manufacturing and agricultural sectors. Capital and labor are utilized in fixed proportions for agricultural produce but are interchangeable for the production of goods. Land is specific to agricultural produce.An economy is Malthusian when the land factor can effectively constrain population increase. …

An Ongoing Reversal of Fortune Among Russian Cities: City Age, Natural Resources, and Changing Spatial Income Distribution

This paper documents the negative link between the age of Russian cities and their average wage. This link is robust to various definitions of city age and sample censuring, the inclusion of regional and time fixed effects, dependent variable spatial lag and many urban characteristics. This link is revealed especially for cities founded after the Soviet industrialization and for upper quintiles of cities by their average wage. To determine a mechanism behind the established fact, hypotheses as to spatial patterns of economic performance are discussed, including the increasing return hypothesis, the institutions hypothesis and the geography hypothesis. Following the sophisticated version of the geography hypothesis, a model of growth in n-city and two-sector economy is developed. The model replicates the link between age and per capita income and contains testable hypotheses that enable one to check whether a mechanism outlined in the model is behind the link between city age and wage. Our empirical strategy is based on a quasi-experiment, in which the treatment effect is made by time and various age groups of the cities are broken up into treatment and control groups. The results are strongly in favor of the sophisticated geography hypothesis. The revealed mechanism suggests that the changing spatial patterns of wage differentials are explained by the changing remaining stocks of natural resources. Older cities are getting relatively poorer due to the shrinking of their remaining resource stocks, while new cities are emerging in resource-rich territories with the respective income advantages.

Монополистическая конкуренция в двухсекторной экономике при неопределенном спросе

Институтом экономических исследований Дальневосточного отделения Российской академии наук, при поддержке Научного Совета по вопросам регионального развития при Президиуме РАН, издается научный журнал «Пространственная экономика».

Unanticipated vs. Anticipated Tax Reforms in a Two-Sector Open Economy

We use a two-sector neoclassical open economy model with traded and non-traded goods to investigate the effects of unanticipated and anticipated tax reforms. First, an unanticipated tax reform produces an expansion of GDP, labor, and investment, while an anticipated tax reform has opposite effects before the implementation of the labor tax cut. Quantitatively, if the traded sector is more capital intensive, GDP increases by 1.6 percentage points or declines by 2.7 percentage points after three years, depending on whether the tax cut is unanticipated or anticipated. Second, we find that GDP change masks a wide dispersion in sectoral output responses. As long as investment is both traded and non traded, a tax reform substantially raises the relative size of the non-traded sector after three years while traded output always drops. Third, a tax reform improves welfare in all scenarios, more so if the markup is endogenous, but less so if the shock is anticipated. Importantly, we find that welfare gains in a two-sector economy with capital accumulation and perfect access to external borrowing are between 39 % and 89 % higher than those in an economy without physical capital.