When can it be not optimal to adopt a new technology? A viability theory solution to a two‐stage optimal control problem of new technology adoption

Krawczyk, Jacek B.; Serea, Oana-Silvia

doi:10.1002/oca.1030

Cited by 10 publications

(5 citation statements)

References 36 publications

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“…Here we cite [9,[16][17][18][19] among others. Viability theory applications in other economic areas include: finance- [20]; managerial economics- [21]; macroeconomics- [10,13,15,[22][23][24][25][26][27][28]; and microeconomics- [29]. Notwithstanding the economic applications, of which we address one in this paper, the viability theory has been applied to other problems where the uniqueness or optimality of the control strategy is not of major concern.…”

Section: The Meaning Of Viabilitymentioning

confidence: 99%

A Qualitative Game of Interest Rate Adjustments with a Nuisance Agent

Krawczyk

Petkov

2022

Games

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A qualitative game describes a situation in which antagonistic players strive to keep the evolutions of their state variables in predetermined constraint sets. We argue that a qualitative game model is a suitable mathematical representation of the struggle between a domestic central bank of a small open economy and a foreign central bank of a large economy to maintain their respective state variables within an acceptable band regardless of the other player’s choices. The actions of the foreign central bank affect the domestic exchange rate and, hence, domestic inflation, output gap and interest rate. However, these actions do not necessarily aim to destabilise the small open economy, nor do they take into account the state of the latter. The domestic bank’s problem, therefore, is similar to that of a game against nature. We refer to this type of qualitative game as a nuisance-agent game (or NA-game). We use viability theory to derive satisficing rules (in the sense of Simon) of nominal interest-rate adjustments for the domestic central bank of a small open economy in a qualitative NA-game against the foreign central bank.

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Section: The Meaning Of Viabilitymentioning

confidence: 99%

A Qualitative Game of Interest Rate Adjustments with a Nuisance Agent

Krawczyk

Petkov

2022

Games

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“…As a consequence, the agent has to take into account 9 These authors provide optimality conditions for two-stage, finite time dynamic optimization problems. An extension to an infinite horizon is provided by Makris (2001); and applications of this theory to two-stage optimal control problems can, for example, be found in Boucekkine et al (2004), Saglam (2011), Grass et al (2012), Caulkins et al (2013), Krawczyk and Serea (2013), Moser et al (2014), Long et al (2017), and Seidl et al (2018.…”

Section: A )mentioning

confidence: 99%

Harvesting a remote renewable resource

Behringer¹,

Upmann²

2018

Proceeding of the International Conference "Optimal Control and Differential Games" Dedicated to the 110th Anniversary of L. S.

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In standard models of spatial harvesting, a resource is distributed over a continuous domain with an agent who may harvest everywhere all the time. For some cases though (e.g., fruits, mushrooms, algae), it is more realistic to assume that the resource is located at a fixed point within that domain so that an agent has to travel in order to be able to harvest. This creates a combined travelling-and-harvesting problem where slower travel implies a lower travelling cost and, due to a later arrival, a higher abundance of the resource at the beginning of the harvesting period; this, though, has to be traded off against less time left for harvesting, given a fixed planning horizon. Possible bounds on the controls render the problem even more intricate. We scrutinise this bioeconomic setting using a two-stage optimal control approach, and find that the agent economises on the travelling cost and thus avoids to arrive at the location of the resource too early. More specifically, the agent adjusts the travelling time so as to be able to harvest with maximum intensity at the beginning and the end of the harvesting period, but may also find it optimal to harvest at a sustainable level, where the harvesting and the growth rate of the stock coincide, in an intermediate time interval.

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“…Viability theory has been successfully applied to environmental economics problems, see , De Lara, Doyen, Guilbaud, and Rochet (2006) and Martinet, Thébaud, and Doyen (2007); for applications to financial analysis see Pujal and Saint-Pierre (2006) and the references provided there; for a solution to a managerial economics problem see Krawczyk, Sissons, and Vincent (2012). Along with Krawczyk and Kim (2009a), Bonneuil and Saint-Pierre (2008), Bonneuil and Boucekkine (2008), Krawczyk and Kim (2004), Krawczyk and Sethi (2007), Clément-Pitiot and Saint-Pierre (2006) and Clément-Pitiot and Doyen (1999) deal with viable solutions to macroeconomic problems; see Krawczyk and Serea (2011) for a microeconomic problem solution. Our goal in this paper is to use viability theory for an analysis of a tax model based on Judd (1987).…”

Section: A Brief On Viability Theory and Viable Solutions 21 An Intrmentioning

confidence: 99%

A Note on Determining Viable Economic States in a Dynamic Model of Taxation

Krawczyk

Judd

2015

Macroecon. Dynam.

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Viability theory is the study of dynamical systems that asks what set of initial conditions will generate evolutions that obey the laws of motion of a system and some state constraints, for the length of the evolution. We apply viability theory to Judd's dynamic tax model [The welfare cost of factor taxation in a perfect-foresight model, Journal of Political Economy 95(4), 675–709 (1987)] to identify which economic states today are sustainable under only slightly constrained tax-rate adjustments in the future, when the dynamic budget constraint and the consumers' transversality condition at infinity are satisfied. We call the set of such states the economic viability kernel. In broad terms, knowledge of the viability kernel can tell the planner what economic objectives are achievable and assist in the choice of suitable controls to realize them. We observe that high consumption levels can only be sustained when capital is abundant and, unsurprisingly, that a very high consumption economy lies outside such kernels, at least for annual tax-adjustment levels limited by 20 percentage points. Furthermore, we notice that by and large the sizes of the kernel slices do not diminish as the tax rate rises; hence high-taxation economies are not necessarily more prone to explode, or implode, than their low-taxation counterparts. In fact, higher tax rates are necessary to keep many consumption choices viable, especially when capital approaches the constraint-set boundaries.

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When can it be not optimal to adopt a new technology? A viability theory solution to a two‐stage optimal control problem of new technology adoption

Cited by 10 publications

References 36 publications

A Qualitative Game of Interest Rate Adjustments with a Nuisance Agent

A Qualitative Game of Interest Rate Adjustments with a Nuisance Agent

Harvesting a remote renewable resource

A Note on Determining Viable Economic States in a Dynamic Model of Taxation

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