Optimal Emission Prices Over the Business Cycles

We prove that under the most typical circumstances optimal emission prices are procyclical, i.e., prices should be lower during recessions. The procyclicality is more likely when emissions propagate very slowly into environmental damage. A prime example of such process is $$\hbox {CO}_2$$ CO 2 emissions. We show that carbon prices should be closely linked to the fluctuations of the marginal utility of consumption, which implies relatively modest magnitude of carbon price fluctuations. Our findings imply that climate policies should focus on setting the carbon price to the optimal growth path level and give carbon price fluctuations only a secondary role. Opposite to the carbon price, the cyclicality of optimal emissions depends on the production technology in the energy sector, and may become countercyclical in future if the technology mix becomes less fossil dependent.

A tree’s quest for light—optimal height and diameter growth under a shading canopy

For trees in forests, striving for light is matter of life and death, either by growing taller toward brighter conditions or by expanding the crown to capture more of the available light. Here, we present a mechanistic model for the development path of stem height and crown size, accounting for light capture and growth, as well as mortality risk. We determine the optimal growth path among all possible trajectories using dynamic programming. The optimal growth path follows a sequence of distinct phases: (i) initial crown size expansion, (ii) stem height growth toward the canopy, (iii) final expansion of the crown in the canopy and (iv) seed production without further increase in size. The transition points between these phases can be optimized by maximizing fitness, defined as expected lifetime reproductive production. The results imply that to reach the canopy in an optimal way, trees must consider the full profile of expected increasing light levels toward the canopy. A shortsighted maximization of growth based on initial light conditions can result in arrested height growth, preventing the tree from reaching the canopy. The previous result can explain canopy stratification, and why canopy species often get stuck at a certain size under a shading canopy. The model explains why trees with lower wood density have a larger diameter at a given tree height and grow taller than trees with higher wood density. The model can be used to implement plasticity in height versus diameter growth in individual-based vegetation and forestry models.

Productivity and profitability of alternative steer growth paths resulting from accessing high-quality forage systems in the subtropics of northern Australia: a modelling approach

Beef producers have to determine the best allocation of a limited resource of high-quality forage. This analysis assessed the most profitable way of incorporating high-quality forages into the whole-of-life steer growth path on forage systems in central Queensland, using property-level, regionally relevant herd models that determine whole-of-business productivity and profitability over a 30-year investment period. Twenty-two growth paths (liveweight change over time) from weaning to marketing were investigated for steers grazing buffel grass (Cenchrus ciliaris) pastures with and without access to leucaena–grass pastures (Leucaena leucocephala spp. glabrata + perennial, tropical grass (C4) species) or forage oats (Avena sativa) for varying intervals throughout their growth path. The production, economic and financial effect of each growth path was assessed by comparison to a base scenario that produced finished, slaughter steers (605 kg) from buffel grass pastures. The relative profitability of marketing steers at feedlot entry (feed-on) weight (474 kg) instead of slaughter weights was also assessed. The growth paths were applied within two beef enterprises, namely (1) steer turnover and (2) breeding and finishing. For both enterprises, grazing steers on leucaena-grass pastures from weaning until they achieved feedlot entry weight (474 kg) was substantially more profitable than any other growth path. Compared with the base scenario, this optimal growth path improved profitability by 121% and 37% for the steer turnover and the breeding and finishing enterprises respectively. The purchase of additional breeders for the latter enterprise was required to optimise utilisation of the leucaena–grass pastures immediately. Incorporating leucaena–grass pastures at any steer age improved the profitability of the steer turnover enterprise (AU$7368–AU$106508 extra profit/annum), and similarly for the breeding and finishing enterprise (AU$1754–AU$31383 extra profit/annum) except for two scenarios where leucaena–grass pastures were provided to older steers targeted at the feed-on market (AU$4816 and AU$23886 less profit/annum). However, incorporation of leucaena–grass into steer growth paths also resulted in increased peak deficit levels and financial risk to the business compared with buffel grass-only production systems, with payback periods for the most profitable growth path of 8 and 14 years for the steer turnover and the breeding and finishing enterprise respectively. All growth paths that incorporated forage oats and leucaena–grass resulted in lower economic and financial performance than did comparable growth paths that incorporated leucaena–grass only. Furthermore, incorporating oats into buffel grass-only growth paths always reduced the enterprise profitability. There was no relationship, across scenarios within an enterprise, between change in profit and the number of extra weaners produced or the amount of extra beef produced per hectare.

OPTIMAL GROWTH, DEBT DYNAMICS, AND WELFARE UNDER GDP-BASED COLLATERALS

We analyze the consequences of external debt collaterals on the optimal growth path of a country. We develop a small open economy model of endogenous growth where public spending can be financed by borrowing on imperfect international financial markets, where the country's borrowing capacity is limited. In contrast to the existing literature, which assumes that debt is constrained by the stock of capital, we investigate the consequences of gross domestic product (GDP)-based collaterals. First, we demonstrate that the economy may converge in a finite time, which is determined endogenously, to the regime with binding collaterals. Second, in such regime the steady-state public expenditures-to-GDP ratio is greater than that of the existing literature's models. Finally, we show that the degree of financial openness rises welfare if the collateral constraint is nonbinding and reduces welfare if the constraint binds. The first effect prevails always over the second and total intertemporal welfare increases.

Proposed Optimal Growth Pathfinding Method Based on Growth Trajectories

In this study, the authors propose an optimal growth pathfinding method to support learners in effectively mastering a set of capabilities. Under the assumption of prerequisite relationships among learning objectives, the main processes of the method are as follows: (1) extracting the capability structure from growth trajectories, (2) remodeling the problem as a traveling salesman problem with restrictions among learning objectives, and (3) generating the cost matrix and obtaining the optimal growth path. In addition, a flexible approach to data standardization as a step of capability structure extraction is discussed. The proposed method is also applied to a software engineer growth dataset with 30 responders.

Theory of Environmental Kuznets Curve

The paper develops a two-state-variable environmental growth model to derive the optimal growth path for the relationship between pollution and economic growth, which is used to verify the existence of the Environmental Kuznets Curve (EKC) hypothesis. It is found that the theoretical outcomes imply the existence of the EKC relationship between environmental degradation and economic growth, which is dependent on the combining effects of the pollution intensity, abatement technology of pollution emission, production technology, and the return rate of capital stock.