Dynamics of Dengue epidemics using optimal control

We present an application of optimal control theory to Dengue epidemics. This epidemiologic disease is an important theme in tropical countries due to the growing number of infected individuals. The dynamic model is described by a set of nonlinear ordinary differential equations, that depend on the dynamic of the Dengue mosquito, the number of infected individuals, and the people's motivation to combat the mosquito. The cost functional depends not only on the costs of medical treatment of the infected people but also on the costs related to educational and sanitary campaigns. Two approaches to solve the problem are considered: one using optimal control theory, another one by discretizing first the problem and then solving it with nonlinear programming. The results obtained with OC-ODE and IPOPT solvers are given and discussed. We observe that with current computational tools it is easy to obtain, in an efficient way, better solutions to Dengue problems, leading to a decrease of infected mosquitoes and individuals in less time and with lower costs.Comment: Submitted to Mathematical and Computer Modelling 25/Oct/2009; accepted for publication, after revision, 22/June/201

Crop supply dynamics and the illusion of partial adjustment

We use field-level data to estimate the response of corn and soybean acreage to price shocks. Our sample contains more than eight million observations derived from satellite imagery and includes every field in Iowa, Illinois, and Indiana. We estimate that aggregate crop acreage responds more to price shocks in the short run than in the long run, and we show theoretically how the benefits of crop rotation generate this response pattern. In essence, farmers who change crops due to a price shock have an incentive to switch back to the previous crop to capture the benefits of crop rotation. Our result contradicts the long-held belief that agricultural supply responds gradually to price shocks through partial adjustment. We would not have obtained this result had we used county-level panel data. Standard econometric methods applied to county-level data produce estimates consistent with partial adjustment. We show that this apparent partial adjustment is illusory, and we demonstrate how it arises from the fact that fields in the same county are more similar to each other than to fields in other counties. This result underscores the importance of using models with appropriate micro-foundations and cautions against inferring micro-level rigidities from inertia in aggregate panel data. Our preferred estimate of the own-price long-run elasticity of corn acreage is 0.29 and the cross-price elasticity is -0.22. The corresponding elasticities for soybean acreage are 0.26 and -0.33. Our estimated short-run elasticities are 37 percent larger than their long-run counterparts

Short-Term Global Crop Acreage Response to International Food Prices and Implications of Volatility

Understanding how producers make decisions to allot acreage among crops and how decisions about land use are affected by changes in prices and their volatility is fundamental for predicting the supply of staple crops and, hence, assessing the global food supply situation. The innovations of the present paper are estimates of monthly (i.e. seasonal) versus annual global acreage response models for four staple crops: wheat, soybeans, corn and rice. We focus on the impact of (expected) crop prices, oil and fertilizer prices and market risks as main determinants for farmers’ decisions on how to allocate their land. Primary emphasis is given to the magnitude and speed of the allocation process. Estimation of intra-annual acreage elasticity is crucial for expected supply and for input demand, especially in the light of the recent short-term volatility in food prices. Such aggregate estimates are also valuable to verify whether involved country-specific estimations add up to patterns that are apparent in the aggregate international data. The econometric results indicate that global crop acreage responds to crop prices and price risks, input costs as well as a time trend. Depending on respective crop, short-run elasticities are about 0.05 to 0.25; price volatility tends to reduce acreage response of some crops; comparison of the annual and the monthly acreage response elasticities suggests that acreage adjusts seasonally around the globe to new information and expectations. Given the seasonality of agriculture, time is of the essence for acreage response: The analysis indicates that acreage allocation is more sensitive to prices in northern hemisphere spring than in winter and the response varies across months

Estimation of TFP growth:a semiparametric smooth coefficient approach

This article uses a semiparametric smooth coefficient model (SPSCM) to estimate TFP growth and its components (scale and technical change). The SPSCM is derived from a nonparametric specification of the production technology represented by an input distance function (IDF), using a growth formulation. The functional coefficients of the SPSCM come naturally from the model and are fully flexible in the sense that no functional form of the underlying production technology is used to derive them. Another advantage of the SPSCM is that it can estimate bias (input and scale) in technical change in a fully flexible manner. We also used a translog IDF framework to estimate TFP growth components. A panel of U.S. electricity generating plants for the period 1986–1998 is used for this purpose. Comparing estimated TFP growth results from both parametric and semiparametric models against the Divisia TFP growth, we conclude that the SPSCM performs the best in tracking the temporal behavior of TFP growth

Сутність та класифікація ризиків інвестиційної діяльності

Наводиться визначення поняттю "ризики інвестиційної діяльності" за рахунок поєднання його сутнісних характеристик, виконано узагальнення класифікації цих ризиків, запропоновано введення нової класифікаційної групи – "корпоративні ризики", які пов'язані з можливістю втрати контролю над підприємством інвестором-акціонером

Dinkelbach Approach to Solving a Class of Fractional Optimal Control Problems

We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control. Since the standard optimal control theory cannot be used directly to solve a problem of this kind, we apply Dinkelbach’s approach to linearize it. Indeed, the fractional optimal control problem can be transformed into an equivalent monoparametric family { P q } of linear optimal control problems. The special structure of the class of problems considered allows solving the fractional problem either explicitly or requiring straightforward classical numerical techniques to solve a single equation. An application to advertising efficiency maximization is presented

Interactions between cigarette and alcohol consumption in rural China

The objective of this paper is to analyze interdependencies between cigarette and alcohol consumption in rural China, using panel data for 10 years (1994–2003) for rural areas of 26 Chinese provinces. There have been many studies in which cigarette and alcohol consumption have been considered separately but few to date for China on interactions between the consumption of these two products. Taxes are often recommended as a tool to reduce alcohol and cigarette consumption. If cigarettes and alcohol are complements, taxing one will reduce the consumption of both and thus achieve a double public health dividend. However, if they are substitutes, taxing one will induce consumers to increase consumption of the other, offsetting the public health benefits of the tax. Our results indicate that the demands for both cigarettes and alcohol are very sensitive to the price of alcohol, but not to the price of cigarettes or to income. This suggests that taxes on alcohol can have a double dividend. On the other hand, an increase in cigarette taxes may not be effective in curbing cigarette or alcohol consumption in rural China