Yuri Yatsenko

Adaptation and mitigation in long-term climate policies

The paper analytically explores the optimal policy mix between mitigation and environmental adaptation against climate change at a macroeconomic level. The constructed economic-environmental model is formulated as a social planner problem with the adaptation and abatement investments as separate decision variables. The authors prove the existence of a unique steady state and provide a comparative static analysis of the optimal investment. It leads to essential implications for associated long-term environmental policies. In particular, the dependence of the optimal ratio between abatement and adaptation investments on economic efficiency appears to have an inverted U-shape. Data calibration and numerical simulation are provided to illustrate theoretical outcomes.

Optimal equipment replacement without paradoxes: A continuous analysis

Combining known continuous- and discrete-time models of equipment replacement, we show that the optimal equipment lifetime is shorter when the embodied technological change is more intense. The paper has been inspired by a paradox in the equipment replacement raised by Cheevaprawatdomrong and Smith in Oper. Res. Lett. 31 (2003).

Integral-functional equations for optimal renovation problems

The integral-functional equations with the unknown variable in the upper limit of integration are introduced and studied. They arise in the optimization problems for integral dynamical models and allow to analyze the variable aftereffect duration of dynamical system

Investment in vintage capital

We study an economy in which firms use labor and various vintages of capital in a CES production function for the final good. We explicitly solve for the investment in capital of a given vintage as a function of its age, and for the resulting stocks of capital. We show that for reasonable parameter values, inverted-U-shaped dynamics of investment and S-shaped dynamics for capital arise in equilibrium. We view the model as an explanation of intra-firm adoption lags, i.e., the observation that firms adopt innovations over time and not instantaneously.

The dynamics of asset lifetime under technological change

The variable lifetime of assets is analyzed in a serial replacement problem. Technological change impacts the maintenance cost and new asset cost. The optimal asset lifetime appears to be constant only when both costs decrease with the same rate. We identify cases when the technological change decreases or increases the optimal lifetime.

Maximum principle for a size-structured model of forest and carbon sequestration management

Abstract The paper analyzes nonlinear optimal control of integral–differential equations that describe the optimal management of a forest taking into account intra-species competition and carbon sequestration. The objective function includes the revenues from timber production, operational expenses, and the net benefits from carbon sequestration. A dual system is derived and a necessary extremum condition is established.

Concavity in a vintage capital model with nonlinear utility

An optimization problem in an economic vintage capital model with nonlinear utility is investigated. It is described by non-linear Volterra integral equations with an unknown in the limits of integration. The concavity of the problem is proven, the condition for an extremum is established, and their relevance to applications is demonstrated.

Structure of optimal trajectories in a nonlinear dynamic model with endogenous delay

An exact solution is constructed to a nonlinear optimization problem in an integral dynamic model with delay. The problem involves the unknown duration of the delay and has important applications to the optimal replacement of capital equipment under technological change.

Age-structured PDEs in economics, ecology, and demography: Optimal control and sustainability

Optimal control of partial differential equations arises in population ecology, economics, and demography. The consistency of mathematical treatment is demonstrated for the Lotka-McKendrick model and its nonlinear modifications of increasing complexity. The obtained qualitative optimal dynamics show that the models have either the bang-bang structure of optimal controls or follow balanced growth dynamics.

Network economics and optimal replacement of age-structured IT capital

The constructed hierarchical optimization model of vintage capital replacement takes into account network effects and the age-dependent technological structure of capital equipment. It involves the control of a network coalition choice, endogenous investments, capital structure, and capital lifetime. The qualitative analysis of the model shows how the lifetime and financial structure of the IT capital depends on technological change. These results are relevant for strategic management on a firm level. Provided numeric examples simulate the optimal lifetime of personal computers.