Using an endogenous growth model in which learning by doing, although bounded in each good, exhibits spillovers across goods, this paper investigates the dynamic effects of international trade. Examining an LDC and a DC, the latter distinguished by a higher initial level of knowledge, under autarky and free trade, I find that under free trade the LDC (DC) experiences rates of technical progress and GOP growth less than or equal (greater than or equal) to those enjoyed under autarky. Unless the LDC's population is several orders of magnitude greater than that of the DC and the initial technical gap between the two economies is not large, the LDC will be unable to catch up with its trading partner. Hence, in terms of technical progress and growth, the LDC experiences dynamic losses from trade, whilst the DC experiences dynamic gains. However, since technical progress abroad can improve welfare at home, LDC consumers may enjoy - higher intertemporal utility along the free trade path. In the case of DC consumers, as long as their economy is not overtaken by the LDC they will enjoy both more rapid technical progress and the traditional static gains from trade, and hence experience an unambiguous improvement in intertemporal welfare.

Learning by Doing and the Dynamic Effects of International Trade

This paper gives a survey of the various forms of Pontryagin’s maximum principle for optimal control problems with state variable inequality constraints. The relations between the different sets of optimality conditions arising in these forms are shown. Furthermore, the application of these maximum principle conditions is demonstrated by solving some illustrative examples.

A survey of the maximum principles for optimal control problems with state constraints

By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQP-methods [10]. Convergence properties of the discretization are derived. Prom a solution of this method known as direct collocation, these properties are used to obtain reliable estimates of adjoint variables. In the presence of active state constraints, these estimates can be significantly improved by including the switching structure of the state constraint into the optimization procedure. Two numerical examples are presented.

/pdf/numerical-solution-of-optimal-control-problems-by-direct-220zeazp0o.pdf

Numerical Solution of Optimal Control Problems by Direct Collocation

https://ntrs.nasa.gov/api/citations/19700002504/downloads/19700002504.pdf

New necessary conditions of optimality for control problems with state-variable inequality constraints

Simultaneous optimization and solution methods for batch reactor control profiles

Thrust, bank angle and angle of attack of aircraft minimum fuel lateral turns at constant altitude and specified velocities

Minimum fuel lateral turns at constant altitude.

A proof of the convergence of the Kelley-Bryson penalty function technique for state-constrained control problems

: Recent investigations into necessary conditions of optimality for control problems with inequality constraints on the state variables have shown that, for a specific class of problems, the optimal trajectory does not stay on the constraint boundary for non-zero intervals of time. This result permits, a priori, some insight into the structure of the optimal solution. For certain problems in growth economics, this result is of some significance, as is shown by three examples from two different areas. The first two examples are concerned with the problem of optimal employment; interestingly enough, they indicate that, for the models used, the optimal solution is such that full employment is attained at most instantaneously and is not maintained for non-zero intervals of time. The third example is concerned with the optimal investment and foreign aid policies for an underdeveloped economy. An institutional constraint on the stock of foreign debts may be derived from the 'debt-service' ratio. It appears that, contrary to earlier results obtained from simpler models, this constraint is binding at most instantaneously along the optimal trajectory. (Author)

/pdf/qualitative-application-of-a-result-in-control-theory-to-ryzgfbm94w.pdf

Qualitative application of a result in control theory to problems of economic growth

·".l'he investigation is based on a -dynamic, development-planning model -<Which assumes open unemployment --of unskilled labor. The standard devia­ ,;:tion of capital holdings across households enters as a t\ltate variable and ·£eeds back on the system through its effect -on demand composition and the -1.abor-intensity of the output mix. The system is controlled by varying ~he average level and progressivity of taJCes and subsidies which depend ;:on capital income. From this model, the behavior of summary measures of -,capital and income inequality-along a consumption-optimal trajectory is ,Jdetermined. For example, conclusions are drawn concerning possibly diver­ gent changes in capital and income inequality and the relationship between -:these dispersion measures and output growth. Also investigated are changes ~4n the marginal tax rate on income from human and non-human capital. *The authors are grateful to Professor Kenneth Arrow for helpful connnents and criticisms. .INTRODUCTION .Of late economists have focussed considerable attention on the rela­ 1 et:ionship of income dispersion to questions relating to the general efficiency ,;of resource allocation. A major area of concern has been the factor oppor­ .tunity cost effect [5]. It is contended that a reduction in income disper-.ion will increase the output share of commodities with low factor opportunity costs. So, it is argued, demand for goods which are intense in the relatively ;abundant factors will rise, while the demand for goods intense in the rela­ -tively scarce factors will fall. 'There i.s also the more traditional argument that a more even distribu­ tion of income causes a decline in the aggregate savings rate, thereby retard­ --d.ng growth. (See [ 9 ], [14], [16] .) This is open to question. there is <1ittle doubt that the marginal propensity to save out of corporate profits :is greater than that out of wage income. But, to some extent, the associa­ .,tlon of income dispersion with the rate of c-.apital formation is based on the :assumption that the household marginal propensity to save varies either with "the kind or the level of income earned. these are points of considerable :empirical and theoretical disagreement, as indicated in [6], [7] and [8). Moreover, even if the marginal propensity to save did change as hypothesized, the reduction in private savings could be offset by increases in tax revenues .;;and public savings. Amore important theoretical question, not considered hitherto, is: --rowhat extent can increases in the capital-labor ratio affect the size dis­ tribution of income in economies where a shortage of capital has led to con­ siderable open unemployment? 1In this paper we use the term 'dispersion• as a measure of inequities in the distribution of the variable under discussion.

https://elischolar.library.yale.edu/cgi/viewcontent.cgi?article=1204&context=egcenter-discussion-paper-series

Milind M. Lele

Papers

New necessary conditions of optimality for control problems with state-variable inequality constraints

Minimum fuel lateral turns at constant altitude.

A proof of the convergence of the Kelley-Bryson penalty function technique for state-constrained control problems

Qualitative application of a result in control theory to problems of economic growth

Income Distribution and Optimal Growth: The Case of Open Unemployment