Technical Change, Technical Efficiency, and Their Impact on Input Demand in the Agricultural and Manufacturing Sectors of Pakistan

Technical change has been considered as one of the most important determinants of economic growth. In developed economies, a proportionately higher percentage of GDP growth is attributable to technological progress and technical efficiency. However, technical change in developing countries is in its early stages and increased use of factor inputs is still the dominant source of economic growth. An attempt has been made in this paper to analyse technological progress and technical efficiency and their contribution to economic growth along with other factors of production by using more efficient methods in the manufacturing and agriculture sectors of Pakistan. There are a few studies on technological growth and technical efficiency change in Pakistan but they suffer from certain limitations. Most of them use the terms of technical change and productivity synonymously. Further, all of them use Hicks’s formula of neutral technical change and assume that technical change is happening at a constant rate. We have attempted to measure technical change, technical efficiency, and productivity in the form of the Hicks neutral technical change as well as in the form of variable and continuous and discrete technical change. Besides, this paper also analyses the impact of technical change on input demand (i.e., its impact on labour and capital demand) and examines the issue of technical change being either labour-saving or capital-saving. We found that technical change was taking place at a continuous and variable rate. The major contributor to the growth of output and value-added in both sectors was capital, contributing over 50 percent. Labour share was about 20 percent in the agriculture sector and about 10 percent in the manufacturing sector. Technical change share was very significant in manufacturing but not so in agriculture. The manufacturing sector in Pakistan has grown at an annual rate of about 6 percent during 1970s and at 8.7 percent during 1980s, and its share in GDP has increased from 16.5 percent to about 19 percent, but it has failed to generate new employment opportunities for the labour force. The employment growth rate is only about 2 percent.

Small loop spaces and covering theory of non-homotopically Hausdorff spaces

In this paper we devote to spaces that are not homotopically hausdorff and study their covering spaces. We introduce the notion of small covering and prove that every small covering of $X$ is the universal covering in categorical sense. Also, we introduce the notion of semi-locally small loop space which is the necessary and sufficient condition for existence of universal cover for non-homotopically hausdorff spaces, equivalently existence of small covering spaces. Also, we prove that for semi-locally small loop spaces, $X$ is a small loop space if and only if every cover of $X$ is trivial if and only if $\pi_1^{top}(X)$ is an indiscrete topological group.Comment: 7 page

Spanier spaces and covering theory of non-homotopically path Hausdorff spaces

H. Fischer et al. (Topology and its Application, 158 (2011) 397-408.) introduced the Spanier group of a based space $(X,x)$ which is denoted by \psp. By a Spanier space we mean a space $X$ such that \psp=\pi_1(X,x), for every $x\in X$. In this paper, first we give an example of Spanier spaces. Then we study the influence of the Spanier group on covering theory and introduce Spanier coverings which are universal coverings in the categorical sense. Second, we give a necessary and sufficient condition for the existence of Spanier coverings for non-homotopically path Hausdorff spaces. Finally, we study the topological properties of Spanier groups and find out a criteria for the Hausdorffness of topological fundamental groups.Comment: 14 pages, 2 figures. arXiv admin note: text overlap with arXiv:1102.0993 by other author

On locally 1-connectedness of quotient spaces and its applications to fundamental groups

Let $X$ be a locally 1-connected metric space and $A_1,A_2,...,A_n$ be connected, locally path connected and compact pairwise disjoint subspaces of $X$. In this paper, we show that the quotient space $X/(A_1,A_2,...,A_n)$ obtained from $X$ by collapsing each of the sets $A_i$'s to a point, is also locally 1-connected. Moreover, we prove that the induced continuous homomorphism of quasitopological fundamental groups is surjective. Finally, we give some applications to find out some properties of the fundamental group of the quotient space $X/(A_1,A_2,...,A_n)$.Comment: 11 page