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Arguments That Convergence is Neither Inevitable Nor Likely

Arguments That Convergence Is neither Inevitable nor Likely

If the growth of an economy depended only on the deepening of human capital and physical capital, then the growth rate of that economy would be expected to slow down over the long run because of diminishing marginal returns. However, there is another crucial factor in the aggregate production function: technology.

The development of new technology can provide a way for an economy to sidestep the diminishing marginal returns of capital deepening. This figure shows how. The horizontal axis of the figure measures the amount of capital deepening, which on this figure is an overall measure that includes deepening of both physical and human capital. The amount of human and physical capital per worker increases as you move from left to right, from C1 to C2 to C3. The vertical axis of the diagram measures per capita output. Start by considering the lowest line in this diagram, labeled Technology 1. Along this aggregate production function, the level of technology is being held constant, so the line shows only the relationship between capital deepening and output. As capital deepens from C1 to C2 to C3 and the economy moves from R to U to W, per capita output does increase—but the way in which the line starts out steeper on the left but then flattens as it moves to the right shows the diminishing marginal returns, as additional marginal amounts of capital deepening increase output by ever-smaller amounts. The shape of the aggregate production line (Technology 1) shows that the ability of capital deepening, by itself, to generate sustained economic growth is limited, since diminishing returns will eventually set in.

Capital Deepening and New Technology

The graph shows three upward arching lines that each represent a different technology. Improvements in technology lead to greater output per capita and deepened physical and human capital.

Imagine that the economy starts at point R, with the level of physical and human capital C1 and the output per capita at G1. If the economy relies only on capital deepening, while remaining at the technology level shown by the Technology 1 line, then it would face diminishing marginal returns as it moved from point R to point U to point W. However, now imagine that capital deepening is combined with improvements in technology. Then, as capital deepens from C1 to C2, technology improves from Technology 1 to Technology 2, and the economy moves from R to S. Similarly, as capital deepens from C2 to C3, technology increases from Technology 2 to Technology 3, and the economy moves from S to T. With improvements in technology, there is no longer any reason that economic growth must necessarily slow down.

Now, bring improvements in technology into the picture. Improved technology means that with a given set of inputs, more output is possible. The production function labeled Technology 1 in the figure is based on one level of technology, but Technology 2 is based on an improved level of technology, so for every level of capital deepening on the horizontal axis, it produces a higher level of output on the vertical axis. In turn, production function Technology 3 represents a still higher level of technology, so that for every level of inputs on the horizontal axis, it produces a higher level of output on the vertical axis than either of the other two aggregate production functions.

Most healthy, growing economies are deepening their human and physical capital and increasing technology at the same time. As a result, the economy can move from a choice like point R on the Technology 1 aggregate production line to a point like S on Technology 2 and a point like T on the still higher aggregate production line (Technology 3). With the combination of technology and capital deepening, the rise in GDP per capita in high-income countries does not need to fade away because of diminishing returns. The gains from technology can offset the diminishing returns involved with capital deepening.

Will technological improvements themselves run into diminishing returns over time? That is, will it become continually harder and more costly to discover new technological improvements? Perhaps someday, but, at least over the last two centuries since the Industrial Revolution, improvements in technology have not run into diminishing marginal returns. Modern inventions, like the Internet or discoveries in genetics or materials science, do not seem to provide smaller gains to output than earlier inventions like the steam engine or the railroad. One reason that technological ideas do not seem to run into diminishing returns is that the ideas of new technology can often be widely applied at a marginal cost that is very low or even zero. A specific additional machine, or an additional year of education, must be used by a specific worker or group of workers. A new technology or invention can be used by many workers across the economy at very low marginal cost.

The argument that it is easier for a low-income country to copy and adapt existing technology than it is for a high-income country to invent new technology is not necessarily true, either. When it comes to adapting and using new technology, a society’s performance is not necessarily guaranteed, but is the result of whether the economic, educational, and public policy institutions of the country are supportive. In theory, perhaps, low-income countries have many opportunities to copy and adapt technology, but if they lack the appropriate supportive economic infrastructure and institutions, the theoretical possibility that backwardness might have certain advantages is of little practical relevance.

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