Economic growth and economic development 510

Introduction to Modern Economic Growth assume that AF (t) evolves exogenously according to the differential equation A˙ F (t) = gF , AF (t) with initial condition AF (0) > Let the human capital of the workforce be denoted by h Notice that this human capital does not feature in the production function, (10.43) This is an extreme case in which human capital does not play any of the productivity enhancing role we have emphasized so far Instead, the role of human capital in the current model will be to facilitate the implementation and use of frontier technology in the production process In particular, the evolution of the technology in use, A (t), is governed by the differential equation A˙ (t) = gA (t) + φ (h) AF (t) , with initial condition A (0) ∈ (0, AF (0)) The parameter g is strictly less than gF and measures the growth rate of technology A (t), resulting from learning by doing or other sources of productivity growth But this is only one source of improvements in technology The other one comes from the second term, and can be interpreted as improvements in technology because of implementation and adoption of frontier technologies The extent of this second source of improvement is determined by the average human capital of the workforce, h This captures the above-mentioned role of human capital, in facilitating coping with technological change In particular, we assume that φ (·) is increasing, with ¯ φ (0) = and φ (h) = gF − g > for all h ≥ h, ¯ > This specification implies that the human capital of the workforce where h regulates the ability of the economy to cope with new developments embedded in the frontier technologies; if the workforce has no human capital, there will be no adoption or implementation of frontier technologies and A (t) will grow at the rate g ¯ there will be very quick adaptation to the frontier technologies If, in contrast, h ≥ h, Since AF (t) = exp (gF t) AF (0), the differential equation for A (t) can be written as A˙ (t) = gA (t) + φ (h) AF (0) exp (gF t) 496