Technology choice: the output and employment tradeoff

American Journal of Economics and Sociology, The,  Jan, 1998  by Kalman Goldberg,  Jannett Highfill,  Michael McAsey

• E-mail
• Print
• Link

A - H + [Epsilon] - [Beta]/[Gamma] (B + H - [Epsilon]) = A - H + [Epsilon] - A - H/B + H (B + H - [Epsilon]) [10]

[since Point 5 is on the technology ray, we have [Gamma](B + H) = [Beta](A - H)]. The right-hand side of (10) is thus equal to

(A - H) + [Epsilon] - (A - H) + [Epsilon]/B + H (A - H) = [Epsilon] + [Epsilon]/B + H (A - H) [greater than] 0

To see that there is a shortage of skilled labor, we compute the difference in the [L.sub.s] coordinates of Points 3 and 5. First reformulate the [L.sub.s] coordinate of Point 3: [L.sub.s] = ([Alpha]/[Beta])(I + [Epsilon]) = ([Alpha]/[Beta])[([Beta]/[Alpha])(B + H) + [Epsilon]] = B + H + [Epsilon]([Alpha]/[Beta]). The difference between the two [L.sub.s] coordinates (Point 3 minus Point 5) is now easily seen to be [Epsilon][([Alpha]/[Beta]) + 1] and hence is positive. It is also easy to see that there is no necessary order relation between the [L.sub.u] coordinates at Points 3 and 4.

Finally, to see the algebraic form of the relationships indicated on Figure 5, assume that H is increased to H + [Epsilon]. Point 6 on Figure 5 lies along the line [L.sub.s] + [L.sub.u] = A + B and so its coordinates are [L.sub.s] = B + H + [Epsilon] and [L.sub.u] = A - H - [Epsilon]. The funds available for capital improvement are I - [Epsilon]. Thus the coordinates of Point 7 are [L.sub.s] = ([Alpha]/[Beta])(I - [Epsilon]) = ([Alpha]/[Beta])(B + H) - ([Alpha]/[Beta])[Epsilon] while [L.sub.u] = ([Alpha]/[Beta])(I - [Epsilon]). The assertion is that there are more skilled workers at Point 6 than at Point 7. To see this algebraically note simply that [L.sub.s] at Point 6 is greater than (B + H) (the value of [L.sub.s] at Point 2) while [L.sub.s] at Point 7 is given by ([Alpha]/[Beta])(I - [Epsilon]) = ([Alpha]/[Beta])I - ([Alpha]/[Beta])[Epsilon], which is the [L.sub.s] coordinate at Point 2 minus ([Alpha]/[Beta])[Epsilon]. Therefore, the two [L.sub.s] coordinates lie on either side of B + H and thus have the desired relationship to each other. As in the previous paragraph, there is no necessary relationship between the [L.sub.u] coordinates of Points 6 and 7.

References

1. Abramovitz, M. and P. A. David, "Reinterpreting Economic Growth: Parables and Realities," American Economic Review, 63:2, May 1973, 428-439.

2. Aghion, Philippe and Peter Howitt, "Growth and Unemployment," Review of Economic Studies, 61, 1994, 477-494.

3. Hagemann, Harald, "The Economy in Traverse: Growth, Technology and Structural Change, Economie Appliquee, 46, 1994, 37-56.

4. Kuznets, Simon, "Quantitative Aspects of the Economic Growth of Nations IV, Distribution of National Income by Factor Shares," Economic Development and Cultural Change, 7, 1959, 1-100.

5. Lowe, Adolph, The Path of Economic Growth, Cambridge University Press, 1976.

6. Lucas, Robert E., "On the Mechanics of Economic Development," Journal of Monetary Economics, 22, June 1988, 3-42.

7. Romer, Paul, "Increasing Returns and Long-ran Growth," Journal of Political Economy, 94, October 1986, 1002-1037.