Technology and Theories of Economic Development : Neo-classical Approach

1. Technology and Theories of Economic Development: Neo-classical Approach Technical Change and the Aggregate Production Function by R. Solow, 1957 The Review of Economics and Statistics, V. 39, N.3

2. Aim • To describe an elementary way of segregating variations in output per labor due to technical change from those due to changes in the availability of capital per labor

3. Theoretical Basis • Q represents output and K and L represent capital and labor inputs Aggregate production function → t for technical change (any kind of shift in the production function)

4. NeutralTechnical Change • MRS untouched whereas increase or decrease in output given inputs Production function →A(t) the cumulated effect of the shifts over time • Differentiating totally with respect to time and divide by Q → where the relative share of capital and labor

5. NeutralTechnical Change • Returns to scale? • Assume that factors are paid their marginal products → Euler’s theorem • → • Let

6. NeutralTechnical Change • Technical change index → output per man hour, capital per man hour, the share of capital • Without technical change being neutral A special form (neutral shifts in production function) obtained by (∂F/ ∂t)/F being independent of K and L

7. Application to the US (1909-1949) • Isolate shifts of the aggregate production function from movements along it (technical change) by using output per unit of labor, capital per unit of labor, the share of capital • Measure of aggregate output → real net national product • if use GNP → share of capital including depreciation • Time series of real private non-farm GNP per man hour • Measure of capital → the annual flow of capital services • Hard to compute the stock of capital (capital in use) • Capital including land, mineral deposits with government, agricultural and consumer durables eliminated and corrected by depreciation • Share of capital (factors share)

8. Application to the US (1909-1949) • Method: replace the time derivatives by year-to-year changes and calculate ∆q/q-wk ∆k/k → estimate of ∆F/F or ∆A/A depending on relative shifts being neutral or not • Use A(1909)=1 and A(t+1)=A(t)(1+ ∆A(t)/A(t)) • A(t) series trend upward • Solow calls the curve ∆A/A instead of ∆F/F because a scatter of ∆F/F against K/L indicated no relationship • Formal conclusion: over the period 1909-49, shifts in the aggregate production function turned out to be neutral • Neutral meaning the shifts were pure scale changes, leaving MRS unchanged at given capital/labor ratios (∆A/A uncorrelated with K/L)

9. A General Conclusion • Over the period, output per man hour approximately doubled • The cumulative upward shift in production function was 80 % • One-eight of the total increase due to increase in capital per man hour (capital intensity) • Remaining seven-eights due to technical change (increased productivity)

10. A General Conclusion • Observed rate of technical progress persisted even if the rate of investment had been much smaller? • Innovation embodied in new plant and equipment to be realized at all • Restricting assumption that output divided by a weighted sum of inputs (computation of output per unit of resource input)

11. The Aggregate Production Function • Given Q=A(t)f(K,L) with assumption of constant returns to scale q=A(t)f(k,1) • By plotting q(t)/A(t) against k(t) → discuss the shape of f(k,1) and reconstruct the aggregate production function • 1943-49 over other points (may not be a shift because of underestimate of capital inputs leading to overestimate of productivity increase) → “leave this a mystery”

12. Regression • Omit the observations 1943-49 to find a curve fitting the scatter • Linear, semi logarithmic, hyperbolic, Cobb-Douglas case etc.

13. Summary • Suggested a simple way of segregating shifts of the aggregate production function form movements along it • Assume that factors are paid their marginal products • Conclusion: over period 1909-49 technical change was neutral on average