1. 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. 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. 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. 4 Neutral Technical 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. 5 Neutral Technical Change Returns to scale?  Assume that factors are paid their marginal products → Euler’s theorem  → Let

6. 6 Neutral Technical 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. 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. 8 Application to the US (1909-1949) Method: replace the time derivatives by year-to-year changes and calculate ∆q/q-w k ∆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. 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. 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. 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. 12 Regression Omit the observations 1943-49 to find a curve fitting the scatter  Linear, semi logarithmic, hyperbolic, Cobb- Douglas case etc.

13. 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