Technology and theories of economic development neo classical approach
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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. Aim.

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Technology and Theories of Economic Development : Neo-classical Approach

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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


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


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)


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


NeutralTechnical Change

  • Returns to scale?

    • Assume that factors are paid their marginal products → Euler’s theorem

  • Let


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


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)


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)


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)


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)


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”


Regression

  • Omit the observations 1943-49 to find a curve fitting the scatter

    • Linear, semi logarithmic, hyperbolic, Cobb-Douglas case etc.


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


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