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

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


Technology and theories of economic development neo classical approach

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

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)


Neutral technical change

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


Neutral technical change1

NeutralTechnical Change

  • Returns to scale?

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

  • Let


Neutral technical change2

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

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 19491

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

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 conclusion1

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

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

Regression

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

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


Summary

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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