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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

- 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

- 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)

- 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

- Returns to scale?
- Assume that factors are paid their marginal products → Euler’s theorem
- →

- Let

- 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

- 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

- if use GNP → share of capital including depreciation
- 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

- Hard to compute the stock of capital (capital in use)
- Share of capital (factors share)

- Measure of aggregate output → real net national product

- 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)

- 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)

- 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)

- Innovation embodied in new plant and equipment to be realized at all

- 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”

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

- 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