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**Chap. 4, The Theory of Aggregate Supply**

Productivity Chap. 4, The Theory of Aggregate Supply

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**Income depends on Output, Output depends on productivity and labor**

GDP, Y, is value produced. GDP can be decomposed: L = Labor is defined as hours worked. Main concern in this chapter is productivity

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**Income per person, 2003 Groningen Growth & Development Center http://www.ggdc.net**

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Productivity

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Employment

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Production Factors of Production Capital Technology Output Labor etc.

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**Factors of Production: Capital**

Capital (Kt) is the stock of durable goods (machines, equipment, buildings, etc.) used to produce other goods. Unit of measure is dollar-value. Difficult to measure directly, so it is defined indirectly.

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Stock vs. Flow Stock: Some variable that accumulates. Flow: Channel of increase or decrease of a stock. Example Stock: Government Debt Flow: Government Revenue, Government Expenditure Capital Flow: Investment (It), Depreciation (Dpnt)

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Stocks and Flows Figure 2.6 ©2002 South-Western College Publishing

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**Capital is Defined Recursivel**

Perpetual Inventory Method Method requires some initial guess at capital stock. As original guess capital depreciates, measure becomes more accurate. Constant Depreciation Rate

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**Hong Kong Investment to Capital Ratio**

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**Hong Kong capital stock**

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**Productivity: Two Concepts**

There are two basic measures of productivity. Average Productivity: The average productivity of a factor is output divided by amount of factor used. Marginal Productivity: The extra output that would be produced if an extra unit of a factor were used.

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Capital Productivity

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**Aggregate Production Function**

Assume aggregate output can be written as an algebraic function of the aggregate factors. Technological change over time is represented as a scaling factor, Qt. Example: Cobb-Douglas

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**Marginal Productivity of Labor**

Holding capital constant, the effect on GDP of increasing labor by a small amount. Y = F(L) MPL = ΔY/ΔL The slope of the production function For very small increases in labor, can be calculated with first derivative of output with respect to labor. MPL = F’(L) Diminishing returns suggests that if you hold one factor constant, marginal returns are a diminishing function.

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**Production Function (fixed K)**

Y ΔY ΔL ΔY ΔL L

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**Marginal Productivity Function (fixed K)**

MPL MPL L

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**Marginal Productivity Function (fixed L)**

MPK MPK K

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**Advantages of Cobb-Douglas Production Function Constant Returns to Scale**

If you increase both capital and labor by a factor of N, then you will also increase output by a factor of N Implications for Country Size: Output per capita depends only on capital per capita and labor per capita, not on population size itself.

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**Productivity Function**

Labor productivity is a function of technology and the capital-labor ratio.

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**Advantages of Cobb-Douglas Production Function Average Product & Marginal Product**

Under Cobb-Douglas, the marginal product is proportional to average product. All intuition about things that change average productivity carry-over 1-to-1 to marginal productivity.

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**Advantages of Cobb-Douglas Production Function Log-linear**

Take natural log of output Growth rate of output is a linear function of the growth rate of capital, labor, and technology.

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**Marginal Product = Marginal Cost**

A firm can raise its profits by increasing labor as long as the cost of the extra labor is less than the extra goods produced. Since the extra goods produced drops as more labor is added, firms will hire more labor until the marginal product falls as low as the real wage. Profit maximization suggests that the marginal product of a factor should equal its real cost. The real cost of labor is the real wage, the dollar wage rate divided by the price level.

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**Labor Demand Schedule (fixed K)**

W/P MPL L

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**Advantages of Cobb-Douglas Production Function Factor Shares**

Labor compensation is the product of the wage rate and the quantity of labor WtLt. Income left over to owners of capital is also a constant share of output a∙Yt

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Implications Labor share of income (labor intensity) is equal to the ratio of the marginal product of labor to the average product.

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Labor Intensity ≡1- a ≈2/3

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**Total Factor Productivity**

Total factor productivity measures the total effectiveness of an economy in applying all of its factors of production. TFP is a geometrically weighted average of capital and labor productivity with factor intensity, at and 1-at = used as weights.

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**TFP Growth TFP is log linear**

TFP growth rate is the gap between GDP growth rate and the weighted average of the growth rate of the factors of production.

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**TFP Growth Rates over time**

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**Advantages of Cobb-Douglas Production Function TFP equals technology**

If production is according to Cobb-Douglas, then TFP directly measures technology. at =a.

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Growth Accounting When we measure growth, we might want to determine if this is caused by capital growth, labor growth or capital growth. Growth caused by gY Capital a×gK Labor (1-a)×gL Technology gTFP

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**The East Asian Miracle 1965-2001**

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**Myth of the East Asian Miracle Alwyn Young, QJE 2001**

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Criticisms Critics of Young’s work that because of data mismeasurement, they assumed that East Asian production functions were different (greater capital intensity) than developed economies. Even using same production functions, most East Asian growth differentials are due to factor accumulation not TFP growth. One key point, capital productivity was declining in East Asia over this time period.

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Growth Accounting:

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Capital Productivity

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