6 ProductionFactors of ProductionCapitalTechnologyOutputLaboretc.
7 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.
8 Stock vs. FlowStock: Some variable that accumulates. Flow: Channel of increase or decrease of a stock.ExampleStock: Government DebtFlow: Government Revenue, Government ExpenditureCapitalFlow: Investment (It), Depreciation (Dpnt)
10 Capital is Defined Recursivel Perpetual Inventory MethodMethod requires some initial guess at capital stock. As original guess capital depreciates, measure becomes more accurate.Constant Depreciation Rate
13 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.
15 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
16 Marginal Productivity of Labor Holding capital constant, the effect on GDP of increasing labor by a small amount. Y = F(L) MPL = ΔY/ΔLThe slope of the production functionFor 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.
18 Marginal Productivity Function (fixed K) MPLMPLL
19 Marginal Productivity Function (fixed L) MPKMPKK
20 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 NImplications for Country Size: Output per capita depends only on capital per capita and labor per capita, not on population size itself.
21 Productivity Function Labor productivity is a function of technology and the capital-labor ratio.
22 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.
23 Advantages of Cobb-Douglas Production Function Log-linear Take natural log of outputGrowth rate of output is a linear function of the growth rate of capital, labor, and technology.
24 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.
26 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
27 ImplicationsLabor share of income (labor intensity) is equal to the ratio of the marginal product of labor to the average product.
29 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.
30 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.
35 Myth of the East Asian Miracle Alwyn Young, QJE 2001
36 CriticismsCritics 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.