prod - Productivity Output and Employment 6 September 2011...

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Productivity, Output, and Employment 6 September 2011 1 Reading Chapter 3 of Abel/Bernanke/Croushore 2 The Production Function What determines the quantity of goods and services than an economy produce in period of time? 1. Quantities of various inputs — capital equipment, labor, raw materials, land, and energy. 2. The technology of production — the level of e ciency with which the factor inputs are combined. Technology encompasses not only technical e ciency, but also factors such as management practices, the business environment, property rights and the like. The production function represents the relationship between output and inputs: Y = AF ( K, N ) , where K = the capital stock, N = the number of labor hours hired, A = total factor productivity, or simply productivity. Two main properties of production functions: 1. Slopes upward: more of any input produces more output. 2. Slope becomes fl atter as input rises: diminishing marginal product as input increases. The marginal product of capital (MPK), Y/ K > 0 but diminishes as capital input increases; i.e., 2 Y/ K 2 < 0 . 1
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Figure 1: Output as a function of capital Figure 2: Output as a function of labor input 2
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Figure 3: Supply Shock The marginal product of labor (MPN), Y/ N > 0 but diminishes as labor input increases; i.e., 2 Y/ N 2 < 0 . Supply shocks, or productivity shocks, refer to abrupt and usually unexpected changes to productivity. It is easiest to model supply shocks by changes to total factor productivity, A . Supply shocks can be positive or negative. Examples: weather, inventions and innovations, government regulations, oil prices, states of the fi nancial market. A positive supply shock usually not only raises output but also the marginal products, and likewise for a negative supply shock. 3 Labor demand Assumptions: 1. Hold capital stock fi xed; i.e., a short-run analysis. 2. Workers are all alike. 3. Markets are competitive. 3
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Figure 4: Labor demand A given fi rm maximizes: short - run profit = P × AF ( K, N ) W × N, yielding a fi rst order condition: P × Y N W = 0; i.e., MPN = W P = w, where w is known as the real wage — units of output the nominal wage W can buy. The (horizontal) sum of individual fi rms’ labor demand constitutes the aggre- gate labor demand curve. In so far as a positive (negative) supply shock raises (lowers) the MPN for each N , the labor demand curve shifts up (down) in response. If capital and labor input are complements (substitutes); i.e., 2 Y K N > ( < ) 0 , the labor demand curve shifts up (down) when capital is more abundant. His- torically, capital and labor inputs had appeared to be complements; while in 4
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Figure 5: A favorable (positive) supply shock recent times, empirical studies have shown that capital and skilled labor are complements whereas capital and unskilled labor are substitutes.
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