14.02_Lectures_3-4

14.02_Lectures_3-4 - TOPIC TOPIC 2 The Supply Side of the...

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TOPIC 2 The Supply Side of the Economy
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Goals of Topic 2 Introduce the Supply Side of the Macro Economy: 1. Production Function 2. Labor Market: Labor Demand Labor Supply Equilibrium Wages and Employment 2
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Production Function
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The Production Function GDP (Y) is produced with capital ( K ) and labor ( N ): =AF(K ,N) Y A F(K,N) where A is Total Factor Productivity ( TFP ) = an index of efficiency in the use of inputs ( technology ) Sometimes, I will modify the production function as follows: Y = A F(K,N, other inputs) where other inputs include energy/oil! Realistic Example is a Cobb Douglas function for F(.): =AK α 1- α 4 Y =A K N with 0< α <1
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Measurement Y is GDP (it is measured in dollars). As noted above, we want to measure Y in “real” terms.<<you should know what this means from lecture 2>>. For our Cobb Douglas production function, N is measured in number of workers and K in dollars: K often is measured as the replacement cost of capital N often is measured in number of workers N can also be measured using total hours worked = number of workers × hours per worker Wage differentials can help to measure “effective labor supply”, taking into account “skill” differentials. 5 N.B.: sometimes we will use N to denote total population (e.g. income per capitaY/N)
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Graphical Representation 1 Hold A and N constant (at levels A* and N*) Graph Y as a function of K Y A*F(K,N*) K 1. As K increases Y increases (the curve is upward-sloping ) 6 2. As K increases the marginal increase in production decreases (the curve becomes flatter as K increases )
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Graphical Representation 2 Hold A and K constant (at levels A* and K*) Graph Y as a function of N Y A*F(K*,N) N 1. As N increases Y increases (the curve is upward-sloping ) 7 2. As N increases the marginal increase in production decreases (the curve becomes flatter as N increases )
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Aggregate Production Function: Fact 1 1. Constant Returns to Scale FACT 1: If you double the inputs, you double the output! Y = AF(2K,2N) 2Y AF(2K,2N) Cobb-Douglas: Y = (2K) α N) 1- α = 2A K α 1- α 2Y A (2K) (2N) 2A K N CRUCIAL: α + (1- α ) = 1! 8
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Aggregate Production Function: Fact 2 2. Diminishing Returns to N and K Define MPN = Marginal Product of Labor = dY/dN Define MPK = Marginal Product of Capital = dY/dK ACT 2: PN decreases with N and MPK decreases with K FACT 2: MPN decreases with N and MPK decreases with K Cobb-Douglas: MPN = (1- α ) A (K/N) α Fixing A and K, MPN falls when N increases MPK = α A (N/K) (1- α ) Fixing A and N, MPK falls when K increases 9
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Aggregate Production Function: Fact 3 3. Complementarities between A, K and N FACT 3: The higher the level of capital (or technology), the higher the marginal product of labor (and symmetrically for capital!) Cobb-Douglas: MPN = (1- α )A±(K/N) α creasing A or K increases MPN Increasing A or K, increases MPN MPK = α A (N/K) (1- α ) Increasing A or N, increases MPK 10
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