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handout1

# handout1 - Handout 1 1 CRS Cobb-Douglas function 2 Constant...

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Handout 1 1. CRS: Cobb-Douglas function A · (2 · K ) β · (2 · L ) 1 β = A · 2 β · K β · 2 1 β · L 1 β = 2 · A · K β · L 1 β . 2. Constant factor shares: Cobb-Douglas function The capital income = MPK · K = β · A · K β 1 · L 1 β · K = β · A · K β · L 1 β , and The labor income = MPL · L = (1 β ) · A · K β · L β · L = (1 β ) A · K β · L 1 β . 3. Growth accounting: Take logarithms of both sides of Y = AK β L 1 β , which gives ln Y = ln A + β ln K + (1 β ) ln L. Then di ff erentiate the last equation, which gives dY Y = dA A + β dK K + (1 β ) dL L . Then replace dY with Y and so on. 4. Equations in the Solow model. Divide by L t +1 in both sides of K t +1 = K t + s · A · ( K t ) β · ( L t ) 1 β δ · K t , and then in the left side, replace K t +1 L t with K t +1 L t +1 L t +1 L t . Then we obtain K t +1 L t +1 L t +1 L t = Kt L t + s · A · ( K t ) β · ( L t ) 1 β L t δ · K t L t . Because L t +1 L t = 1 + n , it follows that k t +1
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