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Cobb – Douglas Production Function: Y = K a L (1-a) a < 1, say a = kapital share of Y = 1/3

Cobb – Douglas Production Function: Y = K a L (1-a) a < 1, say a = kapital share of Y = 1/3. Show constant returns to scale: Double both inputs  Double outputs Show decreasing returns to capital: Double capital but leave labor constant  dY/dK=? Show decreasing returns to labor:

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Cobb – Douglas Production Function: Y = K a L (1-a) a < 1, say a = kapital share of Y = 1/3

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  1. Cobb – Douglas Production Function: Y = Ka L(1-a)a < 1, say a = kapital share of Y = 1/3 • Show constant returns to scale: • Double both inputs  Double outputs • Show decreasing returns to capital: Double capital but leave labor constant  dY/dK=? • Show decreasing returns to labor: Double labor but leave capital constant  dY/dN=? • Express y = Y/N as function of k = K/N • For given saving rate, s, and depreciation rate, δ, find steady state k and y. s=.32 and δ=.08  y=? Now s=.16 and δ=.08  y=?

  2. Golden Rule: Maximize steady state consumption per worker, c = C/N • Let Y = .5 K.5 N.5 . • Saving rate = s; depreciation rate = δ • Derive steady state k* = K*/N, y* = Y*/N • For δ = .05, compute y* and c* = (1-s)y* for s = .1,.2, …,.9. • Graph y* and c* as functions of s.

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