Show constant returns to scale: Double both inputs  Double outputs 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=?

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.