ECON
NOTESONSOLOWGROWTHMODEL

NOTESONSOLOWGROWTHMODEL - NOTES ON SOLOW GROWTH MODEL Lt =...

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NOTES ON SOLOW GROWTH MODEL L t = Labor Force at beginning of year t K t = Capital Stock at beginning of year t C t = Consumption over year t I t = Investment over year t Y t = Output over year t k t = K t /L t = capital per worker c t = C t /L t = consumption per worker (“standard of living”) i t = I t /L t = investment per worker y t = Y t /L t = output per worker Distinguish between LR economic growth versus fluctuations around the trend Assumptions : 1. NX = 0 and G = 0 barb2right Y = C + I 2. Labor force grows at the same rate as the population (let n = population growth rate) 3. Cobb-Douglas production function: Y t = A*K t α L t 1- α . PER-WORKER PRODUCTION FUNCTION To convert this production function into the “per-worker production function”, divide both sides by L t : (Y t /L t )= (A*K t α L t 1- α )/L t = A*K t α L t - α = (A) (K t /L t ) α barb2right y = Ak α . This is the per-worker production function. For convenience, I will be dropping the time subscript for the per-worker variables (with a few exceptions) and use lower-case letters. y ( output per worker) y = Ak α Δ y Δ k k (capital per worker) Slope = ( Δ y/ Δ k) = MPK Notice that the slope gets flatter and flatter. This is due to diminishing marginal returns to capital (i.e., MPK falls as k rises, other things constant )

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