simplified output-capital relationship
- assumes that population and participation rate are constant, and there is no technological progress
- constant population, participation rate >> constant employment N
- no technological progress >> technology doesn't change over time >> no shifts in production function over time
- Y/N = f(K/N) = F(K/N, 1)
- works for functions satisfying constant returns to scale
- investments - assumes no public saving
- I = S + (T-G) = S = sY
- I = sY, where s = saving rate
investment-capital accumulation
- depreciation rate (d) - proportion of capital stock that becomes worthless each year
- Kt+1 = (1-d)Kt + It
- Kt+1/N = (1-d)Kt/N + It/N
- Kt+1/N = (1-d)Kt/N + (sYt)/N
- Kt+1/N - Kt/N = (sYt)/N - dKt/N
- Kt+1/N - Kt/N = D(K/N) = sf(Kt/N) - dKt/N
- change in capital equal to difference of investment and capital depreciation
steady state - in long run, investment equals capital depreciation
- steady state
- depreciation (dKt/N)
- investment (sf(Kt/N)
- output (f(Kt/N)
- in long run, capital per worker will always converge to the steady state
- start to the left, investment is greater than depreciation, so K/N will increase to steady state
- start to the right, depreciation is greater than investment, so K/N will decrease to steady state
Subject:
Subject X2:
