aggregate production function - relation between output and inputs
- Y = F(K,N)
- K = capital, N = labor
- treats all workers equally in this simplification
- state of technology - determines how much output per quantity of capital and labor
returns to scale - relation between scaling inputs and effect on output
- constant returns to scale - doubling quantities and labor doubles the output
- xY = F(xK, xN)
- decreasing returns to capital - increases in capital result in smaller and smaller increases in output
- initial monetary increase produces the largest output increase
- decreasing returns to labor - increases in labor result in smaller and smaller increases in output
constant returns to scale - can relate production per worker
- situation where x = 1/N
- Y/N = F(K/N, N/N) = F(K/N, 1)
- states that output per worker depends on capital per worker
- assuming that labor stays constant
- shows decreasing returns to capital in this model
- slope of graph decreases
- eventually, increasing K/N will not increase Y/N
sources of growth -
- capital per worker increase >> output per worker increases
- capital accumulation
- improve state of technology >> more output per worker
- technological progress
- shifts production function curve up
- saving rate - sustains level of output
- w/ decreasing returns to capital, capital increases must get larger to sustain output growth
- saving rate cannot increase growth rate of output in long run
- higher saving rate >> higher standard of living, but rate stays unchanged
- sustained technological progress >> sustained growth
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