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