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Production Function w/ Effective Labor

technological progress (A) -  

  • could result from better efficiency, higher quality, new products, more variety of products, etc
  • state of technology - variable representing how much output can be produced from given amounts of capital, labor
  • Y = F(K,N,A) = F(K,AN)
    • AN = effective labor, how many virtual workers are available
    • assuming constants returns to scale: xY = F(xF, xAN)
  • Y/(AN) = F(K/(AN), 1) = f(K/(AN))
    • terms calculated per effective worker

output vs capital - follows same rules as previous model w/o technological progress  

  • only main difference is that terms calculated per effective worker (/AN) instead of per worker (/N)
  • investment - must account for depreciation, growth in population, technological progress
    • (d + gA + gN)K
    • gA - growth of technology
    • gN - growth of population

 

  • steady state
  • output per effective worker (f(K/AN))
  • required investment ((d + gA + gN)K /AN)
  • investment (sf(K/AN))
  • at steady state, Y/AN and K/AN is constant, so Y and K growing at same rate as AN >> Y and K growing at rate (gA+gN) at steady state
Subject: 
Economics
Subject X2: 
Economics

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