Marginal product of labor and capital, Macroeconomics

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We define marginal product of labor, MPL as the derivative of f with respect to the L - which is, as (approximately) how much Y will increase when L increases by one unit. We also describe the marginal product of capital, MPK as the derivative of f with respect to K. Note that MPL and MPK will rely on both L and K (MPL and MPK are functions, not variables). 

MPL = df/dL, MPK= df/dK

  • since f is increasing in L, MPLshould be positive for all values of L and K.
  • MPLpresumed to be decreasing in L - the more work that is used, the lower the marginal product of labor.
  • MPLpresumed to be increasing in K - the more capital, the higher the marginal product of labor.
  • Similarly MPKshould be positive for all values of L and K.
  • MPK is presumed to be decreasing in K and increasing in L.

When we view Y as a function of L holding K fix, Y will be increasing in L however at a decreasing pace (Because of the fact that MPL is positive though decreasing in L). 

1638_Marginal product of labor and capital.png

Figure:Production function

We state labour productivity as Y/L that is, as GDP per hour worked. Labour productivity tells us how much we can produce by employing one hour of labour and it relies on the amount of capital and the technology.


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