The Cobb-Douglas production function is a good approximation of how economies convert capital and labor into output.
-If the factors of production always earn their marginal product, the Cobb-Douglas function results in constant factor shares.
-F(K, L)=AK^α L^(1-α)
--Capital Income=MPK x K=αY
--Labor Income=MPK x L=(1-α)Y
Properties of the Cobb-Douglas Function
-Constant Returns to Scale
What can change the marginal products?
-An increase in K will increase the MPL, but reduce the MPK.
-An increase in L will increase the MPK, but reduce the MPL.
-An increase in technology (A) will increase both MPL and MPK.
Notice another important result.
-The MPL is proportional to the output per worker or the average labor productivity.
-The MPK is proportional to the output per machine or the average capital productivity.
Does α really determine how much income goes to labor and how much income goes to capital?
-Labor Income=MPLxL=(1-α)Y, so (1-α) is labors' share of income.
-Capital Income=MPKxK=αY, so α is capital's share of income.
-The ratio of labors' share of income to capitals' share of income, (1-α)/α, is constant.
--The amount of labor, capital, or the level of technology do not affect the factor shares of income.
The share of income going to labor has remained very stable, but not constant.
-Since the 1970s, the share of income going to labor has been slowly decreasing.
-One explanation may be that changes in technology (A) may have altered the relative important of labor and capital in the production process; the value of α may have changed.
8th EditionN. Gregory Mankiw
2nd EditionDavid Anderson, Margaret Ray
6th EditionN. Gregory Mankiw
1st EditionAlan Krueger