Lectures in Macroeconomics- Charles W. Upton The Cobb-Douglas Production Function Y = AK  L (1-  )

The Cobb-Douglas Production Function History Developed by Paul Douglas and C. W. Cobb in the 1930’s

The Cobb-Douglas Production Function History Developed by Paul Douglas and C. W. Cobb in the 1930’s –Douglas went on to be professor at Chicago and U.S. Senator –Cobb - ??

The Cobb-Douglas Production Function The General Problem An increase in a nation’s capital stock or labor force means more output. Is there a mathematical formula that relates capital, labor and output?

The Cobb-Douglas Production Function The General Form

The Cobb-Douglas Production Function Increasing Capital

The Cobb-Douglas Production Function Increasing Capital

The Cobb-Douglas Production Function Increasing Capital Diminishing returns to proportion

The Cobb-Douglas Production Function Increasing Labor

The Cobb-Douglas Production Function Increasing Labor

The Cobb-Douglas Production Function Increasing Labor Diminishing returns to proportion

The Cobb-Douglas Production Function Increasing Both

The Cobb-Douglas Production Function Increasing Both

The Cobb-Douglas Production Function Increasing Both Constant returns to scale

The Cobb-Douglas Production Function Substitution Capital and Labor Can be Substituted

The Cobb-Douglas Production Function An Illustration

The Cobb-Douglas Production Function An Illustration

The Cobb-Douglas Production Function An Illustration

The Cobb-Douglas Production Function An Illustration A =3L =10 K =10

The Cobb-Douglas Production Function An Illustration

The Cobb-Douglas Production Function Doubling Capital

The Cobb-Douglas Production Function Constant Returns to Scale

The Cobb-Douglas Production Function Substitution

The Cobb-Douglas Production Function Estimation

The Cobb-Douglas Production Function Estimation

The Cobb-Douglas Production Function Estimation Statistical issues abound!

The Cobb-Douglas Production Function Best Estimate

The Cobb-Douglas Production Function Factor Payments  = % of Income going to owners of capital 1-  = % of Income going to workers

The Cobb-Douglas Production Function How well does it work? You can’t beat something with nothing

The Cobb-Douglas Production Function CES Production Function

The Cobb-Douglas Production Function CES Production Function Suppose 10% increase in wage rate leads to 10% increase in capital labor ratio.  = 1.

The Cobb-Douglas Production Function CES Production Function Suppose 10% increase in wage rate leads to 5% increase in capital labor ratio.  = ½.

The Cobb-Douglas Production Function CES Production Function In the Cobb-Douglas Production Function,  = 1.

The Cobb-Douglas Production Function CES Production Function The CES allows for a different elasticity of substitution. Little gained.

The Cobb-Douglas Production Function Leontief Production Function K L

The Cobb-Douglas Production Function Leontief Production Function K = aY L = bY K L

The Cobb-Douglas Production Function Leontief Production Function K = aY L = bY K L

The Cobb-Douglas Production Function Leontief Production Function K = aY L = bY K L  = 0

The Cobb-Douglas Production Function Leontief Production Function K = aY L = bY K L Doesn’t work. We can and do substitute labor for capital all the time

The Cobb-Douglas Production Function Other Factors?

The Cobb-Douglas Production Function And in Conclusion…

The Cobb-Douglas Production Function End ©2003 Charles W. Upton. All rights reserved