Cobb douglas

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Freejaffacake

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Why do developed countries have a high K/L ratio while a smaller alpha as compared to developing markets? Why do I keep thinking of a contradiction between the two statements?
 
Alpha is the elasticity of production (output) due changes in physical capital (K). So, due developed countries have already invested a lot in capital, their K/L ratio is high and any increase in capital, despite it is a great amount, the change in production is minimal. This relation is captured in a small alpha.
The theory behind is the deminishing returns of capital, the more you invest in a single factor, the lesser the increase in output. This means you cannot invest 100% of resources in a single factor; the optimal is to invest also in labor, technology, etc.
 
Thanks a lot. I got the alpha and K/L concept. I m still struggling in understanding why marginal product is constant while marginal productivity is diminishing. Any idea?
 
Can you tell please the exact chapter, page, book and level you seen that? Thanks.
 
Total product increases when labor increases, and when capital increases. However, marginal product decreases with an increase in total labor (capital held constant), and marginal product decreases with an increase in total capital (labor held constant); these are diminishing marginal productivity of labor and diminishing marginal productivity of capital, respectively.
Things are quite different when both labor and capital increase. In the version of the Cobb-Douglas function presented in the CFA curriculum, if labor and capital both increase by a given percentage (with total factor productivity – generally a measure of technology – held constant), total product will increase by that same percentage. This is known as constant returns to scale. In the Cobb-Douglas function, this is characterized by the sum of the exponents on K and L being 1:
Y = A(K^α)(L^β)
α + β = 1
Other forms of Cobb-Douglas have:
  • Increasing returns to scale (α + β > 1), or
  • Decreasing returns to scale (α + β < 1)
I wrote an article (for Level III) on the Cobb-Douglas production function that may be of some help here: http://financialexamhelp123.com/cobb-douglas-production-function/
 
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