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Lecture

Cobb-Douglas.pdf

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Department
Economics
Course
ECON 2000
Professor
Mokhles Hossain
Semester
Fall

Description
Cobb-Douglas Production function: Firms, according to the Neo Classical Theory, earn zero economic profit. Y = + Where, Y = Real GDP. = Total Capital income = Total Labour income. Therefore, = Capital’s Share of National Income. = Labour’s Share of National Income. Cobb Douglas Production Function is a neo classical production function with a unique feature. It gives us constant factor shares Such that: = Capital’s Share of National Income =  = Labour’s Share of National Income = 1-  is a constant between 0 and 1. We write the C-D production function as: ( )  . A is a parameter reflecting the level of technology. Why does the C-D function look like this? 1. It exhibits constant returns to scale. Without which we do not have competitive market. 2. It ensures that the MPL and MPK diminish with L and K, respectively. Otherwise we do not have downward sloping factor demand curves. 3. It generates the Euler’s equation. CRTS: ( ). in other words, ( )   = Y ( ) ( ) ( )  . ( )   = zY. MPK and MPL Define MPK = F ( ) ( ). Therefore MPK is nothing but the contribution of an additional unit of capital towards output/national income. Note that L stays the same. Suppose, ( )  . Find the Marginal Product of Capital: Numerical (tedious/time consuming) way: Assume the initial values for K, L and some constant values for A and  Suppose K = 10, L =10, A = 1,  . Thus, ( ) ( ) ( ) = 10 ( ) ( ) ( ) = 10.5 Therefore, MPK = 10.5 – 10 = 0.5 What Happens to MPK when K changes? In other wo
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