Answer discussion question Essay Example
Given the Cobb-Douglas production function,
Yt = AtKt ^α. Lt ^ (1 – α).
*(α and (1 – α) is the power of Kt and Lt)
The above function exhibits constant returns to scale since;
[1 – α] = 0, therefore α = 1.
The equation shows a Cobb–Douglas function where the total production in given economy is represented by Y. A is the level of technology, t is the time factor in which the inputs are converted to output, K represent the capital, L is labor and (α) parameter measures output elasticity of capital. In special case where α=1, the production function portrays an element of linearity in capital and does not show the decreasing returns to scale property in the capital stock (Robert, 2008). However the property would prevail if the value of the capital intensity ranges between 0 and 1.
The Marginal Product of Labour (MPL)
MPL= dYt / dLt
= AtKt^ α. (-α+1) Lt^- α
The marginal product of labour is a shown above which measure the physical increase in firm’s output. This output is a result of hiring an additional worker, given that all factors are held constant (Robert, 2008).
Growth Accounting in relation to the above Cobb- Douglas function
If we introduce a scaling parameter (B) to the initial function it can be re-written as;
Yt = BKt ^α .At Lt ^(1 – α).
At, is time t aggregate factor productivity or the augmenting technical change of labour. Kt represents the capital stock while Lt is the labour. The α parameter represents the income share received by capital owners in return for use of capital.1- α is the share of income the workers receive (Robert, 2008). Therefore in this case α- parameter represent the ‘capital cost share’ since it is the cost share assigned to capital in the production of the Gross Domestic Product (GDP). However, given the appropriate data, the expression of the growth accounting provides us with the information on the amount of capital, labour as well as the technical change (productivity factor, At) that contributes to the growth of Gross Domestic Product over a given period of time.
Robert J Barro, 2008. Macroeconomics: A modern Approach. Mason: Thomson
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