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    • Thread Starter

    I need some help again :P Hopefully someone can answer my questions this time ^^

    -- Explain the concept of scale elasticity.

    I know the basic definition is : % Change in output / % change in input

    But how would I expand upon this?

    -- Show how Cobb-Douglas function can be used to provide information abouts a firms "returns to scale"

    I understand how we get from: Q = (L^a) * (K^b) to dQ/dL = [aL^(a-1)] * (K^b)

    But how do I convert it to a+b is =,> or < 1 to gain the scale elasticity. I think it is something to do with the Elasticity of L and K being MPx / APl = elasticity of output.

    Not sure tbh, lots of rep availible ^^

    Thanks in advance
    • PS Reviewer

    PS Reviewer
    I'm not sure what 'scale elasticity' is but for the question about returns to scale you can just do something like:

    Given production function: f(L, K) = cL^aK^b

    For constant returns to scale: f(tL, tK) = tf(L, K)
    Substitute in production function: c(tL)^a(tK)^b = tcL^aK^b
    ct^at^bL^aK^b = tcL^aK^b
    t^at^b = t
    a + b = 1

    For decreasing returns to scale: f(tL, tK) &lt; tf(L, K)
    t^at^b &lt; t
    a + b &lt; 1

    For increasing returns to scale: f(tL, tK) &gt; tf(L, K)
    t^at^b &gt; t
    a + b &gt; 1

    Hope this helps.
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Updated: November 13, 2008


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