A small firm in Indonesia has the following estimated production function: ln(q) = 10 + 2.6ln(L) - 0.4(ln(L))2 Derive the firm's marginal and average product of labor as functions of q and L
What is the elasticity of output with respect to labor?
Total differentiate both sides of the function with respect to L:
(1/q)(dq/dL) = (2.6 - 0.8ln(L))(1/L)
Rearrange to get:
MP = (q/L)(2.6 - 0.8ln(L))
The AP = q/L.
The elasticity is (dq/dL)(L/q) = MP/AP = 2.6 - 0.8ln(L).
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Refer to the data in the table above.
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