# Supply and Demand and Marginal Cost

From Lecture Module 3 Equation 4 we learned the alternative formulation of elasticity.

Alternative formulation of elasticity

EP = dQ/dP * P/Q = dlnQ/dlnP Natural log: ln, uses the base “e” How? ∂lnQ/∂lnP =(d lnQ/dQ) * (dQ/dP) * (dP/dlnP) [ Note: dY/dX = 1/(dX/dY) since, dlnX/dX = 1/X, dX/dlnX = X]

Example: Q = AP-α A:Constant>0 lnQ=lnA + ln(P-α) =lnA – αlnP EP = dlnQ/dlnP = -α

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Wage rate and rental rate are given by w and r respectively.

(2ia) Show whether or not the above productions function exhibits diminishing marginal productivity of labor (8 points).

We know from our test and from the notes by Dr. Ghosh that:

Q = LK

MPL= ∂Q/∂L = K

MPL does not fall with respect to L and the second order derivative did not give a negative value thus does not reflect diminishing marginal productivity.

(2ib) Determine the nature of the Return to Scale as exhibited by the above production function (12 points).

We know from module 4 created by Dr. Ghosh that:

Cobb-Douglas Production Function:

Q = ALα Kβ, A > 0, α > 0, β > 0 if α + β = 1, CRS if α + β > 1, IRS if α + β < 1, DRS

Note if A =1 and α = β = 1, we have the production function, Q = LK

As such the production function results in increasing Returns to Scale as α + β > 1 and 1+ 1 > 1.