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Consider the following production function Q(K,L)=100(?^1/2 + ?^1/2 )^2/3 where K is capital and L is...

Consider the following production function

Q(K,L)=100(?^1/2 + ?^1/2 )^2/3

where K is capital and L is labor.

  1. 1.1) Determine the returns of scale.

  2. 1.2) Find the output elasticity for the production function.

  3. 1.3) Interpret your answer in part (1.2)?

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Answer #1

a)   Conditional factor demand is the cost-minimizing level of an input (factor of production) such as labor or capital, required to produce a given level of output, for given unit input costs (wage rate and rental rate) of the input factors.

Minimize wL + rK subject to KL = q

It can be written as minimize wL + r(q/L) w.r.t L

w + rq(-1/L2) = 0

L = Squareroot(rq/w)

K = q/L = Squareroot(qw/r)

b) Cost function = wL + rK = Squareroot(wrq) + Squareroot(wrq) = 2squareroot(wrq) = C

C) ATC = C/q = 2squareroot(wr/q)

MC = Differentiate C w.r.t L(the variable factor) = w

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