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) Determine the returns of scale.
1.2) Find the output elasticity for the production function.
1.3) Interpret your answer in part (1.2)?
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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