the town of podunk has decided to provide security services to its resident by h

Question

the town of podunk has decided to provide security services to its resident by hiring workers (L) and guard gogs(D).security services (S) are produced according to the production function S=squr LD
and residents of town wish to consume 10 units of such services per period
suppose now that podunk is only hirer of peaple who work with guard dogs and supply curve for such workers is given L = 10w where is per period wage of guard dog handlers .if dogs continue to rent for $1per period how much of each input should the town hire to produce the desired services at minimal cost? what will those costs be?what will the wage rate of dog handelers be?
thanks

Explanation / Answer

Given we have to produce 10 units of s

as S= sqrt(LD) =10

so LD = 100

now L = 10W

so S = (10WD)1/2 = 10 (given)

so 10WD = 100

using property

Arithmetic mean >or = Geometric meam

(10W + D)/2 >= sqrt(10WD)

for minimum

so (10W + D)/2 = 10

as WD = 10 so D= 10/W

so 10W + 10/W = 20

so W2 - 2W +1 =0

so W = 1 (solving equation)

and D =10

ans D = 10 , wage rate = W = 1 $ per period Cost = 10W + D = 10 + 10 = 20 $

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