thanks Question 3: 1M town of Podunk has decided to provide security services to

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Question 3: 1M town of Podunk has decided to provide security services to its residents by hiring workers (L) and guard dogs (D) Security 'cokes (S) am produced according to the Production function S and readmit of the town with to consume ICI win of ash seniors per period. a) Suppose we that L and D both tent for $1 per period Now much of each input should the town hire to produce the desired services at minimal cost? What will that cost be? (b) Suppose now that Podank is the only hirer of people who week with guard dogs and that the weed, cure for nth weaken is goes by L law when w is the period wage of guard dog handlers If dn. continue to run for SI per peeled: how much of each input should the town hire to produce the dewed services at minimal cow? What will those cows be? What will the wage rue of dog handlers, be?

Explanation / Answer

A)Given we have to produce 10 units of s

as S= sqrt(LD) =10

so LD = 100

using property

Arithmetic mean >or = Geometric meam

(L+D)/2 >= (LD)1/2

So (L+D)/2 = 10

L+D = 20 and LD = 100

for L= 10 and D =10 cost will be minimum and minimum cost = 20$

B) now L = 10W

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

so 10WD = 100

using AM >= GM

(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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