Question

Afir's production engineers have estimated its production function as Q(KL) = 2K2/1/2 = 2-K L=2KL where ' and 'L' represent the amounts of capital and labour, respectively, used in production each period, and 'Q' represents the amount of output produced each period. The firm pays a wage, w, for each person-hour of labour of $16. The rental rate of a machine-hour of capital, wk, is $100. What will be the firm's minimum cost of producing 10 units of output? What is its minimum cost of producing 30 units of output? What is the firm's cost function (this can either be derived or inferred from the patter of minimum cost at various levels of output)? 1) C(10) = $410, C(30) = $1,230, C(O) = 410 | 2) C10) = $400, C(30) = $1,200, C(0) = 400 3) C(10) = $400, C(30) = $800.CO) - 400 4) C(10) = $400. C(30) - $3,600, C1Q) = 402 5) C(10) - $410, C(30) -5820, CO) 410

Answer 1

Cost minimization condition,

MPk/r=MPL/w

√L/r√K=√K/w√L

w*L=rK

L=100k/16=25k/4

Q=10

10=2√25k^2/4=2*5K/2=5K

K=10/5=2

L=25*2/4=12.5

C=12.5*16+2*100=400

Q=30

30=5K

K=6

L=25*6/4=37.5

C=37.5*16+6*100=1200

So given Q=30 ,C=400

Q=30 ,C=1200

So we can derive cost function,C=40 Q

Option b is correct