Question

. Lulu owns a firm that produces leggings. The production function is given by Q = 2VKVL, so that MPL VK Vī VI and MPK Q is Lulu's VK output, K is capital, Lis labor, and MP is the marginal product. The wage (w) rate per worker (L) is $40 per day and rental rate (r) per unit of capital (K) is $10 per day. Lulu currently hires 4 workers and rents 9 machines to produce 12 leggings. Is Lulu minimizing her costs? How do you know?

dont need a big answer

Answer 1

K=9

L=4

W=$40

R=$10

At cost minimization level,

MPL/Wage rate= MPk/rental rate

(√k/√L)/40= (√L/√K)/10

(√9/√4)/40=(√4/√9)/10

(120/2)=(20/3)

60≠ 6.7

Since MPL/w≠ MPk/r

this is not a cost minimizing level.

To reduce the cost we need to increases Labor and reduce capital.