Question

Homework: HW-6: Chapter 7 5 of 10 (3 complete) Score: 0 of 1 pt Text Question 2.11 A Chinese high technology manufacturing firm has a production function of q-11L080020 (based on Zhang, et al., 2012). It faces prices of w $8 and r $2. What are its short-run average variable and marginal cost curves? Let K be fixed in the short nun The firm's short-run average variable cost curve, AVC, as a function of K and a is $(Property format your expression using the tools in the palette. Hover over tools to see kayboard shortouts. Eg, a superseript can be created with the character)

Answer 1

q = 11L^0.8K^0.2

Cost is minimized when MPL/MPK = w/r = 8/2 = 4

MPL = $\dpi{80} \partial$ q/$\dpi{80} \partial$L = 11 x 0.8 x (K/L)^0.2

MPK = $\dpi{80} \partial$ q/$\dpi{80} \partial$K = 11 x 0.2 x (L/K)^0.8

MPL/MPK = (0.8/0.2) x (K/L) = 4K/L = 4

4K = 4L

K = L

Substituting in production function,

q = 11L^0.8L^0.2

q = 11L

L = (q/11)

K = L = (q/11)

Substituting in total cost function,

TC = wL + rK

If K is fixed in short run,

TVC = wL

TVC = 8 x (q/11)

AVC = TVC/q = [8 x (q/11)] / q = 8/11 = 0.73