Question

Suppose a firm can manufacture a product using the following production function:

Q = f (K,L) =

"K^0.60

"L^0.40

(a) What is the APL when the firm uses 10 units of fixed capital and 30units of labor?

(b) How does the APL change when the firm uses 100 units of labor?

(c) Write out an expression for the MPL when capital is fixed (d) Show that the MPL depends on the amount of labor that is employed by calculating the MPL for 30 and 100 units of labor. (e) Is the function linear? Why?

Answer 1

Production function is Q = K0.60 L0.40

a) APL = average product of labor and is computed as APL = TP/L or Q/L. In this case Q = (10)0.60 L0.40

APL = (10)0.60 L0.40/L

= (10)0.60 L-0.60

= (10)0.60 (30)-0.60

= 0.517

b) For L = 100, we have APL =  (10)0.60 (100)-0.60 = 0.251. APL falls as L rises

c) MPL = dQ/dL = d(10^0.60* L^0.40)/dL = 0.40*(10^0.60)*(L^-0.60) = 1.59(L^-0.60)

d) MPL when L = 30 and L = 100

MPL (L = 30) = 1.59 (30^-0.60) = 0.207

MPL (L = 100) = 1.59 (100^-0.60) = 0.10

Hence MPL falls as L is increased

e) No the function MPL is not linear as MPL shows diminishing marginal returns.