Question

Suppose a firms production function initially took the form Q=500(L+3K). however, as a result of a manufacturing innovation, it's production function is now Q=1,000(0.5+10K). a) Show that the innovation has resulted in technological progress in the sense defined in the text. b) is the technological progress neutral, labor saving, or capital saving?

Answer 1

A) We can rewrite the production function-

Q1= 500L+1500K

Q2=500L+10000K

Q2>Q1 for all quantities of K and L. The firm can produce more output for a given level of input. Therefore this innovation has resulted in technological progress.

B)Marginal rate of technical substitution-

In original production function,

MPk= 1500, MPl= 500. MRTS= MPl/MPk= 500/1500=1/3=0.33

In new production function,

MPk= 10000, MPl= 500. MRTS= MPl/MPk= 500/10000=0.05

MRTS new<MRTS original

0.05<0.33

Since MRTS of labour for capital has decreased. Therefore this is labour saving technological progress.

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