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Analyzing cost function of a firm

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Find the range of outputs for which the cost function C(q) = f +cq^2 where c>0 is characterized by

A. i) economies of scale, (ii) diseconomies of scale, and (iii) constant return to scale

B. Are there economies of scale if f = 0.

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Solution Summary

Solution explains the methodology to find the range of output for which given cost function has economies of scale, diseconomies of scale and constant return to scale.

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Solution:

Average cost AC=C(q)/q=(f/q)+cq

For economies of scale to happen, Average cost decreases as output increases i.e.
d(AC)/dq<0
(-f/q^2)+c<0
-f+cq^2<0
q<(f/c)^0.5
For q<(f/c)^0.5, cost function is ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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