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Knowing range of economies & diseconomies for cost function

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You are given the following long run cost function:
TC=160Q-20Q2+1.2Q3 Go from Q=0 to Q=12
A. Calculate the long run average cost and marginal cost. Plot these costs on a graph.
I need this set up in excel.
B. Describe the nature of this functions scale of economies. Over what range of output does economies of scale exist? Diseconomies of scale? Show this on the graph.

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Solution Summary

Solution describes the steps in calculating LRAC and LRMC for given output range. Graph for Long run average cost (LRAC) and Long run marginal costs(LRMC) is plotted. Output ranges have been worked out for which economies and diseconomies of scale exits.

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Please see the attached file for complete solutions. Graph will not print here.

a)
Total Cost Fucntion is given by
TC = 160Q-20Q^2+1.2Q^3
LRAC =TC/Q
Long Run Average Cost function is given by
LRAC = 160-20Q+1.2Q^2 -----------------------------------(1)
Long Run Marginal Cost function is given by
LRMC = d(TC)/dQ = 160-40Q+3.6Q^2 ------------------------(2)

We can calculate value of Average Cost and Marginal Costs by above relations and get the following ...

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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