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Finding optimal production level

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Suppose that a firm comes to you with the following information:

P=1.5
TC=(1/70)q^2-(25/35)q+100
MC=(1/35)q-(25/35)

i.What is the total profit/loss if the firm stays in business?
ii.What is the total profit/loss if the firm shuts down?
iii.Would you recommend that the firm stay in business or shutdown? Why?
iv.Please graph (i) including the numbers.

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Solution Summary

Solution describes the steps to calculate optimal level of output level and checks whether it should continue or shut down its operations at the current level.

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Please refer attached file for graphs and better clarity of tables.

1.What is the total profit/loss if the firm stays in business?

A firm will maximize its profits by selecting its output level such that MR=MC.
In this case P=MR. So, put P=MC to find optimal output level.

1.5=(1/35)q-(25/35)
52.5=q-25
q=52.5+25=77.5
Optimal output level=77.5 units

Total Revenue=TR=P*q=1.5*77.5=116.25
TC (at q=77.5)=(1/70)*77.5^2-(25/35)*77.5+100=130.45

Total ...

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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