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Finding optimal output level

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The supply and demand equations for a hypothetical perfectly competitive market are given by QS = -100 + 3P and QD = 500 - 2P.
a. Determine the firm's optimal (i.e. profit maximizing) level of output and its profit or loss.
b. Graph the MR and MC curves and use the graph to find the output at which the two curves intersect.
(**The graph must be used to provide the answer to the question).

Total Fixed Total Variable
Output cost cost
0 $100 $ 0
1 100 100
2 100 180
3 100 240
4 100 320
5 100 440
6 100 600
7 100 800
8 100 1040
9 100 1340
10 100 1800

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Please refer attached file for missing graph.

a. Determine the  firm's optimal (i.e. profit maximizing level of output) and its profit or loss.

First we find equilibrium price,
Qs=-100+3P
Qd=500-2P
In equilibrium Qs=Qd
-100+3P=500-2P
5P=600
P=$120

Every firm is a price taker in perfectly competitive market. So,
Marginal Revenue=Market Price=$120

A competitive firm will sets its output level such that MR=MC=P to maximize its profits.

If we refer the following graph, we find that MR and MC curves intersects each other at a output level ...

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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