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Here is a problem that I'm trying to solve:

No reaction will result in the monthly demand and marginal revenue functions:

P = \$150-\$0.1Q
MR = \$150-\$0.2Q

A major reaction will lead to the more elastic curves:

P = \$130-\$0.4Q
MR = \$130-\$0.8Q

The total monthly cost for marketing this product is composed of \$3000 additional administrative expenses and \$50 per unit for production and distribution costs. The relevant total cos and marginal cost are:

TC = \$3000+\$50Q
MC = \$50

a.) what is the profit-maximizing price, assuming not competitor reaction?
b.) calculate this price based on the assumption competitors will react.
c.) in light of cost conditions and absent any substanial barriers to entry, which secenario is more likely?

I'm going to show how I am attempting to solve this problem, but I will like to know if I am on the right track.

a.)
P = 150-0.1Q
= 150-50
= 100

MR = MC
150-0.2Q=50
100 =0.2Q
500 =Q

TR = TC
=100(500) - 3000 + 50(500)
=50000-28000
=\$22000

b.)
P=100; P=90

TR = TC
= 90(100) - 3000 + 50(100)
= 9000 - 3000 + 50(100)
= 9000 - 8000
= 1000

https://brainmass.com/economics/production-function/profit-maximizing-solved-39974

Solution Preview

a) For profit maximization, MR = MC
i.e., 150 - 0.2Q = 50
Therefore, 0.2Q = 150-50 = 100
Therefore, Q = 100/0.2 = 500
At Q = 500, P ...

Solution Summary

The profit maximizing solved for monthly demand and marginal revenues are examined.

\$2.49