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Transfer pricing/Optimal output equation

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A firm sells specialized electronic computers. Each of the computers has a unique chip produced at a California plant at cost of Cw(Qc)=Q^2 c
[C subscript w *(Q subscript c)=Q squared subscript c.]

Once produced, the chips are shipped to the firm's new jersey east coast plant where the computers are then assembled, packaged and shipped to market at a cost of Ce(Q)=200Q. [C sub e * Q=200Q]
Demand was recently estimated for the computers and found to be P=5000-Q.

Given this,
1. what is optimal output for the computers?
2. what is optimal transfer price between the two plants?

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Solution Summary

The solution calculates the optimal output and optimal transfer price for the given question.

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Answer 1:

Optimal output of computers occur at the Profit Maximization level.
That this level MR = MC

P = 5000 - Q
Thus Total Revenue = PxQ = (5000 - Q)XQ
Thus MR = 5000 - 2Q
TC = 200Q + ...

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