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# Calculating optimal output and price levels

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The Xerxes Company is composed of a marketing division and a production division. The marketing division packages and distributes a plastic item made by the production division. The demand curve for the finished product sold by the marketing division is

P0=200-3Q0

Where P0 is the price sold (in dollars per pound) of the finished product and Q0 is the quantity sold (in thousands of pounds). Excluding the production cost of the basic plastic item, the marketing division's total cost function is

TC0=100+15Q0

Where TC0 is the marketing division's total cost (in thousands of dollars). The productions division's total cost function is
TC1 =5+3Q1+0.4Q1^2

Where TC1 is total production cost (in thousands of dollars) and Q1 is the total quantity produced of the basic plastic item (in thousands of pounds). There is a perfectly competitive market for the basic plastic item, the price being \$20 per pound.

What is the optimal output for the production division?
What is the optimal output for the marketing division?
What is the optimal transfer price for the basic plastic item?
At what price should the marketing division sell its product?

##### Solution Summary

Solution describes the steps to calculate optimal price and output levels for production and marketing division in the given case.

##### Solution Preview

a. What is the optimal output for the production division?

Total cost function for production division is given by
TC1=5+3Q1+0.4Q1^2
Marginal Cost for production division is given by
MC1=dTC1/dQ1=3+0.8Q1

In case of perfectly competitive environment, a firms sets its output level such that marginal cost is equal to price.
Price=\$20 per ...

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###### Education
• BEng (Hons) , Birla Institute of Technology and Science, India
• MSc (Hons) , Birla Institute of Technology and Science, India
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