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Finding the Markup and Optimal Output Levels

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I need some help in answering these two questions:
1. An airplane manufacturer has annual fixed costs of $50 million. Its variable cots are expected to be $2 million per plane. If the manufacturer wants to earn a 10 percent rate of return on its investment of $400 million and expects to produce 100 aircraft this year, what will its markup on total cost have to be? If its expects to produce 150 aircraft, what will its markup have to be?

2. There are only two firms in the widget industry. The total demand for widgets is Q=30-2P. The two firms have identical cost functions, TC=3+10Q. The two firms agree to collude and act as though the industry were a monopoly. At what price and quantity will this cartel maximize its profits?

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Solution:
1. Case 1 : Output, Q=100
Fixed Cost=TFC=$50 million
Per Unit variable Cost=V=$2 milliom
Variable Cost=TVC=V*Q=2*100=$200 million
Total ...

Solution Summary

The solution address the two problems, by depicting steps to estimate the markup on cost and also demonstrates the methodology to find the optimal price and output combination in the given case with step-by-step workings and formulas shown.

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Calculate the optimal parameters in the given case.

Please help with the following problems. Provide step by step calculations.

A monopolist produces trinkets at $2/unit. The demand for trinkets as a function of unit price p is: D(p) = 100-p.

1) At a unit price of $10, what will the demand be?
2) At a unit price of $10, what will total revenue be?
3) At a unit price of $10, what will the total cost of production be?
4) What is the monopolist's profit maximizing price?
5) Use the markup formula to determine the elasticity of demand at this price.
6) What is the monopolist's maximum profit?

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