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Could anyone explain the step how to solve this problem?I guess equilibrium is same thing as profit maximization so I thought I need to know TR and TC first. I would like to solve this problem by myself but I really need someone's explanation because I really don't know the steps...Thank you very much.(For instance, I don't understand what can I get from demand function, and how can I star solving this problem...)

Suppose a monopoly faces the market demand function P = 10 – 2Q. Also, suppose it has no fixed costs and its total cost is given by TC(Q) = c.Q, where c < 10. [Notice that we assume total fixed cost, F, is zero. ] (a) find the equilibrium output, equilibrium market price and equilibrium total economic surplus of the monopoly market , all in terms of c. (Note: equilibriumand profit-maxmimizing mean the same thing.)

emma
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This looks like a macroeconomics problem. You might find some help by searching with that term. But here is some math help:

$Q$ is the price of the commodity, the company sells $10-2Q$ when the price is set to $Q$, and they incur $c\cdot Q$ in costs. Thus the profit as a function of $Q$ is $$(10-2Q)\cdot Q-c\cdot Q=(10-c)Q-2Q^2.$$

To maximize this value we need to find where its derivative equals zero: $$\frac{d}{dQ}\left[ (10-c)Q-2Q^2\right]=10-c-4Q.$$ Setting it equal to zero gives you the equation $$4Q=10-c.$$ This is how you maximize profits, given the assumptions of the problem.

Jeff Snider
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  • Jeff, thank you so much for your explanation. I was not sure what 10-2Q mean but I could understand because of your help! – emma Jan 31 '14 at 07:48