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Profit is equal to total revenue minus total costs, if a firm wants to maximize its profit it has to lower the cost of producing a given level of output and or increase the item price if there is a willing buyer. If a firm is not minimizing costs then there exists a way for the firm to increase profits.

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Q: Prove that profit maximizing firm will always minimise?
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How does maximizing the long-run expected cash flows of the firm translate into maximazing shareholders wealth?

Maximizing the long-run expected cash flows of a firm does not inherently translate into maximizing shareholder wealth. I believe the question that is trying to be posed here is how do long-run expected free cash flows of the firm translate into maximizing shareholder wealth. That answer is because free cash flows are the amount of money available to a firm to either reinvest into the business or distribute out to shareholders. Firms that generate free cash flows and then reinvest in their own business will generally increase their stock price (A company that is making profits and growing will be valued higher) or the firm can pay out some of those free cash flows in the form of dividends (obvious value to the shareholders). Long-run expected cash flows don't prove anything. If I have a million dollars that I want to invest into a lemonade stand, and that lemonade stand costs me $1,000 per month to operate ($1,000 outflow per month) but my monthly revenue is only $800 ($800 inflow per month) then I will have cash flows of -$200 per month. Since I'm ready to invest a million this will be sustainable for quite a long time, but it by no means is maximizing my (me being the sole shareholder) wealth.


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