The opportunity cost is the cost you pay of what you can't do instead. Its value is determined by your second-best alternative.
(a) Since we are handed an objective cardinal utility function and a limited number of alternatives, for the purposes of this problem it's easy to figure out what our opportunity cost is: The best option is worth $1500 to us, and the second-best option is worth $1000 to us, so the opportunity cost is the $1000 of our second-best alternative. Our real economic profit is the difference, $500.
(b) If we are offered a new alternative that's worth $1100 to us, that now becomes our second-best alternative; so our opportunity cost rises from $1000 to $1100. Our real economic profit is now only $400.
(c) It may seem a bit counter-intuitive that the cost we pay and therefore profit we get from doing something depends on something else we didn't do, but the key is to understand that we could have. In fact, most of what we call costs in the real world are ultimately opportunity costs, because a dollar bill has no inherent value; it's only valuable to us because it can be used to buy things. So when you spend $100 on something, you're not actually losing anything by not having the $100; you're losing the opportunity to spend that $100 on something else.
You might even actually feel worse about your decision if you have a higher opportunity cost, thus making that cost directly reflected in your experienced utility. In the question we just answered, we've gone from "paying" dinner with the movie star to "paying" $1100. So we don't feel as thrilled to get the season tickets, because they were $500 better than the dinner date, but only $400 better than the cash.
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