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The slope of the frontier in the graph above measures the costs facing Crusoe. In order to get an extra fish, he must sacrifice two coconuts, and to get another coconut, he must sacrifice onehalf of a fish. Notice that there is no money involved; cost does not depend on money, but rather exists whenever there is scarcity and choice. In economics, the cost of anything refers to whatever is given up in order to get that thing. The cost of going to college, for example, includes not only the money a person spends on tuition (which could be spent on something else), but also includes the time spent studying and going to classes. The value of this time can be estimated by computing the amount of income a person could earn if he did not go to college.
If you reflect on this table, you will see the importance of scarcity. You can think of the productionpossibilities frontier as the way economists visualize scarcity. Which of the options will he choose? We cannot tell because we can only compute costs from this information, not benefits. The favorite assumption of economists is that individuals base their actions on the costs and benefits that they see. Benefits depend on the goals Crusoe has, and the productionpossibilities frontier has no information about them.
Next we see what productionpossibilities frontiers tell us about exchange.