One early example of the tragedy of the commons occurred in the Middle Ages. Sheepherders would graze their sheep on a common pasture. Each herder wanted to feed his or her sheep so that they could get fat and therefore be sold for a higher price. But the more sheep there were on the common, the less grass there was for any single sheep. As a group, it would be better to limit the number of sheep on the common to maintain the resource. But each herder has an incentive to raise more sheep if the other herders are restricting the number of sheep they raise. Therefore, there is a conflict between what is collectively rational and what is individually rational. Let's look at a simple problem to see how this comes about. v 3rd attempt Part 1 (3.3 points) See Hint Suppose there are four villagers who can either raise sheep or bake bread. A sheepherder must buy a sheep for $200, raise it on the common, and then sell it at the market in a nearby town. The table below shows how much a sheepherder can sell a sheep for. In the same time it takes to bring a sheep to the market, bread bakers can make a profit of $35. You will need to copy the table and fill it in as you answer the questions. Number of sheep feeding on the Price of a sheep at Profit earned from one Total profit from sheep Additional profit from common market sheep one sheep 1 $300 2 270 3 240 4 210a. Assuming each villager acts independently, how many sheep will be raised on the common? 3 b. What is the total income of all four villagers? $ Part 2 (1.7 points) See Hint Suppose you are the village elder. You no longer raise sheep or bake. Instead, you sit around all day contemplating the meaning of life. One day you realize that the total profit of the village would be higher if fewer sheep were on the common. How many sheep should be on the common in order to maximize the village's profit? sheep