Question

4 villagers....

Part 1 (2 points) 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 common Price of a sheep at market Profit earned from one sheep Total profit from sheep Additional profit from one sheep 1 $300 2 270 3 240 4 210 a. Assuming each villager acts independently, how many sheep will be raised on the common? b. What is the total income of all four villagers? $ Part 2 (1 point) 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 Part 3 (2 points) Suppose there are two sheep on the common. A villager is considering adding another sheep. If the villager does, he or she is better off by $ compared to what he or she could earn as a baker. However, he or she imposes a cost of $ on the other two villagers who already have sheep on the common.

Answer 1

Part 1
The table is filled as below:

a. Assuming each villager acts independently, the two options available to a villager is to either raise sheep or bake bread. Bread gives a profit of $35. But profit on sheep depends upon the number of sheep feeding on the common. When there are three sheeps feeding on the common, profit per sheep is 40 which is higher than 35. If there are any more sheep feeding on the common, it gives a lower profit than baking bread. So, 3 sheep will be raised on the common.

B C = B - 200 D= CA E = D2-D1 A Number of sheep feeding on the common 1 2 3 Price of a sheep at Profit earned from one market sheep 300 100 270 70 240 40 210 10 Total profit from sheep 100 140 120 40 Additional Profit from one sheep 100 40 -20 -80

b. Total income of all four villagers:

Income Villager 1 40 2 Activity Sheep herding Sheep herding Sheep herding Baking 40 3 40 4 35 155

Part 2

Possible scenarios:

Number of sheep feeding on the common Total profit from sheep 100 140 120 40 1 2 3 4 Income from baking bread 105 70 35 Total Income 205 210 155 40 0

Maximum total profit for the villagers is $210 when there are two sheep feeding on the common.

(It is assumed that there are 4 villagers excluding the village elder)

Part 3

When there are two sheep feeding on the common, the owners of those sheep earn a profit of 70 from each sheep. When a villager decides to add one more sheep to the common, he will get a profit of 40 instead of 35 from baking. So, he is better off by $5 compared to what he or she could earn as a baker.

Cost imposed on the villagers who already had sheep feeding on the common = 70-40 = $30

The third villager imposes a cost of $30 on the other two villagers who already have sheep on the common.