Suppose that the farme-r and the rancher each work 8 hours per day and can devote this time to growing potatoes, raising cattle, or a combination of the two. The table in Figure 1 shows the amount of time each person requires to produce 1 ounce of each good. "The farmer can produce an ounce of potatoes in 15 minutes and an ounce of moat in 60 minutes. The rancher, who is more productive in both activities, can produce an ounce of potatoes in 10 minutes and an ounce of meat in 2ll minutes. The last two columns in the table show the amounts of meat or potatoes the farmer anil rancher can produce if they work an H-hour day producing only that good.
Panel <b) of Figure 1 illustrates the amounts of meat and potatoes that the farmer can produce. If the farmer devotes all 8 hours of his time to potatoes, he produces 32 ounces of potatoes (measured on the horizontal axis) and no meat. If he devotes all his time to meat, he produces 8 ounces of meat (measured on the vertical axis) and no potatoes. If the farmer divides his time equally between the two activities, spending 4 hours on each, he produces 16 ounces of pitatoes and 4 ounces of meat. The figure shows these three possible outcomes and all others in benveen.
This graph is the farmer's production possibilities frontier. As we discussed in Chapter 2, a production possibilities frontier shows the various mixes of output that an economy can produce. It illustrates one of the Tot Prfrrcipfcs of Economics in Chapter 1: People face trade-offs. Here the farmer faces a trade-off between pniducing meat and producing potatoes.
You may recall that the production possibilities frontier in Chapter 2 was drawn bowed out. In that case, the rale at which society could trade one good for the other depended on the amounts that were being produced. Here, however, the farmer's technology for producing meat and potatoes (as siunmarized in Figure I) allows him to switch between the two goods at a constant rate. Whenever the farmer spends 1 hour less producing meal and 1 hour more producing potatoes, lie reduces his output of meat by 1 ounce and raises his output of potatoes by 4 ouikcs—and this is true regardless of how much he is already producing. As a result, the production possibilities frontier is a straight line.
Panel (c) of Figure 1 shows the production possibilities frontier for the rancher. It the rancher devotes all 8 hours of her time to potatoes, she produces -IS ounces of potatoes and no meat. If she devotes all her time to meat, she produces 24 ounces of meal and no potatoes. If the rancher divides her time equally, spending 4 hours on each activity, she produces 24 ounces of potatoes and 12 ounces of meat. Once again, the production possibilities frontier shows all the possible outcomes.
If the farmer and rancher choose to be self-sufficient rather than trade with each other, then each consumes exactly what he or she produces. In this case, Ihe productn>n possibilities frontier is also the consumption possibilities frontier. That is, without trade, Figure 1 shows the possible combinations of meat and potatoes that the farmer and rancher can each produce and then consume
These production possibilities frontiers are useful in showing the trade-offs that the farmer and rancher face, but they do not tell us what the farmer ami rancher will actually choose to do. To determine their chokes, wc need to know the tastes of the farmer and the rancher. Let's suppose they choose Ihe combinations identified by points A and 1) in Figure 1: The farmer produces and consumes 16 ounces of potatoes and 4 ounces of meat, while the rancher produces and consumes 24 ounces of potatoes and 12 ounces of meat.
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