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Chater 2 Homework -Opportunity cost and production possibilities

Chapter 02 Homework- EC110-Principles of Macroeconomics

Question

Jake is a talented artist who sells hand-crafted goods on his website. Jake currently crafts and sells both crochet hats and embroidered sweaters. He spends 8 hours a day working on crafts. The following table gives different daily output scenarios depending on how much of his time is spent on each good.

Chater 2 Homework -Opportunity cost and production possibilities

On the following graph, use the blue points (circle symbol) to plot Jake’s initial production possibilities frontier (PPF).

Chater 2 Homework -Opportunity cost and production possibilities

Solution

Chater 2 Homework -Opportunity cost and production possibilities

Explanation:

Each row of the table refers to one point on the production possibilities frontier. For example, if Jake chooses to spend all of his time producing crochet hats, then he can produce four crochet hats and zero embroidered sweaters; so (4, 0) is one of the points on his initial PPF. Similarly, if he splits his time evenly between producing crochet hats and embroidered sweaters, he will produce two crochet hats and 16 embroidered sweaters; therefore, (2, 16) is another point on his initial PPF.

Solution

  • Suppose Jake is currently using combination D, producing one crochet hat per day. His opportunity cost of producing a second crochet hat per day is 3 embroidered sweaters  Correct per day.
  • Now, suppose Jake is currently using combination C, producing two crochet hats per day. His opportunity cost of producing a third crochet hat per day is 5 embroidered sweaters  Correct per day.
  • From the previous analysis, you can determine that as Jake increases his production of crochet hats, his opportunity cost of producing one more crochet hat increases   Correct .

Explanation

When using combination D, Jake is producing one crochet hat and 19 embroidered sweaters per day. Producing a second crochet hat per day would require him to move to combination C, reducing his production of embroidered sweaters to 16 per day. Since this change involves producing 3 fewer embroidered sweaters per day (19−16=319−16=3), the opportunity cost of producing the second crochet hat per day is 3 embroidered sweaters per day.

Similarly, using combination C, Jake is producing two crochet hats and 16 embroidered sweaters per day. Producing a third crochet hat per day would require him to move to combination B, reducing his production of embroidered sweaters to 11 per day. Since this change involves producing 5 fewer embroidered sweaters per day (16−11=516−11=5), the opportunity cost of producing the third crochet hat per day is 5 embroidered sweaters per day.

Jake’s opportunity cost of producing the second crochet hat per day is 3 embroidered sweaters per day while the opportunity cost of producing the third crochet hat per day is 5 embroidered sweaters per day. Hence, as Jake increases his production of crochet hats, his opportunity cost of producing more crochet hats increases. This change is an example of the law of increasing opportunity costs.

Suppose Jake buys a new tool that enables him to produce twice as many crochet hats per hour as before, but it doesn’t affect his ability to produce embroidered sweaters. Use the green points (triangle symbol) to plot his new PPF on the previous graph.

Solution

  • Because he can now make more crochet hats per hour, Jake’s opportunity cost of producing embroidered sweaters is higher than  Correct it was previously.

Explanation

The new tool causes Jake’s PPF to pivot to the right. In other words, for each point on his PPF, the vertical coordinate is the same as before, but the horizontal coordinate is twice its initial value.

For example, under combination D, Jake spends 2 hours producing crochet hats and 6 hours producing embroidered sweaters. Before he bought the new tool, he could have produced one crochet hat and 19 embroidered sweaters, so (1, 19) was a point on his initial PPF. With the new tool, the same allocation of time results in two crochet hats and 19 embroidered sweaters, so (2, 19) is a point on his new PPF. Notice that one point is the same on the initial PPF and the new PPF. Because the new tool helps Jake make only crochet hats, the tool does not change his output when he spends all of his time making embroidered sweaters. This occurs at output combination E.

The shift in Jake’s PPF is reflected in a corresponding change in his opportunity costs. Again, consider combination D, and consider the effects of moving from there to combination E. Both before and after Jake buys the tool, he can produce 19 embroidered sweaters if he devotes 6 hours to producing them and 20 embroidered sweaters if he devotes 8 hours to producing them. Therefore, spending his last 2 hours producing embroidered sweaters results in one additional embroidered sweater. Before he bought the tool, he would have to give up one crochet hat. However, now that he has the tool, it means giving up two crochet hats. Therefore, Jake’s increased ability to produce crochet hats increases his opportunity cost of producing embroidered sweaters.

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