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Opportunity cost and production possibilities

Opportunity cost and production possibilities

Question

Kate is a talented artist who sells hand-crafted goods on her website. Kate currently crafts and sells both knit caps and pillows. She spends 8 hours a day working on crafts. The following table gives different daily output scenarios depending on how much of her time is spent on each good.

ChoiceHours CraftingProduced
(Knit caps)(Pillows)(Knit caps)(Pillows)
A8040
B62310
C44216
D26119
E08020

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

Opportunity cost and production possibilities

a. Suppose Kate is currently using combination D, producing one knit cap per day. Her opportunity cost of producing a second knit cap per day is_____________per day.

b. Now, suppose Kate is currently using combination C, producing two knit caps per day. Her opportunity cost of producing a third knit cap per day is_____________    per day.

c. From the previous analysis, you can determine that as Kate increases her production of knit caps, her opportunity cost of producing one more knit cap_____________    .

Suppose Kate buys a new tool that enables her to produce twice as many knit caps per hour as before, but it doesn’t affect her ability to produce pillows. Use the green points (triangle symbol) to plot her new PPF on the previous graph.

d. Because she can now make more knit caps per hour, Kate’s opportunity cost of producing pillows is_____________    it was previously.

Solution and Explanation

Opportunity cost and production possibilities

a. Suppose Kate is currently using combination D, producing one knit cap per day. Her opportunity cost of producing a second knit cap per day is 3 pillows  Correct per day.

b. Now, suppose Kate is currently using combination C, producing two knit caps per day. Her opportunity cost of producing a third knit cap per day is 6 pillows  Correct per day.

c. From the previous analysis, you can determine that as Kate increases her production of knit caps, her opportunity cost of producing one more knit cap increases  Correct .

d. Because she can now make more knit caps per hour, Kate’s opportunity cost of producing pillows is higher than  Correct it was previously.

Explanation

  • Each row of the table refers to one point on the production possibilities frontier. For example, if Kate chooses to spend all of her time producing knit caps, then she can produce four knit caps and zero pillows; so (4, 0) is one of the points on her initial PPF. Similarly, if she splits her time evenly between producing knit caps and pillows, she will produce two knit caps and 16 pillows; therefore, (2, 16) is another point on her initial PPF.
  • a. When using combination D, Kate is producing one knit cap and 19 pillows per day. Producing a second knit cap per day would require her to move to combination C, reducing her production of pillows to 16 per day. Since this change involves producing 3 fewer pillows per day (19−16=3), the opportunity cost of producing the second knit cap per day is 3 pillows per day.
  • b & c. Similarly, using combination C, Kate is producing two knit caps and 16 pillows per day. Producing a third knit cap per day would require her to move to combination B, reducing her production of pillows to 10 per day. Since this change involves producing 6 fewer pillows per day (16−10=6), the opportunity cost of producing the third knit cap per day is 6 pillows per day.
  • d. Kate’s opportunity cost of producing the second knit cap per day is 3 pillows per day while the opportunity cost of producing the third knit cap per day is 6 pillows per day. Hence, as Kate increases her production of knit caps, her opportunity cost of producing more knit caps increases. This change is an example of the law of increasing opportunity costs.

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