6. The table below is a set of hypothetical production possibilities for a nation.

Combination Automobiles(thousands) Beef (thousands of tons)
A 0 10
B 2 9
C 4 7
D 6 4
E 8 0

a) Plot the production possibility data. What is the opportunity cost of the first 20000 cars produced? Between which points is the opportunity cost per thousand automobiles highest? Between which points is the opportunity cost per thousand tons of beef highest?

c) Does this production possibilities curve reflect the law of increasing opportunity cost? Explain.

d) What assumptions could be changed to shift the production possibilities curve?

a) To plot the production possibility data, you would create a graph with the x-axis representing automobiles and the y-axis representing beef. Then plot the points A(0,10), B(2,9), C(4,7), D(6,4), and E(8,0).

For the opportunity cost of the first 20,000 cars produced, you need to compare the production between points A and B. At point A, no cars are produced and 10,000 tons of beef are produced. At point B, 2,000 cars are produced and 9,000 tons are produced. So, the opportunity cost of producing the first 20,000 cars is 1,000 tons of beef.

The opportunity cost per thousand automobiles is highest between points C and D because it costs 3,000 tons of beef to produce 2 more thousand automobiles. The opportunity cost per thousand tons of beef is highest between points A and B as one thousand tons of beef would cost 2,000 automobiles.

c) Yes, this production possibilities curve reflects the law of increasing opportunity cost. The law states that as production of one good increases, the opportunity cost of producing it also increases. As we move along the curve from A to E, we can see that the opportunity cost of producing automobiles increases, as does the opportunity cost of producing beef. This is due to the fact that resources become less suited for one type of production as more of that good is produced.

d) There are several assumptions that could be changed to shift the production possibilities curve:

1. Improvements in technology: If the technology used to produce automobiles or beef becomes more advanced, the production possibilities curve would shift outward, allowing the nation to produce more of both goods.

2. Increases in resources: If there were more resources available for the production of automobiles or beef (e.g. more land, labor, or capital), the production possibilities curve would also shift outward.

3. Efficiency improvements: If the efficiency of production for automobiles or beef increases, the nation could produce more of both goods without using additional resources, and the production possibilities curve would shift outward.

4. Changes in consumer preferences: If consumer preferences shift, causing people to demand more automobiles or beef, the nation would likely allocate more resources towards the production of the preferred good, which could shift the production possibilities curve in the direction of the demanded good.

a) To plot the production possibility data, you can create a graph with Automobiles on the x-axis and Beef on the y-axis. Each combination will be represented by a point on the graph.

- Point A: (0, 10)
- Point B: (2, 9)
- Point C: (4, 7)
- Point D: (6, 4)
- Point E: (8, 0)

The opportunity cost of the first 20,000 cars produced can be determined by looking at the quantities of beef that need to be given up. In this case, we can see that to produce the first 20,000 cars, the nation has to give up producing beef entirely. So, the opportunity cost of the first 20,000 cars produced is 10,000 tons of beef.

To determine the points between which the opportunity cost per thousand automobiles is highest, we need to calculate the ratio of the change in beef production to the change in automobile production for each pair of adjacent points:

- Between points A and B: (10 - 9) / (2 - 0) = 1 / 2 = 0.5
- Between points B and C: (9 - 7) / (4 - 2) = 2 / 2 = 1
- Between points C and D: (7 - 4) / (6 - 4) = 3 / 2 = 1.5
- Between points D and E: (4 - 0) / (8 - 6) = 4 / 2 = 2

From the calculations, we can see that the opportunity cost per thousand automobiles is highest between points D and E.

To determine the points between which the opportunity cost per thousand tons of beef is highest, we need to calculate the ratio of the change in automobile production to the change in beef production for each pair of adjacent points:

- Between points A and B: (2 - 0) / (10 - 9) = 2 / 1 = 2
- Between points B and C: (4 - 2) / (9 - 7) = 2 / 2 = 1
- Between points C and D: (6 - 4) / (7 - 4) = 2 / 3 = 0.67
- Between points D and E: (8 - 6) / (4 - 0) = 2 / 4 = 0.5

From the calculations, we can see that the opportunity cost per thousand tons of beef is highest between points A and B.

c) Yes, this production possibilities curve reflects the law of increasing opportunity cost. As we move from left to right along the curve, the opportunity cost of producing additional units of automobiles increases. This is evident from the decreasing quantities of beef that need to be given up as more automobiles are produced.

d) The assumptions that could be changed to shift the production possibilities curve include:

1. Technological advancements: If there are improvements in technology, the nation may be able to produce more automobiles and beef with the same amount of resources, shifting the curve outward.
2. Increase in resources: If the nation acquires more resources, such as additional capital or labor, it would be able to produce more automobiles and beef, resulting in an outward shift of the curve.
3. Changes in trade: If the nation opens up to international trade, it may be able to import automobiles or beef, allowing it to specialize in the production of the other good and shift the curve outward.

a) To plot the production possibility data, you need to create a graph with the horizontal axis representing the quantity of automobiles (in thousands) and the vertical axis representing the quantity of beef (in thousands of tons).

The data points to be plotted on the graph are as follows:
A: (0, 10)
B: (2, 9)
C: (4, 7)
D: (6, 4)
E: (8, 0)

Plotting these points will give you a curve that connects them.

The opportunity cost of the first 20,000 cars produced can be determined by examining the trade-off between automobiles and beef. In this case, the opportunity cost is the quantity of beef that must be given up to produce the cars. To calculate the opportunity cost, you need to find the difference in beef production between two adjacent points on the curve.

For example, between points A and B, the quantity of automobiles increases by 2 (from 0 to 2), while the quantity of beef decreases by 1 (from 10 to 9). Therefore, the opportunity cost of the first 2,000 cars is 1,000 tons of beef.

To find the points between which the opportunity cost per thousand automobiles is highest, you need to calculate the opportunity cost per thousand automobiles for each interval. This can be done by dividing the change in beef production by the change in automobile production. The highest opportunity cost per thousand automobiles will be between the points with the largest ratio. In this case, it would be between points D and E.

Similarly, to find the points between which the opportunity cost per thousand tons of beef is highest, you need to calculate the opportunity cost per thousand tons of beef for each interval. This can be done by dividing the change in automobile production by the change in beef production. The highest opportunity cost per thousand tons of beef will be between the points with the largest ratio.

c) The production possibilities curve reflects the law of increasing opportunity cost. This law states that as you increase the production of one good, the opportunity cost of producing additional units of that good increases. This is evident in the given production possibilities curve because as the quantity of automobiles produced increases, there is a decreasing rate of return in terms of beef production. The curve is concave, meaning that the opportunity cost of producing more automobiles becomes higher as more are produced.

d) The production possibilities curve can be shifted by changing certain assumptions. Some assumptions that could be changed include:

1. Technological advancements: If there are improvements in technology, it can lead to an increase in productivity, allowing the nation to produce more of both goods. This would shift the entire production possibilities curve outward.

2. Increase in resources: If the nation acquires more resources, such as land, labor, or capital, it can increase its production capacity. This would also shift the production possibilities curve outward.

3. Changes in trade: If the nation engages in trade with other countries, it can specialize in producing the good in which it has a comparative advantage and import the other good. This can lead to an increase in overall production possibilities, as the nation can benefit from trade.

These assumptions, among others, can alter the production possibilities curve, either expanding or contracting the range of possible production combinations.