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 can create a graph with the X-axis representing Automobiles (in thousands) and the Y-axis representing Beef (in thousands of tons). Then plot the various combination points (A, B, C, D, and E) on the graph.
Opportunity cost of the first 20,000 cars produced (moving from point A to point B) is 1,000 tons of beef. This is because we give up 1 unit of beef production when we produce 2 units of automobile production. The opportunity cost per thousand automobiles is 1,000 tons/2,000 cars = 0.5 tons of beef per car.
The opportunity cost per thousand automobiles is highest between points B and C, where we give up 2,000 tons of beef to produce 2,000 cars, resulting in an opportunity cost of 1 ton of beef per car.
The opportunity cost per thousand tons of beef is highest between points D and E, where we give up 4,000 automobiles to produce 1,000 tons of beef, resulting in an opportunity cost of 4 automobiles per ton of beef.
c) Yes, this production possibilities curve reflects the law of increasing opportunity cost. As more automobiles are produced, the opportunity cost of producing additional automobiles increases, as shown by the increasing amount of beef we need to give up. This is consistent with the law of increasing opportunity costs, which states that as we increase production of one good, the opportunity cost of producing additional units of that good will also increase.
d) Several assumptions could be changed to shift the production possibilities curve:
1. Technological advancements or improvements in efficiency can increase production capabilities, shifting the curve outward.
2. An increase in available resources, such as land, labor, or capital, can also shift the curve outward by allowing for larger-scale production.
3. Conversely, a decrease in resources or a downturn in technology can shift the curve inward by decreasing production capabilities.
4. Changes in production techniques or consumer preferences can also affect the shape of the curve, causing it to become more or less curved or potentially affecting the slope.
a) To plot the production possibility data, we can create a graph with Automobiles on the x-axis and Beef on the y-axis. Each combination of Automobiles and Beef represents a point on the graph. Based on the given data, we can plot the following points:
Point A: (0, 10)
Point B: (2, 9)
Point C: (4, 7)
Point D: (6, 4)
Point E: (8, 0)
The graph should show a downward-sloping curve connecting these points.
The opportunity cost of the first 20,000 cars produced can be calculated by finding the change in Beef production for each additional 1,000 cars produced.
Opportunity cost = Change in Beef production / Change in Car production
Here, the change in Beef production from Point A to Point B is 1 (10 - 9), and the change in Car production is 2. Therefore, the opportunity cost of the first 2,000 cars produced is 1/2 = 0.5.
Similarly, you can calculate the opportunity cost for each interval of 1,000 cars produced.
To determine the points between which the opportunity cost per thousand automobiles is highest, you need to compare the ratios of the change in Beef production to the change in Car production for each interval. The highest opportunity cost per thousand automobiles will be between the points with the steepest slope on the production possibility curve.
To determine the points between which the opportunity cost per thousand tons of beef is highest, you need to compare the ratios of the change in Car production to the change in Beef production for each interval. The highest opportunity cost per thousand tons of beef will be between the points with the shallowest slope on the production possibility curve.
c) The production possibilities curve reflects the law of increasing opportunity cost if the opportunity cost increases as production of one good increases. To determine if the curve reflects this law, we need to analyze the ratios of the change in Beef production to the change in Car production for each interval. If these ratios increase as more cars are produced, then the curve reflects the law of increasing opportunity cost.
d) The production possibilities curve can shift based on certain assumptions or changes. Some factors that could shift the curve include:
1. Technological advancements: If there are advancements that increase the productivity or efficiency of production, it could shift the production possibilities curve outward, allowing for more production of both Automobiles and Beef.
2. Increase in resource availability: If there is an increase in the availability of resources, such as land, labor, or capital, it could shift the production possibilities curve outward, allowing for more production of both Automobiles and Beef.
3. Changes in trade: If the nation engages in international trade, it could shift the production possibilities curve outward if it can specialize in the production of one good and trade for the other good.
4. Changes in government policies: Government policies, such as taxes, subsidies, or regulations, can impact the production possibilities curve by influencing the cost of production or resource allocation.
These are just a few examples, and there could be other factors that can shift the production possibilities curve.
To plot the production possibility data on a graph, we can use the points given in the table.
On the x-axis, we can represent the number of automobiles produced (in thousands), and on the y-axis, we can represent the amount of beef produced (in thousands of tons). Each combination in the table corresponds to a point on the graph.
Plotting the data, we get the following points:
Combination A: (0,10)
Combination B: (2,9)
Combination C: (4,7)
Combination D: (6,4)
Combination E: (8,0)
Connecting these points, we get a production possibilities curve (PPC) that looks like a downward-sloping curve from the upper left to the lower right.
a) The opportunity cost of producing the first 20,000 cars can be determined by finding the difference in beef production between combinations B and A. In combination B, the automobile production increases by 2 thousand, while the beef production decreases by 1 thousand. Therefore, the opportunity cost of the first 20,000 cars produced is 1,000 tons of beef.
To determine the points between which the opportunity cost per thousand automobiles is highest, we need to find the combinations where the change in beef production per unit increase in automobile production is the highest. We can calculate the opportunity cost per thousand automobiles by dividing the change in beef production by the change in automobile production.
Opportunity cost per thousand automobiles:
Between A and B: (10-9)/(2-0) = 1/2 = 0.5
Between B and C: (9-7)/(4-2) = 2/2 = 1
Between C and D: (7-4)/(6-4) = 3/2 = 1.5
Between D and E: (4-0)/(8-6) = 4/2 = 2
From the above calculations, we can see that the opportunity cost per thousand automobiles increases from 0.5 to 1 to 1.5 to 2. Therefore, the opportunity cost per thousand automobiles is highest between combinations D and E.
To determine the points between which the opportunity cost per thousand tons of beef is highest, we need to find the combinations where the change in automobile production per unit decrease in beef production is the highest. We can calculate the opportunity cost per thousand tons of beef by dividing the change in automobile production by the change in beef production.
Opportunity cost per thousand tons of beef:
Between A and B: (2-0)/(10-9) = 2/1 = 2
Between B and C: (4-2)/(9-7) = 2/2 = 1
Between C and D: (6-4)/(7-4) = 2/3 = 0.67
Between D and E: (8-6)/(4-0) = 2/4 = 0.5
From the above calculations, we can see that the opportunity cost per thousand tons of beef decreases from 2 to 1 to 0.67 to 0.5. Therefore, the opportunity cost per thousand tons of beef is highest between combinations A and B.
c) The production possibilities curve (PPC) reflects the law of increasing opportunity cost. This is because as the production of one good (automobiles) increases, there is a trade-off in terms of sacrificing the production of the other good (beef). As more and more resources are allocated to produce additional units of automobiles, the opportunity cost of producing each additional unit of automobiles increases, resulting in a steeper slope of the PPC. This is evident in the increasing opportunity cost per thousand automobiles and the decreasing opportunity cost per thousand tons of beef between different combinations.
d) The production possibilities curve can be shifted by changing certain assumptions. For example:
1. Technological advancement: If there is a significant advancement in technology, it can lead to an increase in production efficiency and allow for more output to be produced with the same resources. This would shift the PPC outward, indicating an increase in the maximum combination of goods that can be produced.
2. Increase in resource availability: If there is an increase in the availability of resources (e.g., land, labor, capital), it would allow for a greater level of production for both goods. This would also shift the PPC outward.
3. Changes in trade: If the nation engages in international trade and can import or export goods, it would affect the production possibilities curve. By importing goods, the nation can access goods that it may have a comparative disadvantage in producing. This can improve the overall production possibilities and potentially shift the PPC outward.
These are just a few examples of the assumptions that can be changed to shift the production possibilities curve. The actual shift and its direction would depend on the specific circumstances and assumptions that are altered.