Assume Nebraska and Virginia each have 100 acres of farmland. The following table gives hypothetical figures for yield per acre in the two states:
Nebraska Virginia
Wheat 15 5
Cotton 7 4
Who has the comparative advantage in the production of wheat?
*For this answer, I think it is Nebraska but I am confused
Who has the comparative advantage in the production of cotton?
*for this answer, I think it is Virginia but I am confused
What is the marginal rate of transformation when the two states are producing a total of 200 units of corn?
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To determine who has the comparative advantage in the production of wheat and cotton, we need to compare the opportunity costs of producing each good in each state.
The opportunity cost of producing a good is the amount of the other good that must be given up to produce one unit of the desired good. We can calculate the opportunity costs by dividing the units of one good by the units of the other good.
For wheat production:
- In Nebraska, the opportunity cost of producing one unit of wheat is 15/5 = 3 units of cotton.
- In Virginia, the opportunity cost of producing one unit of wheat is 5/15 = 1/3 units of cotton.
Comparing the opportunity costs, we can see that Nebraska's opportunity cost of wheat is higher (3 units of cotton) than Virginia's (1/3 units of cotton). Therefore, Virginia has the comparative advantage in the production of wheat.
For cotton production:
- In Nebraska, the opportunity cost of producing one unit of cotton is 7/15 = 7/15 units of wheat.
- In Virginia, the opportunity cost of producing one unit of cotton is 4/5 = 0.8 units of wheat.
Comparing the opportunity costs, we can see that Nebraska's opportunity cost of cotton is lower (7/15 units of wheat) than Virginia's (0.8 units of wheat). Therefore, Nebraska has the comparative advantage in the production of cotton.
To calculate the marginal rate of transformation (MRT) when the two states are producing a total of 200 units of corn, we need to consider the trade-off between wheat and cotton for each state.
Let's assume Nebraska is producing x units of wheat and y units of cotton, while Virginia is producing z units of wheat and w units of cotton.
The total production of wheat is given by x + z, and the total production of cotton is given by y + w. Since the total production of corn is 200 units, we have x + z = 200.
To calculate the MRT, we need to find the rate at which one good can be exchanged for the other while maintaining the same level of total production (200 units of corn).
In this case, we need to find the ratio of the change in cotton production (dy) to the change in wheat production (dx) for each state.
For Nebraska:
MRT of cotton for wheat (Nebraska) = dy/dx = -1/(dy/dx) = -1/(7/15) = -15/7
For Virginia:
MRT of cotton for wheat (Virginia) = dy/dx = -1/(dy/dx) = -1/(0.8) = -1.25
Therefore, the marginal rate of transformation (MRT) when the two states are producing a total of 200 units of corn is:
- Nebraska: -15/7
- Virginia: -1.25
Please note that the MRT represents the trade-off between wheat and cotton and shows how much of one good needs to be sacrificed to produce more of the other good.