2. Assume that a certain simplified economy produces only two goods, X and Y, with
given resources and technology. The following table gives the various possible
combinations of the production of the two goods (all units are measured in millions of
tons).
Production Possibility Good X Good Y Opportunity Cost of Good X
A 0 100
B 2 90
C 4 60
D 6 20
a) Calculate the opportunity cost of the production of good X at each point. What law
does the trend in those values exhibit?
b) What changes are required for this economy to shift the PPF outward?�
a) The opportunity cost of the production of good X can be calculated by taking the change in the quantity of good Y divided by the change in the quantity of good X.
For points A to B, the change in good Y is -10 (100 - 90) and the change in good X is 2. Therefore, the opportunity cost is -10/2 = -5.
For points B to C, the change in good Y is -30 (90 - 60) and the change in good X is 2. Therefore, the opportunity cost is -30/2 = -15.
For points C to D, the change in good Y is -40 (60 - 20) and the change in good X is 2. Therefore, the opportunity cost is -40/2 = -20.
The trend in these values shows that as more of good X is produced, the opportunity cost of producing an additional unit of good X increases. This is known as the law of increasing opportunity cost.
b) For the economy to shift the PPF outward, there would need to be an increase in resources or an improvement in technology. This would allow for more efficient production and the ability to produce more of both goods X and Y.
a) The opportunity cost of the production of good X can be calculated by dividing the change in the production of good Y by the change in the production of good X.
Opportunity Cost of Good X from A to B = (90 - 100) / (2 - 0) = -10 / 2 = -5
Opportunity Cost of Good X from B to C = (60 - 90) / (4 - 2) = -30 / 2 = -15
Opportunity Cost of Good X from C to D = (20 - 60) / (6 - 4) = -40 / 2 = -20
The trend in the values of the opportunity cost of good X is that it is increasing. This trend exhibits the principle of increasing opportunity cost, also known as the law of diminishing returns. As more of good X is produced, the opportunity cost of producing additional units of good X increases.
b) For this economy to shift the production possibility frontier (PPF) outward, there need to be improvements in resources or technology. These improvements would allow for the production of more goods X and Y using the same amount of resources or the production of the same amount of goods X and Y using fewer resources. This could increase the total output and expand the production possibilities of the economy.