Question

The Acme Corporation producesxandyunits of goods Alpha and Beta, respectively.

a. Use a production possibility frontier to explain how the willingness to produce more or less Alpha depends on the marginal rate of transformation of Alpha or Beta.

b. Consider two cases of production extremes:

(i) Acme produces zero units of Alpha initially, or

(ii) Acme produces zero units of Beta initially.

If Acme always tries to stay on its production possibility frontier, describe the initial positions of cases(i) and (ii). What happens as the Acme Corporation begins to produce both goods?

Short answer

1. The willingness to produce more or less of Alpha depends upon the MRTS of Alpha or Beta since the MRTS is the slope of the production possibilities frontier, and the slope measures the cost of producing two goods.

2. In both the cases initially, there will be a large increase in the production, and eventually, to maintain the production level, more units of the other goods will have to be sacrificed.

Step-by-step solution

Step 1. Explanation for part (a)

The shape of the production possibility frontier determines the quantity of the goods that can be produced given the resources. The shape of the production possibility frontier depends upon the marginal rate of technical substitution. It describes that to produce more units of one good, the unit of other goods needs to be sacrificed. This is because the resources are limited. Thus, a producer cannot keep increasing the cost to produce more.

MRTS depicts the cost of producing goods, and the decision or willingness of producing more or less Alpha, in this case, depends upon the MRTS of Alpha and Beta since the MRTS will show the producer whether producing more or less of Alpha increase or decreases the cost.

Step 2. Explanation for part (b)

The following graph below shows the production possibilities frontiers of Alpa and Beta:

In the first case, if the producer tries to produce only Alpha, then initially he will experience a large increase in the output, but eventually, if he wishes to maintain this heavy production and keep producing Alpha, then he has to give more and more quantities to Beta (downward movement along the PPF). Given the cost of producing two goods, this action will increase the cost of the producer.

The same will happen in the second situation. Initially, the production of Beta will increase, but eventually, more quantities of Beta will have to be given up to keep up with the production of Alpha (upward movement along the PPF).