Refer to Table 3.1. According to the equimarginal principle, in order to minimize the cost of producing 100 units, how would we distribute production between plants A and B?

Question

Quizplus · Accepted Answer

According to the equimarginal principle, we want to distribute production in a way that the marginal cost per unit is equal between the two plants. In this case, we can calculate the marginal cost per unit for each plant by dividing the total cost by the number of units produced. 
For plant A, the marginal cost per unit is:
($300,000 / 50 units) = $6,000/unit
For plant B, the marginal cost per unit is:
($440,000 / 100 units) = $4,400/unit
To minimize cost, we want to produce the 100 units in a way that the marginal cost per unit is equal. So we need to shift some production from plant B to plant A until the marginal cost per unit is equal at both plants. 
For every unit we shift from plant B to plant A, we reduce the marginal cost at plant A by $1,000 and increase the marginal cost at plant B by $2,000. We want to keep shifting production from plant B to plant A until these two values are equal. 
Let's start by shifting one unit from plant B to plant A:
- Marginal cost at plant A = $300,000 / 51 units = $5,882.35
- Marginal cost at plant B = $440,000 / 99 units = $4,444.44
The marginal cost at plant A is still higher than at plant B, so we need to shift more production to plant A. Let's try shifting 2 more units:
- Marginal cost at plant A = $300,000 / 53 units = $5,660.38
- Marginal cost at plant B = $440,000 / 97 units = $4,536.08
Now the marginal cost at plant A is lower than at plant B, so we need to shift some production back to plant B. Let's try shifting 1 unit from plant A to plant B:
- Marginal cost at plant A = $300,000 / 52 units = $5,769.23
- Marginal cost at plant B = $440,000 / 98 units = $4,489.80
Now the two marginal costs are very close, but plant A is still slightly higher. We need to shift production back to plant B. Let's try shifting 1 unit from plant A to plant B again:
- Marginal cost at plant A = $300,000 / 51 units = $5,882.35
- Marginal cost at plant B = $440,000 / 99 units = $4,444.44
Now the two marginal costs are equal. So we want to produce 38 units at plant A and 62 units at plant B to minimize cost.