Two dairy farmers, Ben and Jerry, share a common pasture. Each has a choice of grazing 1 or 2 cows on the pasture. If 2 cows graze on the pasture, each will give 1,000 gallons of milk each year, which may be sold for $1 each at the local farmers' market. If 3 cows graze on the pasture, the grass will be thinner, and each will give 750 gallons of milk. If 4 cows graze on the pasture, the grass will have little chance to recover, and each cow will only give 400 gallons of milk.
a. What is the efficient number of cows to keep on the common pasture - 2, 3, or 4?
Efficient number of cows = ________

To determine the efficient number of cows to keep on the common pasture, we need to consider the total revenue generated from milk production with different numbers of cows and the impact on the quality of the pasture.

Let's calculate the revenue generated from milk production with each option:

If 2 cows graze on the pasture:

Each cow produces 1,000 gallons of milk.

Total milk production = 2 cows * 1,000 gallons/cow = 2,000 gallons

Total revenue = 2,000 gallons * $1/gallon = $2,000

If 3 cows graze on the pasture:

Each cow produces 750 gallons of milk.

Total milk production = 3 cows * 750 gallons/cow = 2,250 gallons

Total revenue = 2,250 gallons * $1/gallon = $2,250

If 4 cows graze on the pasture:

Each cow produces 400 gallons of milk.

Total milk production = 4 cows * 400 gallons/cow = 1,600 gallons

Total revenue = 1,600 gallons * $1/gallon = $1,600

Now, let's compare the total revenue for each scenario:

2 cows: $2,000

3 cows: $2,250

4 cows: $1,600

The efficient number of cows to keep on the common pasture is the number that maximizes total revenue. In this case, grazing 3 cows generates the highest total revenue of $2,250. Therefore, the efficient number of cows to keep on the common pasture is 3.