Question

3. You are thinking about starting a bee keeping business to produce honey. You also plan to sell pollination services to almond growers in California. Below is the cost function you have estimated for producing honey and pollination services with 450 hives:
C(QH, QP) = 5,000 + 12QH + 100QP + 0.002 QH QP
where QH is the number of pounds of honey produced and QP is the number of acres of almond trees pollinated.

(5) a. You have contracted to produce 3,000 pounds of honey and pollinate 1,000 acres of almonds. What would your costs be if you fulfilled these contracts with a single set of 450 hives?

(5) b. What would your total costs be if you operated a set of 450 hives to fulfill your honey contract and a separate set of 450 hives to fulfill your pollination services contract?

(5) c. What do your results in parts a and b tell you about the about economies of scope for honey production and pollination services when you produce 3,000 pounds of honey and pollinate 1,000 acres of almonds?

Answer 1

Given: C(QH, QP) = 5,000 + 12QH + 100QP + 0.002 QH QP

a.) Here, QH = 3000 and QP = 1000

Substitutiong these values in the equation -

C(QH, QP) = 5,000 + 12QH + 100QP + 0.002 QH QP

C(QH, QP) = 5,000 + 12(3000) + 100(1000) + 0.002 (3000)(1000)

C(QH, QP) = 5,000 + 36000 + 100000 + 6000

C(QH, QP) = 1,47,000

If you fulfilled these contracts with a single set of 450 hives, your cost would be $ 147000

b.) If you operated a set of 450 hives to fulfill your honey contract only, then QH = 3000 and QP = 0

C(QH, QP) = 5,000 + 12(3000) + 100(0) + 0.002 (3000)(0)

C(QH, QP) = 5,000 + 36000 + 0 + 0

C(QH, QP) = 41000

Similarly, If you operated a set of 450 hives to fulfill your pollination services contract only, then QH = 0 and QP = 1000

C(QH, QP) = 5,000 + 12(0) + 100(1000) + 0.002 (0)(1000)

C(QH, QP) = 5,000 + 0 + 100000 + 0

C(QH, QP) = 105000

Therefore total cost would be $ 41000 + 105000 = $ 146000

c.) Economies of scope do not seem to exist in this case. The cost of providing these two services separately ($ 146000) is lesser than the cost of providing them together ($ 147000). Hence, no economies of scope exist in this scenario.