Honey Bee Pollination

6
Dec/06
0

Honey Bee Pollination
Can someone help me with an Econ question?

I'm trying to draw the graph representing the beekeeper's marginal costs and benefits, but I don't have the equation of the curve for marginal benefits so how am I supposed to graph it?? Pleassseee help!

Question
Bee keepers are well known to provide positive externalities for owners of fruit orchards, since bees kept on land adjoining the orchard raise the fruit yield of the trees. Suppose that a beekeeper is located next to a 20-acre apple orchard. It takes four hives of bees to pollinate an acre of orchard. Pollination raises the value of the apple output by $100 per acre. Suppose that each beehive produces $50 worth of honey and that the marginal cost to the beekeeper for maintaining additional hives is described by MC = 30 + 0.5H, where H is the number of hives the beekeeper keeps.

a) Draw a graph representing the beekeeper's marginal costs and benefits. In the absence of any bargaining, how many hives will the beekeeper keep?

The benefits are
1. $50 per hive in benefits for the honey (to the beekeeper)

2. $100 per acre in additional apples (to the neighbour). As 4 hives are required to pollinate one acre the benefit per hive is $25 for additional apples. The apple orchard is 20 acres therefore the maximum number of hives where there would be a benefit in apples would be 20 x 4 = 80

The Beekeepers (own) marginal benefits are $50 (straight line irrespective of the number of hives). As there is "no bargaining" do not include the additional benefit in apples as that does not apply to the beekeeper but to his neighbour. The question asks for the "beekeeper's" marginal benefit - not the "marginal benefit of beekeeping" ie just the beekeeper not the beekeeper plus the orchard owner.

With bargaining of course you may well be able to add a bit more in benefits depending on the arrangement with the neighbour.

MC = MB when H = 40 hives. Therefore the beekeeper will keep 40 hives.
The MC of the 40th hive = 30 + 0.5 x 40 = 30+20 = $50
The MB of the 40th hive (or any other) is $50.

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