Question

Phoebe keeps a bee farm next door to an apple orchard. She chooses her optimal number of beehives by selecting the honey output level at which her private marginal benefit from beekeeping equals her private marginal cost. Use the following graph to answer the questions below.

a. Assuming that Phoebe’s private marginal benefit and marginal cost curves from beekeeping are normally shaped, identify which curve is the private marginal benefit curve and which one is the private marginal cost curve.

Instructions: In the graph above, use the dropdowns to label each curve.

b. Phoebe’s bees help to pollinate the blossoms in the neighboring apple orchard, and the more beehives she keeps, the larger the fruit yield will be. Draw the social marginal benefit from Phoebe's beekeeping.

Instructions: In the graph above, use the tool "MB_social" to draw the social marginal benefit curve.

c. Phoebe’s bees are Africanized killer bees that aggressively sting anyone who steps into their flight path, and the more beehives Phoebe keeps, the more people will be stung. Phoebe, fortunately, is naturally immune to the bees’ venom. Show the social marginal cost curve from Phoebe’s beekeeping.

Instructions: In the graph above, use the tool "MC_social" to draw the social marginal cost curve.

d. The socially optimal quantity of beehives:

• is greater than the privately optimal quantity.

• is less than the privately optimal quantity.

• could be greater than or less than the privately optimal quantity.

Answer 1

(a) Phoebe's private marginal benefit and marginal cost curve are normally shaped. So, MC curve is upward sloping and MB is downward sloping as shown below. The market output is denoted by X* at which MB and MC intersect.

(b) Phoebe’s bees help to pollinate the blossoms in the neighboring apple orchard, and the more beehives she keeps, the larger the fruit yield will be. This implies the positive externality .So, the social marginal benefit curve lies to the right of private marginal benefit curve. The socially optimal quantity is denoted by X** which is greater than market output X*. This is shown in the below graph.

(c) Phoebe’s bees are killer bees that aggressively sting anyone who steps into their flight path . Phoebe. fortunately is immune to the bee's venom. This implies the negative externality.So, the social marginal cost curve lies to the left of private marginal cost curve . The socially optimal quantity is denoted by X** which is less than the market output X*. This is shown in the below graph.

(d) By combining both these effects. We can see that if positive effect is larger than negative effect then social benefit curve shift by large amount than social cost curve ,then socially optimal quantity is greater than private quantity.

And if negative effect is larger than positive effect, then social cost curve shift by large amount than social benefit curve , then socially optimal quantity is less than private quantity.

Hence, the socially optimal quantity of beehives could be greater than or less than the privately optimal quantity.