Question

Farmers who grow apple trees provide a benefit to the beekeepers in Australia. The beekeepers get a good source of nectar to help make more honey. Suppose that the external benefit created by growing apple trees is $0.20 per apple. The perfectly competitive equilibrium price of an apple is $1.

1. On an appropriate diagram, label the equilibrium quantity in the Australian apple market as Q_market. Also, show the quantity of apple that would maximize social surplus from the apple market as Q_optimum. Does Q_market equal to the perfectly competitive equilibrium quantity? Fully explain your answer and label the area of deadweight loss (if any).

b) An economics student in ECW1101 class suggests an alternative policy. She says that if the government sets a price floor of $1.20 per apple then this will maximize social surplus. Is she correct? If she is correct, show the social gain under the student’s policy compared to the perfectly competitive equilibrium. If the student is incorrect, show the deadweight loss under her policy.

Answer 1

This is a case of positive externality, i.e. when consuming/producing a good causes a postive impact on the third party, with the third party not directly involved with the market transaction. Here, this external positive benefit created by apple tree growers for the beekeepers is $0.20 per apple. Take a look at fig 1 for the equilibrium Australian apple market.

MSC = Marginal social cost,

MPC = marginal private cost, MPB = marginal private benefit, MSB = marginal social benefit , Marginal external benefit = MEB = 0.20

First, let us suppose we know nothing about this externality, so market equilibrium will take place at the intersection of the supply and demand curves i.e. MPC and MPB curves. Notice that here, MPC = MSC as there is no external cost/benefit. This occurs at Q_market. This is the perfectly competitive equilibrium quantity.

The market surplus at Q₁ is computed by deducting total private costs from total private benefits = (b+c) - (c) = b.

The social surplus at this equilibrium quantity is computed by deducting total social costs from total social benefits = (a+b+c) - (c) = (a+b)

Now, you can see in the graph, the MSB curve lies above the MPB curve for all the quantities because for each unit of private consumption , there is a spill-over benefit to the non-market/third party participants, so the marginal social benefit is more than the marginal private benefit. This area between the MSB and MPB curve equals to the external benefit.

So, MPB + MEB = MSB.

So, if now we increase the quantity more than the equilibrium quantity, i.e. Q_optimum, the market surplus will be : (b+c+g) - (c+f+g) =(b-f)

The social surplus at this quantity will be equal to (a+b+c+d+f+g) - (c+f+g) = (a+b+d)

So, we see at this quantity the social surplus is maximum , inspite of the fact that the participants of the market are made worse off. So, there has been a potential pareto improvement in this case. So, (d+f) is is the gain of the non-market participants due to the increase in production from Q_market to Q_optimum.

And 'f' is the loss to the participants in the market due to excess production. Also, 'd' is the deadweightloss of the economy in the presence of a positive externality, It is shown as the shaded part in the figure,

So, we see that the perfectly competitive quantity does not yield maximum social surplus as markets tend to under-produce as producers do not consider these additional benefits to others. So, Q_market < Q_optimum

b) Now setting a price floor above the equilibrium price, as in this case, it will have a binding effect. This implies that at this high price, the producers will have an incentive to supply, and consumers will not demand as much at a higher price. So, the supply will exceed the demand and there will be a surplus. Quantity _demanded and Q_Supplied are shown on the graph. So the quantity supplied now will be equal to the socially optimum quantity as producers no longer need to under produce. They have an incentive to increase their production. So, because the quantity is at the optimum level, social surplus will be maximized. So, the student is correct. The social gain as compared to that obtained from the competitive equilibrium can be seen in fig 2. It is shaded part and that part of the deadweight loss which has been transformed into social gain