Part I. Coase example An externality can be corrected via a tax, leading to the efficient alloca- tion. Likewise, two parties could mutually agree to solve the externality even without the intervention of the government. This problem illustrates this using an adaptation of a famous example of externalities, with honey bees and an orchard. The idea is that the bees benefit from the orchard, and the orchard benefits from the bees, so there is a mutual externality. In our example, we will make the benefits flow in only one direction to simplify the algebra. Still, we are doing something different than lecture in the algebra because the externality from the bees will shift the cost function of the orchard. As a result, the external benefits from bees depends on the level of production of the orchard. Suppose that a beekeeper makes honey, which she sells in a competitive market with equi- librium price P = 10. The total cost of producing honey is TCH = 0.5H? + 4H, where H denotes the quantify of honey produced. The beekeeper is located next to an orchard that grows apples that the orchard owner sells on a competitive market at price P4 = 20. The total cost of producing apples is TC4 = A% 4+ 24A HA, where A denotes the quantity of apples. Note that the cost of producing apples depends on the amount of honey. The idea is that more honey requires more bees, and the more bees there are, the easier it is to grow apples. The benefit that bees provide to the orchard is a classic example of an externality. 1. Suppose that there is no policy and there is no Coasian bargaining, so the beekeeper and the orchard owner each maximize their profits taking the behavior of the other as given. What is the equilibrium quantity of honey and the equilibrium quantity of apples? We will denote these quantities as H? and AP. (2 points) Answer HP: I:' Answer AP: |: 2. Now, find the socially optimal level of honey production and apple production. We will denote these as H* and A*. (2 points) (Hint: You can write total profits as a function of both H and A and take partial derivatives, yielding two equations in 2 unknowns. Or, you can solve for AP as a function of H, and then substitute this into an expression for total profitsboth honey and applein the economy, yielding an equation with only one unknown.)