While nitrogen and phosphorus fertilizers enhance crop productivity, only a fraction of the applied fertilizer reaches the roots of the crop and is absorbed by the plant. The remaining fraction either leaches downward through the soil and contaminates groundwater or washes off the surface into nearby lakes, ponds, and estuaries and produces excessive algae growth in those receiving waters. These effects on water quality are part of the external costs associated with the private transactions between fertilizer producers and farmers. Farmers are willing to pay for fertilizer because it leads to higher crop output. Manufacturers are willing to sell fertilizer to farmers because they can receive payments in excess of their private costs (their expenditures on labor, energy, materials, etc.). However, neither party has an immediate incentive to consider the external costs of their activities. Let's first consider the fertilizer market just from the perspective of the direct participants: the farmers and the fertilizer producers. Let the private marginal benefits of fertilizer to farmers (PMB) be given by the equation PMB = 10 - Q. On the other side of the market, fertilizer manufacturers are willing to supply fertilizer to farmers according to their private marginal costs (PMC), which are given by the equation PMC = 2 + Q. Use these functional relationships when responding to the following:

a. Sketch the PMB and PMC curves together on a graph. Be sure to label your graph carefully and accurately. You will upload your graph, along with your work for all the other exam questions, as a single pdf at the end of the exam.

b. Solve for the equilibrium quantity and price of fertilizer that would emerge in a competitive market. Indicate those values in the blanks below and on your graph.

The equilibrium quantity of fertilizer is .

The equilibrium price of fertilizer is $ .

Now recall that each pound of fertilizer generates a pollution externality. Assume that these external costs can be captured by the following marginal external cost (MEC) function: MEC = 0.5Q.

c. Plot the social marginal cost (SMC) function on the graph you started in part a.

d. Solve for the allocatively efficient quantity and price of fertilizer. Indicate these values in the blanks below and on your graph.

The allocatively efficient quantity of fertilizer is .

The allocatively efficient price of fertilizer is $ .

e. What is the total external cost at Qc (the competitive market equilibrium quantity) and Qe (the allocatively efficient quantity)? Indicate these values in the blanks below and identify the areas that represent these costs on your graph.

The total external cost at Qc is .

The total external cost at Qe is .

f. What is the change in total welfare that society would realize if output shifted from the competitive market quantity of fertilizer to the allocatively efficient quantity?

The change in welfare for society would be $