Suppose that the demand for broccoli is given by

Demand: Q = 1,000 – 5P

where Q is quantity per year measured in hundreds of bushels and P is price in dollars per hundred bushels. The long-run supply curve for broccoli is given by

Supply: Q = 4P – 80

a. Show that the equilibrium quantity here is Q = 400. At this output, what is the equilibrium price? How much in total is spent on broccoli? What is consumer surplus at this equilibrium? What is producer surplus at this equilibrium?

b. How much in total consumer and producer surplus would be lost if Q = 300 instead of Q = 400?

c. Show how the allocation of the loss of total consumer and producer surplus between suppliers and demanders described in part b depends on the price at which broccoli is sold. How would the loss be shared if P = 140? How about if P = 95?

d. What would the total loss of consumer and producer surplus be if Q = 450 rather than Q = 400? Show that the size of this total loss also is independent of the price at which the broccoli is sold.

e. Graph your results.