Imagine a CEO retreat in the desert in which CEOs spend hours in a sauna each day and cannot leave the desert between sauna sessions. The folks running the retreat (our rm) sell lemonade after each sauna session. They are a monopoly in the market of refreshments for this CEO camp in the desert. Imagine CEOs at the retreat have the inverse demand function p(Q) = 1200 100Q for lemonade after using the sauna. Furthermore, the folks running the retreat have the cost-function C(Q) = 100Q^2 + 100 for lemonade.

A. What are the new post-price cap equilibrium price and equilibrium quantity?

B. What is the folks running the retreat's new prot at the equilibrium?

C. Prove that this new prot level is a global maximum.

D. Show the new equilibrium price and equalibrium quantity graphically. Include the original and regulated inverse demand curves, rm's marginal revenue curve, and rm's marginal cost curve.

E. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium?