I only have need to know how to solve question 4. Question 2 and 3 are only for preference

Question 2

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 firm) 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) = 12000 1000Q for lemonade after using the sauna. Furthermore, the folks running the retreat have the cost-function C(Q) = 1000Q2 + 1000 for lemonade.

A. What are equilibrium price and equilibrium quantity?

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

C. Prove that this profit level is a global maximum.

D. Show the equilibrium price and equalibrium quantity graphically. Include the inverse demand curve, firm's marginal revenue curve, and firm's marginal cost curve.

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

Question 3 Now imagine that the government (of Mexico in this case) decides to tax lemonade using a specific tax of 4000 per unit of lemonade produced and sold.

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

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

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

D. Show the new equilibrium price and equalibrium quantity graphically. Include the inverse demand curve, firm's marginal revenue curve, and firm's pre- and post-tax marginal cost curves.

E. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? How have these quantities changed from the no-tax case in Question 2?

Question 4 The government of Mexico has decided it would rather ensure that there is no deadweight loss in this market for after-sauna lemonade at the CEO retreat by removing the tax and instead setting a price cap.

A. At what price should the government cap lemonade sales?

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

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

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

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

E. What are consumer surplus, producer surplus, and deadweight loss at the equilibrium? How have these quantities changed from the no-tax case in Question 2?