The  fez is the typical Arabic hat in the shape of a short red cylinder. Historians believe it was manufactured in the city of Fes, in Morocco, during the 17^th century. It has been used as a head cover of the Arabic world for centuries and was also adopted by the Ottoman Empire as part of its military uniform. The fez is still the most ordinary hat in North Africa and the Middle East; the hat was banned at the starting of 20th century in Turkey. Suppose that the city of Marrakech in Morocco has a daily demand for fezzes given by:

where Q is the total amount of fezzes formed.

a) Obtain the equilibrium price and quantity supposing that the market for fezzes is a monopoly.

b) Obtain the equilibrium price and quantity supposing that the market of fezzes is perfectly competitive.