3. Suppose the reduced form demand for towels is given by Q\" = 100 5PT, and the reduced form supply of towels is given by Q5 = NH. a. b. c. Graph the supply and demand curves. Solve for the equilibrium price and quantity (using algebraic method). Suppose that supply changes so that at each price, 20 fewer towels are offered for sale at every given price. Derive and graph the new supply curve. Solve for the new equilibrium price and quantity (using algebraic method). Show that the law ofdemand holds using calculus. Is the supply curve upward sloping (show using calculus)? Suppose that a towel rack is a complement to towels. The expanded demand curve for the towels then is 0.\" = 150 - 5PT- PR, where PR is the price of the towel rack. Suppose that this current price of a towel rack is $50. Show that this expanded demand curve is consistent with the reduced for demand relationship given in the setup to the problem. If the price of towel racks increases to 560, what is the equation for the new demand curve? In which direction has the demand curve shifted? Using calculus, derive and apply the formula that indicates the impact of the towel rack price shock on the equilibrium price and quantity of towels