Let the market demand for widgets be given by P $=100$ Q$/10$ and let the average and marginal cost of production be constant at AC $=$ MC $=$ $$20.$a$.$Find the equilibrium price, quantity, and amount of consumer surplus if the market for widgets were perfectly competitive.$$b$.$Find the equilibrium price, quantity, profit, amount of consumer surplus, and amount of deadweight loss if the market for widgets were a pure monopoly.