Consider the Cournot duopoly model discussed in Lecture 8. In this model, each firm chooses how much output to produce (taking the output produced by the other firm as given) and then price adjusts to clear the market. We want to find the Cournot equilibrium for the following situation.Grinch owns a mineral water spring that provides him with unlimited supply of water at no cost. He can bottle the water at a cost of $1 per litre. Grinch's neighbour, Scrooge, found a mineral spring of his own, that provides him with the same water quality as that of Grinch. It costs him $3 per litre to get his water out of the ground and bottle it. The inverse demand curve for mineral water is given by P(Q) = 20-0.2Q, where P is the price per litre and Q is the number of litres sold. (a) How much output qi will Grinch produce, given output q2 produced by Scrooge, in order to maximise his profit? (b) How much output q2 will Scrooge produce, given q1, to maximise his profit? (c) How many litres will Grinch sell in the Cournot equilibrium? How many litres will Scrooge sell? What is the equilibrium price of a litre of water? How much profit will each of them earn