Question: An average revenue function \((AR)\) is given in the general form: \(R = f(y)\). (i) What is the relationship between the \(AR\) curve and the demand curve? (ii) Prove that for any downward slopping \(AR\) curve, the Marginal Revenue \(MR\) will always differ from \(AR\) by a certain amount \(g\), \(MR-AR=g\) where \(g\) can be expressed as a functional relationship of \(y\). Determine the expression for \(g\) for (a) downward slopping nonlinear \(AR\) curve and (b) linear downward slopping \(AR\) curve, and comment whether \(g\) is positive or negative (iii) Determine what happens to your analysis and value of \(g\) in part (ii) when we have perfect competition.

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