3. We have a linear market demand curve given P = 12 29. a) Derive an expression for the point elasticity of demand as a function of output, 9. Determine where on your demand curve the elasticy (dened to be positive] is exactly equal to 1. Verify your answer using your formta. b) More generally, any demand curve can be represented by P{q); a decreasing function of output. Revenue is then P(q) q. Derive an expression for marginal revenue. Express your marginal revenue curve in terms of the price elasticity of demand (as a function of output). c) Suppose the industry just has 1 rm, and that rm has no costs, so it only cares about revenue. Would such a rm ever choose to operate at a level of output where the elasticity is strictly less than 1'? Explain. (20 pts)