Reference: Many who have poor knowledge of how market works believe that, "the higher the price, the higher the profits." Assume a firm has control over the price and can set its price. Further, assume the market (inverse) demand is linear and is given by: p = a-bq and the marginal cost is constant and equals c. Using these demand and cost conditions..

4. (a) Prot-maximizing price must equal 13 = i M C , where e is the price elasticity of demand. What are the requirements for this condition to hold? In other words, explain both the necessary and sufcient conditions and the requirement related to e. (b) Show that for an elastic demand, by lowering the price prots may go up or down; for an inelastic demand loweing the price must lower the prots. What happens when the elasticity is 1 and price is lowered or raised? (c) Show that for a linear demand, 39 = a bQ, the elasticity is changing from 00 to 0 as price decreases (quantity increases) but the slope is constant; but for the demand function Q = 100 / P, the elasticity is constant but the slope is changing