the total cost function is taken. For example, assume cost, C, equals 420 + 60Q + Q2. Then MC = 60 + 2Q. Equating MR to MC and solving for Q gives Q = 20. So 20 is the profit maximizing quantity: to find the profit-maximizing price simply plug the value of Q into the inverse demand equation and solve for P. Residual demand curve The demand curve facing a particular firm is called the residual demand curve. The residual demand curve is the market demand that is not met by other firms in the industry at a given price. The residual demand curve is the market demand curve D(p), minus the supply of other organizations, So(p): Dr(p) = D(p) - So(p) Demand function and total revenue If the demand curve is linear, then it has the form: p = a - b*q, where p is the price of the good and q is the quantity demanded. The intercept of the curve and the vertical axis is represented by a, meaning the price when no quantity demanded. and b is the slope of the demand function. If the demand function has the form like that, then the Total Revenue should equal quantity demanded times the price of the good, which can be represented by: TR= q*p = q(a-bq). Is the demand curve for PC firm really flat? Practically every introductory microeconomics text describes the demand curve facing a perfectly competitive firm as being flat or horizontal. A horizontal demand curve is perfectly elastic. If there are n identical firms in the market then the elasticity of demand PED facing any one firm is PEDmi = nPEDm - (n - 1) PES where PEDm is the market elasticity of demand, PES is the elasticity of supply of each of the other firms, and (n -1) is the number of other firms. This formula suggests two things. The demand curve is not perfectly elastic and if there are a large number of firms in the industry the elasticity of demand for any individual firm will be extremely high and the demand curve facing the firm will be nearly flat. For example, assume that there are 80 firms in the industry and that the demand elasticity for industry is -1.0 and the price elasticity of supply is 3. Then PEDmi = (80 x (-1)) - (79 x 3) = -80 - 237 =