rofessor Jay Bhattacharya Spring 00 Firm Objectives Cost minimization: Given a fixed output level (without any story about how this output is determined) firms choose the minimum cost combination of inputs. rofit maximization: Firms choose that level of output that yields the highest level of profits. rofit rofit = Revenue Cost Last class, we analyzed costs in detail. The cost minimization problem produces a function C(), which represents minimum costs given output. Revenue is output multiplied by the price at which that output sells R() =. Spring 00 Econ --Lecture 3 Spring 00 Econ --Lecture 3 rofit Maximization Choosing Output maxπ = R() C() First order condition: dπ dr dc dr dc = = 0 = d d d d d Interpretation: To maximize profits, set marginal revenue (dr/d) eual to marginal cost (dc/d). Supply: How much will firms produce? If a firm produces at all, it will produce an amount such that MR = MC. If the extra revenue generated from producing extra unit of output (MR) exceeds the additional cost of producing that unit, then the firm can increase its profit by expanding output by unit. Spring 00 Econ --Lecture 3 3 Spring 00 Econ --Lecture 3 4 Second Order Condition Graphical resentation d Π d R d C = < d d d 0 slope = R= Π R()-C() The SOC is important because of S shaped cost curves. Also, if price falls below AVC, the firm (if it produced positive amounts of output) would earn a loss. Instead, it should go out of business C() 0 ** * ** * Spring 00 Econ --Lecture 3 5 Spring 00 Econ --Lecture 3 6 Econ --Lecture 3
rofessor Jay Bhattacharya Spring 00 Nicholson Example roblem Would a lump-sum profits tax affect the profit maximizing uantity of output? How about a proportional tax on profits? How about a tax assessed on each unit of output? Lump-Sum Tax rofit maximization under a lump-sum profits tax: (T is the lump-sum tax) Π= C( ) T First order condition is exactly the same: dπ dr dc = = 0 d d d Spring 00 Econ --Lecture 3 7 Spring 00 Econ --Lecture 3 8 Lump-Sum Tax (continued) roportional Tax on rofits However, it may be optimal for firms to go out of business if the lump sum tax is high enough: C() R= R=-T * Spring 00 Econ --Lecture 3 9 Under a proportional tax on profits (say, t) the firm s problem is: ( C ( ) )( t) Π= The first order condition is: dπ dr dc dr dc = ( t) = 0 = d d d d d Spring 00 Econ --Lecture 3 0 roportional Tax (continued) The firm makes less profits, but the marginal and limit conditions are the same: If the firm produces positive without the tax, it produces positive withthetax. C() R= (-t)c() R=(-t) * Spring 00 Econ --Lecture 3 Tax on Output Under a tax (say, t) on output the firm s problem is: ( ) ( ) Π= t C The first order condition is: dπ dr ( t) dc 0 dr ( t) dc = = = d d d d d Spring 00 Econ --Lecture 3 Econ --Lecture 3
rofessor Jay Bhattacharya Spring 00 Tax on Output (continued) rices and Industry Structure This tax distorts the firm s FOC the optimal differs from * : The firm is more likely to go out of business with this risky tax scheme. C() R= The price that firms can charge will depend upon the structure of the industry. In a competitive industry, firms cannot affect prices by cutting back on (or increasing) output. In a monopolistic or oligopolistic industry, changes in output affect market price. In general, output prices that firm faces will be a function of the firm s output: =() This is exactly the (inverse) market demand function. * new Spring 00 Econ --Lecture 3 3 Spring 00 Econ --Lecture 3 4 Competitive Supply In a competitive industry, firms take prices as fixed. If firms charge prices higher than marginal costs, they lose all their business. If firms charge prices lower than marginal costs, they make negative profits. For price taking firms, dr/d = The first order condition is = MC = dc/d The firm will choose output at a point where price is eual to marginal cost. Supply Curve C ( ) Spring 00 Econ --Lecture 3 5 Spring 00 Econ --Lecture 3 6 How Does Supply Vary with Input rices An increase in marginal cost = a shift in the supply curve For example, an increase in wages shifts supply back since it increases marginal costs. Spring 00 Econ --Lecture 3 7 Monopoly Supply Monopolists do not sit back and take prices. They manipulate prices by curtailing output below competitive levels. For monopolists, prices are a function of uantity produced (the inverse market demand curve). However, like firms in a competitive industry, monopolists still maximize profits. The FOC is: dr d ( ) d = d + ( ) dc d Spring 00 Econ --Lecture 3 8 = Econ --Lecture 3 3
rofessor Jay Bhattacharya Spring 00 Monopoly Supply (Graphical) Nicholson Example roblem # Area in box = Total revenue dr/d Marginal Revenue curve C ( ) () Demandcurve Universal Widget produces high-uality widgets at its plant in Gulch, Nevada, for sale throughout the world. The cost function for total widget production () is given by TC = 0.5. Widgets are demanded only in Australia (where demand is = 00 p), and Lapland (where demand is = 00 4p). If Universal Widget can control in each market, how many should it sell in each location in order to maximize profits? What price will be charged in each location? (monopoly) (competitive) Spring 00 Econ --Lecture 3 9 Spring 00 Econ --Lecture 3 0 Example # Solved Let be the amount sold in Australia at price p. Let be the amount sold in Lapland at price p. The firm s total revenues from the two locations eual p + p. The firm s total costs of producing + are 0.5( + ). Example # Solution (continued) The firm chooses and to maximize profits: max Π = ( ) p + p +, Inverting two demand functions yields: p = + 50 p = + 5 4 Spring 00 Econ --Lecture 3 Spring 00 Econ --Lecture 3 Example # Solution (III) lugging the inverse demand functions back into the profit function gives the firm s maximization problem in terms of and : max Π = 50, + + 4 + 5 ( + ) Example # Solution (IV) The first order conditions for the firm s problem and their solution are: 3 + 50 = 0 + 5 = 0 = 30 p = 35 = 0 p =.5 Spring 00 Econ --Lecture 3 3 Spring 00 Econ --Lecture 3 4 Econ --Lecture 3 4
rofessor Jay Bhattacharya Spring 00 roducer Surplus roducer surplus = Revenue - Variable Cost rofit = Revenue - Total Cost roducer surplus = rofit if no fixed costs or if in the long-run AKA operating profit 3WaystoMeasureS S = Revenue - Variable Cost S = Area where rice > MC S = Area to the left of the supply curve Spring 00 Econ --Lecture 3 5 Spring 00 Econ --Lecture 3 6 roducer Surplus = C ( ) Market price line Industry Supply The industry supply curve is the horizontal sum of the existing firms supply curves Spring 00 Econ --Lecture 3 7 + Spring 00 Econ --Lecture 3 8 Econ --Lecture 3 5