Micro economic about demand supply, Lecture notes of Microeconomics

Download Micro economic about demand supply and more Lecture notes Microeconomics in PDF only on Docsity! MICROECONOMICS II LECTURE NOTE By Adem E (BSc in AgEc) Department of Agec, Assosa University CHAPTER 1: OLIGOPOLY • Oligopoly is a market structure which is dominated by a few large producers of a homogeneous or differentiated product. • Crucially, these few firms recognize their rivalry and interdependence, fully aware that any action on their part is likely to induce counter-actions by their rivals. • This leads us to consider strategies and counter-strategies between market participants. Types of oligopoly models • There are different models to explain the behavior of oligopolistic firms. • There are non-collusive models and collusive models. • The classification of oligopoly firms as collusive or non-collusive is based up on whether there exist some agreements between firms or not. • When firms enter into some form of agreement as to the price level they charge or the quantity of output they produce, such firms are said to be collusive oligopoly. • On the other hand, if there is no any form of agreement between firms, firms are said to be non-collusive oligopoly. A. Non-collusive oligopoly • In non-collusive type of oligopoly market, there is no collusion - there is no cooperation among rivals. • Hence, the common feature of non-collusive oligopoly models is there is no cooperation among rival firms. • Thus, under non-collusive oligopoly each firm develops an expectation about what the other firms are likely to do. • Since firms are mutually interdependent, a firm expects some reaction from its rivals when it decides to take a given course of action. • Fore example, when a firm increases its own output or price, it expects some reaction from the rivals to its action; increment of output or price. • However, the question is ‘what kind of reaction’ does a firm expect to its action? • What then is the implication of this expectation on the behavioral pattern of oligopolists? 1. Sweezy’s kinked demand curve model of oligopoly • This model is developed by Paul Sweezy to explain why prices in oligopoly markets are stable or rigid, even when costs rise. • If you closely look at the prices of products produced by oligopoly firms, • You may easily see that prices are more stable as compared to the prices of products in other market structures.  Example, the prices of soft drinks, beer, cigarettes and other similar products, you come to realize that once price is set it remains relatively for a long period of time. This is because firms come to believe that If they cut prices their rivals will follow the price cut and, as a result, the price cut will not produce much of an increase in sales. • However, a price increase will not be followed and will, therefore, result in a significant loss of sales to the firm raising its price. • As a result, once a price is reached, it tends to remain in effect for long periods. • An oligopoly firm will face two demand curves for different ranges of prices. • Suppose a firm knows that any time it raises its prices, all other firms in the industry will do the same. • In this case it faces AB, which is a relatively inelastic curve. • If, on the other hand, no other firms follow its changes in prices the firm will instead find itself on CD, a much more elastic demand curve. • If the firm is the only one to raise prices, it will experience a large drop in sales. The MC curve intersects the MR curve in the vertical segment. quantity $ D MR Q* P* MC If costs shift up slightly, but MC still intersects MR in the vertical segment, there will be no change in price. This price rigidity is seen in real world oligopoly markets. quantity $ D MRQ* P* MC MC’ The ATC curve can be added to the graph. To show positive profits, part of ATC curve must lie under part of the demand curve. quantity $ D MRQ* P* MC ATC • Assume that firm A is the first to start producing and selling mineral water (and refer to Figure 2.1 below). It will produce quantity A and sells at price P1 because MR = MC (= 0) at point A – the mid-way between O and D'. • Now, firm B enters into the industry and assumes that A will keep its output fixed at OA and hence considers that its own demand curve is CD’. • It produces AB (=1/2AD’) and charges price P2 in order to maximize profit. • Firm A, faced with this situation, assumes that, B will retain its quantity constant in the next period. • Therefore, A will produce ½ of the market that is not supplied by B [=1/2(1- 1/4) OD’]. • B (again) reacts and will produce ½ of the unsupplied market [=1/2(1-3/8) OD’]. • This action-reaction pattern continues until equilibrium is reached. • At equilibrium, each firm produces one-third (1/3) of the total market (a total of 2/3); one – third of the market remains unsupplied. • Example - Assume the total market demand of mineral water is 100 bottles per week. • If firm A is the only firm in the market, it will produce one-half of the total demand-50 bottles. • Then, when firm B enters into the industry, it assumes that firm A will keep on producing 50 bottles and considers that its demand will be the remaining 50 bottle. • Firm B, facing an unsatisfied market demand of 50 bottles, produces half of this demand, which is 25 bottles (one-fourth of the total market demand). • In general terms, if there are n firms in the industry each will provide 1/(n +1) of the market, and the industry output will then be n /(n +1) of the total demand. • Clearly, if four firms are assumed to exist in the industry, the higher the total quantity supplied and hence the lower the price. • As more firms are assumed to exist in the industry, the larger the total quantity supplied and hence the lower the price. • The larger the number of firms the closer is output and price to the competitive level. • Example - Assume there are 10000 firms in the industry. • The individual supply will then be 1/10001 of the total supply which is very small proportion as compared to the total supply – the same as in competitive market. • In competitive market, the supply of each firm is very small proportion to the total supply. • When we see the total supply and price, the total supply of these firms will be 10000/10001 which is nearly equal with the total demand. • The price in competitive market is equal to the MC. In our example, the MC is zero. • The price in this case is also zero because firms supply nearly the total demand – OD’. • From the demand curve it can be seen that OD’ can be sold if the price is zero. • Let us now relax the assumption of zero marginal cost and see the equilibrium of a duopoly market (Cournot’s equilibrium) based on the reaction-curves approach. • Reaction curve is a curve that shows the relationship between a firm’s profit maximizing output and the amount it thinks its competitor will produce. • It shows how firm A will determine its output as a reaction to B's decision to produce a certain level of output. • For instance, if we have two firms (A&B), firm A’s reaction function (curve) shows how much output A must produce in order to maximize its own profit for every specific level of output of its rival (B). • The reaction functions of firms under Cournot’s behavioral assumption are downward sloping in a quantity set of axes. Consider the following numerical example. • Find the Cournot’s equilibrium if the market demand and the costs of the duopolists are: • P =100 – 0.5X where X = X1+X2 • C1 = 5 X1 and C2 = 0.5 X2 2 • Step 1: Define the profit functions of the two firms. • Firm 1’s profit is given by π1 = P X1 – TC1 = [100 – 0.5 (X1+X2)] X1 – 5 X1 = 100 X1 – 0.5 X1 2 – 0.5 X1X2 – 5 X1 = 95 X1 – 0.5 X1 2 – 0.5 X1X2 • Firm 2’s profit is given by Õ2 = P X2 – TC2 = [100 – 0.5 (X1+X2)] X2 – 0.5 X2 2 = 100 X2 – 0.5 X1X2 – 0.5 X2 2 – 0.5 X2 2 = 100 X2 – 0.5 X1X2 – X2 2 • Step 2: Maximize the profit function of each firm with respect to its own output (find the reaction function of each firm). • Profit maximization Þ ¶Õ1/¶X1 = 0 and ¶Õ2/¶X2 = 0 • ¶Õ1/¶X1 = 95 – X1 – 0.5 X2 = 0 • Þ 95 – 0.5 X2 = X1……………firm 1’s reaction function [eq.1]. • ¶Õ2/¶X2 = 100 – 2 X2 – 0.5X1 = 0 • Þ X2 = 50 – 0.25X1……. firm 2’s reaction function [eq.2]. Step 3: Solve equations 1&2 simultaneously to find equilibrium quantities of the two firms. • X1 = 95 – 0.5X2 • X2 = 50 – 0.25X1 • Þ X1 = 95 – 0.5(50 – 0.25X1) • X1 = 95 – 25 + 0.125X1 • X1– 0.125X1 = 70 • 0.875 X1 = 70 • X1 = 80 • And X2 = 50 – 0.25X1 = 50 – 0.25(80) = 50 –20 = 30 • The total output in the market is X = X1+X2 = 80+30 = 110. • Þ The market (equilibrium) price is P =100 – 0.5X = 100 – 0.5(110) = 45.  The profit of each duopolist is Firm 1 profit = R1-C1 = P*X1- 5X1 = 45*80- 5*80 = 3200 Firm 2 profit = R2-C2 = P*X2- 0.5X2 2 = 45*30- 0.5*302 = 900 Total industry profit = 3200+900 = 4100 • Note that whether the quantities supplied by the firms are equal or not depends on whether they face the same cost structure or not. 3. Stackelberg’s Duopoly Model • This model was developed by Heinrich von Stackelberg and is an extension of Cournot’s model. • Unlike the Cournot’s model, where firms are naïve (do not recognize their rivalry) and where the two firms make their output decisions at the same time, under Stackelberg’s model, (at least) one of the two firms is sufficiently sophisticated to recognize that its competitor is naïve and thus sets its output before the other. • Consider the example below (which is the same as the example under Cournot’s model). • Assume that in a duopoly market the demand function is P =100 – 0.5(X1+X2) and the duopolists’ costs are C1 = 5 X1 and C2 = 0.5 X2 2. • 1. Stackelberg’s solution with firm 1 being the sophisticated leader: • Firm 1 knows the reaction function of firm 2, substitutes this reaction function into its own profit function, and maximizes its profit as if it were a monopolist. • Step 1: Reaction function of firm 2: • Õ2 = P X2 – C2 • = [100 – 0.5 X1 – 0.5X2] X2 – 0.5 X2 2 • = 100 X2 – 0.5 X1X2 – 0.5 X2 2 – 0.5 X2 2 • = 100 X2 – 0.5 X1X2 – X2 2 • ¶Õ2/¶X2 = 100 – 2 X2 – 0.5 X1 = 0. • Þ X2 = 50 – 0.25X1 firm 2’s reaction function • Step 2: Substitute this into firm 1’s profit function and maximize. • Õ1 = P X1 – C1 = [100 – 0.5 (X1+X2)] X1 – 5 X1 • = 100 X1 – 0.5 X1 2 – 0.5 X1X2 – 5 X1 • = 95 X1 – 0.5 X1 2 – 0.5 X1X2 • Þ Õ1 = 95 X1 – 0.5 X1 2 – 0.5 X1 (50 – 0.25X1). • = 95 X1 – 0.5 X1 2 – 25 X1 + 0.125 X1 2 • = 70X1 – 0.375 X1 2 • Þ¶Õ1/¶X1 = 70 – 0.75 X1 = 0 ÞX1 = 280/3. (Check the second order condition) • Step 3: Firm 2 would assume that firm 1 produces 280/3 units; thus substitutes this amount into its reaction function and produces: • X2 = 50 – 0.25X1 = 50 – 0.25(280/3) = 80/3 units. 4. Bertrand’s Duopoly Model • Bertrand’s duopoly model (which was developed in 1883) differs from Cournot’s in that it assumes that firms choose to compete by setting prices instead of quantities. • Each firm is faced by the same market demand, and aims at the maximization of its own profit on the assumption that the price of the competitor will remain constant. • Like the Cournot’s model, it applies to firms that produce the same (homogeneous) good and make their decisions at the same time. • Thus, if the two firms charge different prices, the lower-price firm will supply the entire market and the higher-price firm will sell nothing. • Because the good is homogeneous, consumers purchase only from the lowest-price seller. • If both firms charge the same price, consumers will be indifferent as to which firm they buy from. • And, the model assumes that each firm will supply half the market. • Consider the following example where the market demand for a good is P = 30 – Q(where Q = Q1+Q2) and both firms have a marginal cost of 3 (MC1 = MC2 = 3). • If the two firms charge the same price of 5 Birr, each could get a per unit margin of Birr 2. • However, at least one will have the incentive to cut price and undersell the other. • This means P = 5 will not be a stable (an equilibrium) price. • In general, as long as price is above the MC, there will be an incentive to reduce price and thus, the equilibrium will be the competitive outcome – where price equals marginal cost. Ø Equilibrium price P* = MC = 3.  Equilibrium quantity Q* is obtained by substituting P = 3 into the market demand: • P = 30 – Q Þ 3 = 30 – Q Þ Q* = 27.  Each firm supplies 27/2 = 13.5 units (Q1 = Q2 = 13.5). • Bertrand’s model is criticized on the same grounds as that of Cournot’s (critics 1and 2 under Critiques of the Cournot’s Model) and on its assumption of the equal market share of total sales by the firms. • Firm 2’s profit: Õ2 = TR2 – TC2= P2Q2 – (15 + 2Q2) • = P2 (24 – 4P2 + 4P1) – [15 + 2(24 – 4P2 + 4P1)] • = 24P2 – 4P2 2+ 4P1P2 –15 – 2(24 – 4P2 + 4P1) • = 24P2 – 4P2 2+ 4P1P2 –15 – 48 + 8 P2 – 8 P1 • = 32P2 – 4P2 2 + 4P1P2 – 8 P1 – 63 • Õ2 is maximized when ¶Õ2/¶P2 = 0 Þ 32 – 8P2 + 4P1 = 0 • Þ P2 = 4 + 0.5 P1… (Eq.2). [Firm 2’s reaction function] Step 2: Solve the two reaction functions simultaneously. • P1 = 4.5 + 0.25 P2 • P2 = 4 + 0.5 P1 Þ P1 = 4.5 + 0.25 (4 + 0.5 P1) Þ P1 = 4.5 + 1 + 0.125 P1 Þ P1 – 0.125 P1 = 5.5 Þ 0.875P1 = 5.5 Þ P1 = 5.5/0.875 = 44/7 » 6.29. Þ P2 = 4 + 0.5 P1 = 4 + 0.5 (44/7) = 50/7 » 7.14. Step 3: Substituting P1 = 44/7 and P2 = 50/7 into the demand functions gives: Þ Q1 = 12 – 2(44/7) + 50/7 = 46/7 and Þ Q2 = 24 – 4(50/7) + 4 (44/7) = 144/7 • Find the profit of each firm! • The following figure depicts the reaction curves of the firms and their equilibrium quantities. A. Cartels Aiming at Joint-Profit Maximization (Centralized Cartels) • In this form of cartel, the aim is to maximize the industry (joint) profit. • The situation is identical with that of a multi – plant monopolist who seeks the maximization of his profit. • Consider a pure oligopoly – an oligopoly where all firms produce a homogeneous product. (This is often the case with centralized cartels). • The firms in the cartel appoint a central agency to which they delegate the authority to decide on: - The total quantity to be produced by the industry, - The price at which the output is sold, - The allocation of production, and - The distribution of the maximum joint-profit among the members. • To do this, the central agency has to assess the cost structure of the industry (and firms) and the market demand. • For the simple case of two firms (duopoly), the equilibrium is determined as follows: • Given P = f (X)…demand function [where X = X1 + X2] • C1 = f (X1) and C2 = f (X2)…cost functions of the two firms. • First Order Condition (F.O.C): MR = MC1 = MC2 • Second Order Condition (S.O.C): ¶2 Õ1/¶ X1< 0 and ¶2 Õ2/¶X2< 0 • Note that these conditions are the same as the conditions for profit-maximizing multi-plant monopolist. § § T=1+™ Qi" Q" Q"=Q*+Q" Figure 2.5: Equilibrium Determination Under a Centralized Cartel • These reasons include: 1. Mistakes in the estimation of market demand and costs. • The central agent might commit mistakes while estimating and aggregating the demands and costs of individual firms. • Or, the firms may purposely report incorrect figures to influence their shares of total profit. • 2. Slow process of cartel negotiations. By the time agreement is reached market conditions may have changed, and the chosen quantity and price may no more be those that result in monopoly profit. • 3. Fear of government interference. The cartel may purposely under operate not to attract the eyes of the government particularly if the monopoly price yields too high profits. • 4. Fear of entry. The fear of attracting new firms to the industry by too high profits is another reason why monopoly profit may not be realized. • 5. Stickiness of the negotiated price. Even if the cartel is aware of changes in market conditions, it needs new negotiation to change the already agreed on price (and quantity) so that profit deviates from the monopoly profit. B. Market – Sharing Cartels • In this type of cartel, firms agree to share the market, but keep a considerable degree of freedom concerning the style of their product, their selling activities and other decisions. • Thus, this type of collusion is more common than centralized cartel. • There are two basic methods for sharing the market: non-price competition and determination of quotas. i. Non-Price Competition Agreements • The member firms agree on a common price, at which each firm can sell any quantity demanded. • The price is set by bargaining, with the low-cost firms pressing for a lower price and the high-cost firms for a higher price. • The agreed on price must be such as to allow some profits to all members. • The firms agree not to charge a price below the cartel price, but they are free to vary the style of their product and/ or their selling activities. Price Leadership • Price leadership is a coordinated behavior of oligopolists where one firm sets the price and the others follow it because,  It is advantageous to them or  They prefer to avoid uncertainty about their competitors’ reactions even if this implies departure of the followers from their profit-maximizing position. • Price leadership allows the members complete freedom regarding their product and selling activities and thus is more acceptable to the followers than a centralized cartel, which requires the surrendering of all freedom of action to the central agency. • The prices charged may differ for different firms (particularly if the product is differentiated), but the direction of their changes will be the same. • There are various forms of price leadership. The most common types of leadership are: • A. Low-cost price leadership • B. Dominant-firm price leadership • C. Barometric price leadership A. Low – Cost Price Leadership • The important condition for this model is that firms have unequal costs. • It is assumed that there are two firms that produce a homogeneous product at different costs, which clearly must be sold at the same price. • Then, the firm with low cost charges a lower price and its price will be followed by high-cost firm although the price doesn’t maximize the profit of the follower. • The follower would obtain a higher profit by producing a lower output and selling it at a higher price. • But the follower prefers to follow the leader sacrificing some of its profit in order to avoid a price war, which would eliminate it if price fell sufficiently low as not to cover its LAC. • Note that the profit- maximizing output of firm 2 would be X2 = 9 units, and • it would sell it at P* = 60, which is found by maximizing firm 2’s profit function if it could act the same way as firm 1.  The firms may agree that they are going to share the market in constant proportions in which case we drop our earlier assumption of equal share of the market. • Consider two firms with shares k1 and k2. • k1 = X1/X …………….(1) and • k2 = X 2/X …………….(2) • Dividing (1) by (2) gives k1/k2 =X1/X2 Þ X1 = k1/k2 * X2 …………………. Reaction function of firm 1. Þ X2 = k2/k1 * X1 …………………. Reaction function of firm 2. • Assume that: • q k1 = 2/3 and k2 = 1/3………Shares • q P1=100-2X1-X2…………….firm 1’s demand function • q C1=2.5X1 2………………….firm 1’s cost function • q The firms agreed that firm 1 would be the low-cost leader. Solution: • Step 1: p1=R1 – C1 = (100 – 2X1 – X2) X1 – 2.5X1 2 • Step 2: Substitute the reaction function of firm 2, X2= , to obtain the profit function of the leader. Þp1 = R1– C1 = (100 – 2X1 – 0.5X1) X1 –2.5X1 2 =100X1 – 5X1 2 • Step 3: Maximize the leader’s profit: • ¶Õ1/¶X1 = 100 – 10X1 = 0. Þ100 = 10X1 Þ X1 =10. • The leader will set the price P1 =100 – 2X1 – X2 • =100 – 2X1 – 0.5X1 • =100 – 2.5X1 • =100 – 2.5(10) =75 • Step 4: The quantity which will be produced by the follower is X2 = 0.5X1 = 5 and he will sell it at the price of the leader P1 = 75. • The dominant firm leader maximizes his profit by equating his MCL to his MRL (sets price P* and sells quantity X*) - panel (b). • The smaller firms are price-takers, and may or may not maximize their profits, depending on their cost structure. • This model is also called ‘the partial monopoly’ model since the large firm acts as a monopolist while the small firms are price-takers and act like firms in pure competition. • Consider the following numerical example. • q Market demand: D = 50 - 0.3P • q Aggregate supply of the smaller firms: S = 0.2P • q Total cost function of the leader firm: CL = 2X • Step 1: The demand of the dominant firm: X = D – S • Þ X = 50 – 0.3P – 0.2P • Þ X = 50 – 0.5P • Or P = 100 – 2X • Step 2: pL =RL – CL = (100 – 2X) X – 2X = 100X – 2X2 – 2X = 98X – 2X2 • Step 3:¶ÕL/¶X = 98 – 4XL = 0. Þ98 = 4XL Þ XL = 24.5. Þ The leader will set the price P = 100 – 2X = 100 – 2 (24.5) = 51 Þ The total quantity demanded D = 50 – 0.3 (51) = 34.7. • The leader supplies X = 24.5 out of the total and the smaller firms produce the remainder (= 34.7 – 24.5 = 10.2). (Alternatively: S = 0.2(P) = 0.2 (51) = 10.2). • Similar to the low-cost price leader, the dominant firm leader must make sure that the smaller firms will not only follow his price but also produce the right quantity – the quantity that will not push him to a non-profit-maximizing position. • Thus, there should be tight (formal or informal) sharing-the-market agreement between (among) firms where price leadership is the form of collusion. • In order to have the power to impose its price the leader must be both a low – cost and a large firm. Þ the power of the leader depends both on its costs and its size. • If a firm has low costs but is very small (compared to some other firm –leader), it may not find it possible to survive a price, or advertising or product – design war that the dominant firm may start. • On the other hand, if the dominant firm loses its cost advantage, it loses also its power to impose an increase in price, since the smaller firms, having lower costs, will normally not follow it in price increases. Contestable Markets • According to the theory of contestable markets developed during the 1980s, even if an industry has only a few sellers (or perhaps only one),  it would still operate as if it were perfectly competitive if entry is “absolutely free” (i.e., if other firms can enter the industry and face exactly the same costs as existing firms) and  if exit is “entirely costless” (i.e., if there are no sunk costs so that the firm can exit the industry without facing any loss of capital). • Firms will sell their products at a price that only covers their average total costs (so that they earn zero economic profit) even if there are only a few firms in the market. • The firms in a contestable market, like those under perfect competition, will produce at minimum cost. • If they produce at more than minimum cost, firms will enter the industry, produce at lower costs than the existing firms, undercut the existing firms’ price, and make a profit. • Thus, costs will be pushed down to the minimum level. • Also price cannot exceed marginal cost. • If existing firms are charging a price in excess of marginal cost, it is profitable for an entrant to undercut the price of the existing firms. • Thus, for an equilibrium to occur price cannot exceed marginal cost. • The existing firms do not collude to push up price because they know that new firms would enter the market very quickly and undercut their price. CHAPTER TWO: PRICING OF FACTORS OF PRODUCTION AND INCOME DISTRIBUTION • In this chapter, we turn our focus to the factor (resource) market and deal with the determination of prices and employment of inputs, and relatedly the distribution of income to their owners. • In many ways the determination of input prices and employment is similar to the pricing and output determination of commodities. • That is, the price and employment of an input is generally determined by the interaction of the forces of market demand and supply. 2.1. Factor Pricing Under Perfect Competition • determining input price and employment when both factor (input) and product (output) markets are perfectly competitive. • In a perfectly competitive product and input markets price is determined by the interaction of demand and supply (market forces). • The interaction market demand for and the market supply of an input determine the input’s price and level of employment. 2.1.1 The Demand for Factors of Production i. The Demand of a Firm for One Variable Productive Factor • The demand for an input by a firm shows the quantities of the input that the firm would hire at various alternative input prices, ceteris paribus. • Here, we assume that only one input is variable (i.e., the amount used of the other inputs is fixed and cannot be changed). • According to the marginal concept, a profit-maximizing firm will continue to hire an input as long as the extra income (receipt) from the sale of the output produced by the input is larger than the extra cost of hiring the input. • The extra income is given by the marginal (physical) product (MPP) of the input times the marginal revenue (MR) of the firm. • This is called the marginal revenue product (MRP). That is, MRP = MPP.MR. • When the firm is a perfect competitor in the product market, its marginal revenue is equal to the commodity price. • In this case the marginal revenue product MRP = MPP. P = VMP (the value of marginal product). • If the variable input is labor, MRPL = MPPL. P = VMPL. • The extra cost of hiring an input or marginal expenditure (ME) is equal to the price of the input if the firm is a perfect competitor in the input market. • Given this MRPL and the equilibrium condition MRPL = VMPL = w, the firm hires L1 units of labor if the wage rate is w1. • Similarly, L2 units of labor will be hired at w2 and L3 at w3. • At e1, VMPL = w1. Þ The firm’s profit is at the maximum for wage rate w1. • To the left of e1, VMPL > w1. Þ The firm would increase its profit by hiring more labor. • The opposite holds to the right of e1. That is, the firm would increase its profit by reducing the amount of labor it uses. • The graph that shows this relationship between the wage rate (input price) and the quantity demanded (hired) of labor (input) is the demand curve (Figure below). • Thus, the demand for a single variable input is the value of marginal product (VMP) of the input under the perfectly competitive markets. d, = MRP, = VMP, L Figure 4.2: The Demand of a Firm for One Variable Productive Factor • Initially, the firm produces a profit – maximizing output X1 with a combination of L1 and K1, given factor prices w and r whose ratios are defined by the slope of the iso-cost line BC (Figure 4.3). • When wage rate falls the iso-cost BC changes to BC* and this new iso- cost (BC*) is tangent to the iso-quant corresponding to output level of X2 at e2. K2 units of capital and L2 units of labor are used. • This movement from e1 to e2 can be split into two: substitution effect and output effect. • To see the substitution effect draw an iso-cost line (B*C**) parallel to the new iso-cost line (BC*) but tangent the old iso-quant (X1). • The movement from e1 to a is the substitution effect. • This shows that the firm substitutes the cheaper labor for the relatively more expensive capital even if it were to produce the original level of output (X1). • Thus, the employment of labor will rise from L1 to L1*. • But when wage rate falls, the firm can hire more of the two factors (L and K) with the same expenditure. • Hence, the firm produces higher level of output with more labor and capital (L2 and K2) and, therefore, the movement from a to e2 is the output effect. • Point e2 is not the final equilibrium of the firm because keeping the total cost /expenditure constant doesn’t maximize its profit. • The fall in wage rate results in a shift in the marginal cost curve downward to the right (from MC1 to MC2) and the profit maximizing output of the firm increases from X' to X". • At the initial wage rate w1, L1 units of labor are employed (which is determined by the intersection of VMPL1 and the supply w1). • The new equilibrium demand for L (when wage rate falls to w2) is at point B on VMPL2. • If w further declines to w3, the new equilibrium will be at point C. • The locus of points A, B and C is the demand curve for labor by the firm when several variable factors are used. • In this case, the demand for an input is not the same as its VMP curve, but derived from changing (shifting) VMP curves. Demand for a variable factor depends on: § The price of the input – increase in input price reduces the quantity demanded of the inputs services, and vice versa. § The marginal physical product of the factor – if the MPP of a factor increases, more of it will be demanded, and vice versa. § The price of the output (commodity) – when the output the firm produces becomes cheaper, the firm will cut its production and thus demands less of the input used. The opposite happens when the commodity gets more expensive. § The amount of other factors which are combined with the factor § The price of other factors – increase in prices of complementary inputs reduces the amount of the complementary inputs to be used with a given productive factor, and thus reduces the productivity of (and demand for) the productive factor. § Technological progress – technological progress could increase or decrease the demand for an input depending on whether it increases or decreases the MPP of the factor.