Meaning of Joint Products Goods jointly produced in fixed proportions: –Interdependence in production –Single marginal cost curve for both products or product package; e.g., beef & hides However, demand curves & MR curves are independent Pricing decision must recognize inter- dependence in production –Marginal revenue of product package is vertical sum of two MR curves;
Pricing of Joint Products w/o Excess production of Hides PHPH PBPB DBDB MR T DHDH MR B MR H MR B Prices etc. Quantity X* MC
Pricing of Joint Products with Excess production of Hides PHPH PBPB DBDB MR T DHDH MR B MR H MR B Prices etc. Quantity XHXH MC XB
Advertising Assumptions –Firm sets only one price –Firm knows Q(P,A) How quantity demanded depends on price and advertising
Q0Q0 P0P0 Q1Q1 P1P1 AR MR AR and MR are average and marginal revenue when the firm doesnt advertise. MC If the firm advertises, its average and marginal revenue curves shift to the right -- average costs rise, but marginal cost does not. AR MR AC Effects of Advertising Quantity $/Q AC
Advertising Choosing Price and Advertising Expenditure A Rule of Thumb for Advertising
Advertising A Rule of Thumb for Advertising To maximize profit, the firms advertising- to-sales ratio should be equal to minus the ratio of the advertising and price elasticities of demand
Advertising – An Example R(Q) = $1 million/yr $10,000 budget for A (advertising--1% of revenues) E A = 0.2 (increase budget $20,000, sales increase by 20% E P = -4 (markup price over MC is substantial) Should the firm increase advertising? YES –A/PQ = -(0.2/-4) = 5% –Increase budget to $50,000
Cost-Plus (Mark-up) Pricing Traditional assumption of theory is that firms increase production until MR = MC and then charge a price according to the demand curve In reality, many firms use cost plus pricing – setting prices that cover the cost of purchasing or producing a product plus enough profit to allow the firm to earn its target rate of return
Mechanics of Cost-Plus Pricing First, determine the total costs of purchasing or producing the product Here Q is used to determine P, but in actuality, Q is determined by P This problem is overcome by using an assumed value of Q, say some percentage of the firms capacity
Mechanics of Cost-Plus Pricing Then determine the markup over cost –The overall objective is to allow the firm to earn its targeted rate of return –If the return requires $X of total profit, then the per unit markup will be $X/Q –Hence, the price is given by the formula:
Mechanics of Cost Plus Pricing Sum of the last 2 terms in the given formula i.e. AFC + X/Q is called the Gross Profit Margin (GPM) The per unit targeted profit (on investment) = X/Q is called the Net Profit Margin (NPM) Hence, a modified mark-up formula can be written as: where K (mark-up proportion) = GPM/AVC Price = (1 + K) AVC
Mark-up Pricing Model D D2 D1 At normal output Q n, AVC=Q n B; AFC=KQ n =BC; net profit margin (NPM)=CF When demand shifts up to D 2, then Q=OQ 2, NPM=C 2 F 2, with GPM constant When demand shifts down to D 1, then Q=OQ 1, NPM=C 1 F 1, with GPM constant
Evaluation of Cost-Plus Pricing - Advantages –Contributes to price stability – price changes may be expensive and provoke undesirable reactions by competitors –Formula is simple and easy to use –Less information is required for cost- plus than for marginal cost pricing –Provides a clear justification for price increases (whenever cost increases)
Evaluation of Cost-Plus Pricing - Disadvantages –Does not take demand conditions into account –Cost data may be the wrong – e.g. historical costs or accounting costs –Most applications are based on fully distributing common costs to the various goods produced
Cost-Plus Pricing and Economic Theory Cost plus pricing appears to be inconsistent with economic theorys postulate of profit maximization However, cost plus pricing may be a tool used by businesses in pursuing long-run profit maximization Frequently, long run marginal and average costs are not greatly different. So, use of average cost as a basis for pricing is a reasonable approximation of marginal cost pricing If markup over cost is based on demand conditions then cost-plus pricing may not be inconsistent with profit-maximization
Cost-Plus Pricing and Economic Theory Thus price P is a markup over costs AC. The markup is a function of price elasticity of demand. Thus cost-plus pricing may simply be the mechanism by which managers pursue profit maximization. Obtaining additional information necessary to generate estimates of marginal costs and revenues may be prohibitively expensive. Thus cost-plus pricing may be the most rational approach to maximizing profits.
Limit Pricing Limit price is the maximum price that an oligopolistic firm can charge above minimum long run average cost (LAC), without inducing new entry. Condition of Entry (E): It measures the extent to which new entry is difficult. (e.g. E=0 when entry is free). where P L = Limit Price and P C = Perfect competition Price. Hence, P L = P C (when entry is free ) and P L > P C (when entry is difficult) E= ( P L - P C ) / P C P L = P C * (1 + E)
Models of Limit Pricing Determination of Limit Price under Oligopoly depends upon whether entry is difficult due to I. Absolute Cost Disadvantage OR II. Relative Cost Disadvantage faced by the new entrant in the market. Accordingly there are 2 models of Limit Pricing, both assuming L-shaped long run average cost (LAC) curve.
Limit Pricing with Absolute Cost Disadvantage Absolute cost disadvantage means that LAC of the new entrant is located above that of the existing firm at all output levels (presuming that the vertical distance between the two is always same). Assumptions: 1. Products of both firms are homogeneous. 2. Existing firm keeps its output constant, even in the face of new entry. 3. L-shaped LAC curve. (i.e. no diseconomies of scale exist).
Absolute Cost Disadvantage - Diagrammatic View New entrant Existing firm Since new entrant can at best supply Q m at P L, existing firm chooses to supply Q L at P L, because if P
P L (e.g. at P 3 ), new entrant is rewarded with super-normal profit. Thus, P L is the limit price
Limit Pricing with Relative Cost Disadvantage Relative cost disadvantage arises when the optimum scale of output is very large compared to existing total demand, hence compelling the new entrant to supply sub-optimal output. Hence either price would fall after entry ( if entrant enters with optimum scale output) or entrants output would be sub-optimal if price is to remain unchanged. Assumptions: 1. Existing firms keep their output constant. 2. LAC is L-shaped and same for new and existing firms. 3. Products for all firms are homogeneous. 4. New firm enters with the optimum scale.
Relative Cost Disadvantage - Diagrammatic View Assuming that the new entrant can enter at optimum scale Q m at P=P c, the existing firm supplies Q L =Q c – Q m at P=P L. If the existing firm chooses P>P L (e.g, at P 2 ), then total supply will be Q 3 =Q m + Q 2, inducing P to fall to P 3, which provides super-normal profit to the new entrant. Hence, P cant exceed P L. If, on the other hand, P
QMQM General Diagram for Entry Limiting Pricing Quantity $/Q MC AC D=AR MR Pm QLQL PLPL Q L A B C D E With monopoly price-quantity combination (P m, Q m ), Π=P m ADC. If limit price is fixed at P L, Π=P L BCE and Q=Q L. Now, super- normal profit is still positive but less. Now a new entrant with Q
Implications of limit pricing Π Time (t) Discounted profit stream under limit pricing Discounted profit stream under usual profit-maximization T The blue or red path will be chosen depending upon whether t>T or t