Managerial Economics Ace Institute of Management Executive MBA
Managerial Economics Ace Institute of Management Executive MBA Program Session 5: Theory of Market and Pricing Instructor Sandeep Basnyat Sandeep_basnyat@yahoo. com 9841 892281
Four Types of Market • • Perfectly Competitive Oligopoly Monopolistically Competitive Monopoly
Characteristics of Perfect Competition 1. Many buyers and many sellers 2. The goods offered for sale are largely the same. 3. Firms can freely enter or exit the market. § Because of 1 & 2, each buyer and seller is a “price taker” – takes the price as given.
MR = P for a Competitive Firm • A competitive firm can keep increasing its output without affecting the market price. • So, each one-unit increase in Q causes revenue to rise by P, i. e. , MR = P is only true for firms in competitive markets.
Profit maximization Rule: MR = MC at the profit-maximizing Q. Costs MC MR P 1 Qa Q 1 Qb Q
Shutdown vs. Exit • Shutdown: A short-run decision not to produce anything because of market conditions. • Exit: A long-run decision to leave the market. • A firm that shuts down temporarily must still pay its fixed costs. A firm that exits the market does not have to pay any costs at all, fixed or variable.
A Firm’s Short-Run Decision to Shut Down • If firm shuts down temporarily, – revenue falls by TR – costs fall by VC • So, the firm should shut down if TR < VC. • Divide both sides by Q: TR/Q < VC/Q • So we can write the firm’s decision as: Shut down if P < AVC Short run equilibrium condition: P = AVC
A Firm’s Long-Run Decision to Exit • If firm exits the market, – revenue falls by TR – costs fall by TC • So, the firm should exit if TR < TC. • Divide both sides by Q to rewrite the firm’s decision as: Exit if P < ATC Long run equilibrium condition: P = ATC
Entry & Exit in the Long Run • In the LR, the number of firms can change due to entry & exit. • If existing firms earn positive economic profit, – New firms enter. – SR market supply curve shifts right. – P falls, reducing firms’ profits. – Entry stops when firms’ economic profits have been driven to zero.
Entry & Exit in the Long Run • In the LR, the number of firms can change due to entry & exit. § If existing firms incur losses, • Some will exit the market. • SR market supply curve shifts left. • P rises, reducing remaining firms’ losses. • Exit stops when firms’ economic losses have been driven to zero.
SR & LR Effects of an Increase in Demand …but then an increase in A firm begins in profits to zero …leading eq’m… to …driving SR Over time, profits induce demand raisesentry, P, … long-run and restoring long-run eq’m. profits for the firm. shifting S to the right, reducing P… P One firm MC Profit Market P ATC P 2 P 1 Q (firm) S 1 S 2 B A C long-run supply D 1 Q 2 Q 3 D 2 Q (market)
The Zero-Profit Condition • Long-run equilibrium: The process of entry or exit is complete – remaining firms earn zero economic profit. • Zero economic profit occurs when P = ATC. • Since firms produce where P = MR = MC, the zero-profit condition is P = MC = ATC. • Recall that MC intersects ATC at minimum ATC. • Hence, in the long run, P = minimum ATC.
Exercise The market demand supply functions for an industry in the perfectly competitive market are Qd = 1000 – 8 P Qs = 100 +10 P The Total Cost function for the industry is: TC = 1000 – 20 Q + Q 2 1) Is the Industry in long run equilibrium? (Hint: Check for Long run equilibrium: P = ATC MC intersects ATC at minimum or MC = ATC) Ans. : P = 50 and ATC = 43. 25 when Q = 31. 6 Since P> ATC, the industry is not in equilibrium 2) Interpret your result forecast the probable impact on price. Ans. : Since P >ATC more firms come in the industry, supply curve shifts to the right and price will fall.
Market Structure Problems Assume the cost function: TC = 1000 + 2 Q + 0. 01 Q 2 and Price is $10 per unit. Calculate the profit maximizing output (Q) and economic profit.
Market Structure Problems Assume the cost function: TC = 1000 + 2 Q + 0. 01 Q 2 and Price is $10 per unit. Calculate the profit maximizing output (Q) and economic profit. Solution: MC = d. TC /d. Q = 2+0. 02 Q In a perfectly competitive market, profit maximizing output is at where P = MC 10 = 2+0. 02 Q Therefore, Q = 400 Economic Profit = TR –TC = 10(400) – (1000 + 2(400) + 0. 01(4002)) =$600
Market Structure Problems Consider a firm which has a horizontal demand curve. The firms Total Cost is given by the function: TVC = 150 Q – 20 Q 2 +Q 3. Below what price should the firm shut down operation?
Market Structure Problems Consider a firm which has a horizontal demand curve. The firms Total Cost is given by the function: TVC = 150 Q – 20 Q 2 +Q 3. Below what price should the firm shut down operation? Solution: In the competitive market, the shut down condition is when Price (P) = Minimum Average Variable Cost But Profit maximization theory require P =MC MC =d. TVC / d. Q = 150 -40 Q +3 Q 2 AVC = TVC /Q = (150 Q – 20 Q 2 +Q 3) / Q = 150 -20 Q +Q 2 Equating, both equations: MC = AVC or 150 -40 Q +3 Q 2 = 150 -20 Q +Q 2 Or, 2 Q 2 – 20 Q = 0 or 2 Q (Q – 10) = 0 Or, Q = 0 and Q = 10 Substituting Q = 10 into marginal cost, P = MC = 150 – 40(10) + 3 (100) = $50 Similarly, substituting Q = 0 in the marginal cost, P = $150 Therefore, if the price falls below $50, the firm shuts down.
Monopoly
Introduction • A monopoly is a firm that is the sole seller of a product without close substitutes. • The key difference: market power: the ability to influence the market price of the product it sells. • A competitive firm has no market power.
Monopoly: Demand Curves A monopolist is the only seller, so it faces the market demand curve. To sell a larger Q, the firm must reduce P. P A monopolist’s demand curve D Q
Monopoly’s Revenue Curve Q P TR AR 0 $4. 50 $0 n. a. 1 4. 00 4 $4. 00 2 3. 50 7 3. 50 3 3. 00 9 3. 00 4 2. 50 10 2. 50 5 2. 00 10 2. 00 6 1. 50 9 1. 50 MR $4 3 2 1 0 – 1 21
Monopoly’s D and MR Curves P, MR $5 4 3 2 1 0 -1 -2 -3 Demand curve (P) MR 0 1 2 3 4 5 6 7 Q
Profit-Maximization Costs and Revenue MC P D MR Q Quantity Profit-maximizing output
Numerical Problems and Solutions 1) Suppose the Total Cost for the Monopoly(TC) = 500 + 20 Q 2 Demand Equation (P) = 400 – 20 Q Total Revenue (TR) = 400 Q – 20 Q 2 What is the profit maximizing price and quantity?
Numerical Problems and Solutions 1) Suppose the Total Cost for the Monopoly(TC) = 500 + 20 Q 2 Demand Equation (P) = 400 – 20 Q Total Revenue (TR) = 400 Q – 20 Q 2 What is the profit maximizing price and quantity? Solution: MR = d. TR / d. Q = 400 -40 Q MC = d. TC / d. Q = 40 Q Profit Maximizing price is achieved when MR =MC Or, 400 – 40 Q = 40 Q Therefore, Q =5 (Profit maximizing output) Putting the value of Q in demand equation Profit Maximizing Price P = 300.
Monopoly’s Pricing Decision • Single Price (without price discrimination) • With price discrimination
Price Discrimination • Price discrimination is the business practice of selling the same good at different prices to different buyers. Some examples: Movie tickets Airline prices Discounts Need-based financial aid
Market Structure Problems Consider a monopolist sells in two markets and has constant marginal cost equal to $2 per unit. The demand marginal revenue equations for two markets are: PI = 14 -2 QI : MRI = 14 -4 QI PII= 10 –QII : MRII = 10 -2 QII a) Using third degree discrimination, find profit maximizing prices and quantities, combined profit from both market. b) What is the profit maximizing price and quantity and total profit without price discrimination. Note: 1 st degree: Charging maximum price for each unit sold. 2 nd degree: Different prices depending upon quantities of goods bought by consumers. 3 rd Degree: Separating consumer market and charge separate prices.
Market Structure Problems Solution: a) Marginal Cost =$2 per unit. The demand marginal revenue equations for two markets are: PI = 14 -2 QI : MRI = 14 -4 QI PII= 10 –QII : MRII = 10 -2 QII Profit maximizing is possible when MRI = MRII =MC So, for Market I: 14 -4 QI = 2. Therefore, QI = 3 For Market II: 10 – 2 QII = 2. Therefore, QII = 4 Substituting values of QI and QII in PI and PII, we have PI = 8 and PII = 6 Profit in Market 1 = TR –TC = (PI x QI) – (MC x QI) = 24 – 6 = $18 Profit in Market. I 1 = TR –TC = (PII x QII) – (MC x QII) = 24 – 8 = $16 So, combined profit = $34.
Market Structure Problems Solution: b) Finding demand functions in terms of quantities: QI = 7 – P/2 QII = 10 – P Total demand: Q = (7 – P/2) + (10 –P) = 17 – 3 P/2 ………. (i) Total demand in terms of P = 34/3 – 2 Q/3 ………………. . (ii) Therefore, TR = P x Q = (34/3 – 2 Q/3)Q = 34 Q/3 – 2 Q 2/3 MR = 34/3 – 4 Q/3 Now, MR = MC 34/3 – 4 Q/3 = 2 Therefore, Q = 7 Substituting the value of Q in Eqn. (ii), P = $6. 67 So, Total Profit = TR – TC = (Px. Q) – (MCx. Q) = 46. 69 – 14 = $32. 69
Oligopoly
Oligopoly - MARKETS WITH ONLY A FEW SELLERS • Characteristics of an Oligopoly Market – Few sellers offering similar or identical products – Interdependent firms – Best off cooperating and acting like a monopolist by producing a small quantity of output and charging a price above marginal cost Because of the few sellers, the key feature of oligopoly is the tension between cooperation and self-interest
Profit maximization in General Oligopoly Costs and Revenue MC P D MR Q Quantity Profit-maximizing output
Other Pricing Structures in Oligopoly • Collusive or Cartel – Centralized – Market Sharing • Non-collusive (Non-cooperative) Oligopoly – Kinked-Demand curve – Price Leadership
Exercise: Centralized Cartel Let a cartel of two firms with centralized cartel model (agreed on price and quantity) face the following demand cost function: Demand function : Q = 120 – 10 P Cost function for firm A : TC 1 = 4 Q 1 + 0. 1 Q 12 Cost function for firm B : TC 2 = 2 Q 2 + 0. 1 Q 22 Find Price, total demand, individual demand of firm A and B and total profit of the cartel industry Hint: • Find MR, MC 1, MC 2 functions and Q 1, Q 2 from MC 1 and MC 2 • Find Q = Q 1 + Q 2 (Add MC 1 and MC 2 to find MC) • Find P, Q, by MC = MR • Find Individual demands by MC 1 = MR and MC 2 = MR • Total Profit = Sum of Individual profits.
Solution Exercise: Centralized Cartel P = 12 – 0. 1 Q TR = 12 Q – 0. 1 Q 2 MR = 12 – 0. 2 Q MC 1 = 4+0. 2 Q 1 : MC 2 = 2+0. 2 Q 2 Q 1 = - 20 + 5 MC 1 Q 2 = - 10 + 5 MC 2 Q = Q 1 + Q 2 = - 30 + 10 MC MC = 3 +0. 1 Q MC = MR Q = 30 P = 9 Since, MR = 6 From, MC 1 = MR: Q 1 = 10 From, MC 2 = MR: Q 2 = 20 π1 = TR 1 - TC 1 = (Px. Q 1) – TC 1 =40 π2 = TR 2 - TC 2 = (Px. Q 2) – TC 2 =100 π = 140
Exercise: Market sharing cartel Let a cartel of two firms with equal market sharing face the following demand function: Q = 120 – 10 P and the Total Cost = 0. 1 Q 2 Find Price (P), total demand (Q), and total profit of each cartel in the industry Hint: • Find half demand by dividing total demand by 2 on the right of equation • Find TR, MC • MR=MC; Find P, Q and Total Profit
Exercise: Market sharing cartel Solution Here, Q = 120 – 10 P Half market share faced by each firm is: Q = 60 – 5 P P = 12 – 0. 2 Q TR = 12 Q – 0. 2 Q 2 MR = 12 – 0. 4 Q MC = 0. 2 Q MC = MR Q = 20 P = 8 π = TR- TC = 120 Profit enjoyed by each firm in market sharing cartel is 120.
Kinked-Demand curve (Price rigidity model) Demand Curve 1 (for P increase) Price Point of MC Intersection MC 1 P MC 2 MR 1 Demand Curve 2 for P cuts MR 2 MR Q D Quantity New Profit-maximizing output At intersection: Q = Q 1=Q 2; P = P 1 = P 2
Exercise: Kinked Demand Curve Model Let the demand functions for price increase and price cuts facing an oligopolist are: Q 1 = 280 - 40 P 1 Q 2 = 100 - 10 P 2 The firm’s Total Cost = 2 Q + 0. 025 Q 2 a) Find Price (P), Quantity (Q), and total profit of the oligopolist. b) Find Upper and lower limits of MR gap (Hint: MR 1 and MR 2). Hint: • Q = Q 1= Q 2 Find P and Q. • Use Q and find Profit = TR - TC • Find MR 1 and MR 2 using TR functions for both.
Exercise: Kinked Demand Curve Model Q 1 = Q 2 280 - 40 P 1 = 100 - 10 P 2 Replacing P = P 1 = P 2 280 – 40 P = 100 – 10 P P = 6 Q = 40 TR = P x Q = 240 TC = 2(40) + 0. 025(40)2 Profit = 120 MR 1 = 7 – 0. 05 Q 1 = 7 – 0. 05(40) = 7 – 2 = 5 MR 2 = 10 – 0. 5 Q 2= 10 – 0. 2(40) = 10 – 8 = 2
Price leadership model • Assumes that in some market, there is one dominant firm in the industry that – Determine the level of demand sets the price – Other firms in the industry behave like perfectly competitive price-taking firms • Possible due to large amount of market share • Price leader maintains the price such that the level of demand remains unreduced
Exercise-I: Price Leadership model: Price determination by dominant firm Total demand function of an industry of a product be: Q = 100 – 5 P Supply function of the small firms be: Qs = 10 + P Marginal cost of all firms be: MC = 2 Q What will be the quantity and price for maximum profit for dominant firm or the leader? Hint: • Find demand for Dominant firm = Total market demand - Qs • Find TR and then MR • MR = MC. Find P and Q
Exercise: Price Leadership model: Price determination by dominant firm The demand function of dominant firm is: Q = (100 – 5 P) – (10 + P) = 90 – 6 P P = 15 – 1/6 Q TR = (15 – 1/6 Q)Q MR = 15 – 1/3 Q MR = MC 15 – 1/3 Q = 2 Q Q = 6. 43 P = 15 – 1/6 QA = 13. 93
Exercise-II: Price Leadership model: Price determination by dominant firm Total demand function of an industry of a product be: P = 100 – Q Marginal cost of leader’s firm = 0. 1 Q Marginal cost for follower’s firm = 0. 25 Q • Find the product profit maximizing P and Q for leader (P = 52; Q = 38. 46) • Find Q for followers (Q = 9 units Approx) Hint: • Find demand for Dominant firm = Total market demand – MC of followers • Find TR and then MR and MR = MC for leader • Followers Q = Total demand – Leader’s Q
Thank You
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