# 1 13.4 Product Differentiation When firms produce similar but differentiated products, they can be differentiated in two ways: Vertical Differentiation.

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1 13.4 Product Differentiation When firms produce similar but differentiated products, they can be differentiated in two ways: Vertical Differentiation – consumers consider one product vastly superior to another ex) Processed Cheddar and Blue Cheese ex) Flip Phone and Smart Phone Horizontal Differentiation – consumers consider one product a POOR substitute for the other, and may pay more for the “better” product ex) Swiss Cheese and Cheddar Cheese ex) Iphone and Samsung Galaxy

2 13.4 Product Differentiation Horizontal Differentiation ≈ Brand Loyalty Firms spend money on advertising and “exclusive deals” to maintain horizontal differentiation A product with WEAK horizontal differentiation will be MORE sensitive to its own and rivals’ price changes. (Small price change =>Large demand change) A product with STRONG horizontal differentiation will be LESS sensitive to its own and rivals’ price changes. (Small price change =>Small demand change)

3 13.4 Product Differentiation Shift in demand is due to a change in rivals’ price.

4 Bertrand Competition – Horizontally Differentiated Products Assumptions: Firms set price* Differentiated product Simultaneous Non-cooperative *Differentiation means that lowering price below your rivals' will not result in capturing the entire market, nor will raising price mean losing the entire market so that residual demand decreases smoothly

5 Chapter Thirteen Q 1 = 100 - 2P 1 + P 2 "Coke's demand" Q 2 = 100 - 2P 2 + P 1 "Pepsi's demand" MC 1 = MC 2 = 5 What is Coke’s residual demand when Pepsi’s price is \$10? \$0? Q 1 (10) = 100 - 2P 1 + 10 = 110 - 2P 1 Q 1 (0) = 100 - 2P 1 + 0 = 100 - 2P 1 Q 1 = 100 - 2P 1 + P 2 "Coke's demand" Q 2 = 100 - 2P 2 + P 1 "Pepsi's demand" MC 1 = MC 2 = 5 What is Coke’s residual demand when Pepsi’s price is \$10? \$0? Q 1 (10) = 100 - 2P 1 + 10 = 110 - 2P 1 Q 1 (0) = 100 - 2P 1 + 0 = 100 - 2P 1 Bertrand Competition – Differentiated

6 0 110 100 D0D0 D 10 Chapter Thirteen Residual Demand Pepsi’s price = \$0 for D 0 and \$10 for D 10 Coke’s Price Coke’s Quantity

7 MR 0 D0D0 0 MR 10 110 100 D 10 Chapter Thirteen Marginal Revenue (from Residual Demand) Pepsi’s price = \$0 for D 0 and \$10 for D 10 Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC Coke’s Price 5

8 5 27.5 MR 0 D0D0 0 D 10 MR 10 30 45 50 110 100 Chapter Thirteen Optimal Price and Quantity When MC=MR, we calculate price and quantity Coke’s Price Coke’s Quantity Example: MR=MC MR R (10) = 55 - Q 1 (10) = 5 Q 1 (10) = 50 P 1 (10) = 30 Therefore, firm 1's best response to a price of \$10 by firm 2 is a price of \$30

9 Reaction Functions Q 1 = 100 - 2P 1 + P 2 "Coke's demand" Q 2 = 100 - 2P 2 + P 1 "Pepsi's demand" MC 1 = MC 2 = 5 Solve for firm 1's reaction function for any arbitrary price by firm 2 P 1 = 50 - Q 1 /2 + P 2 /2 MR = 50 - Q 1 + P 2 /2 MR = MC => 5 = 50 - Q 1 + P 2 /2 Q 1 = 45 + P 2 /2 (continued)

10 Reaction Functions Q 1 = 100 - 2P 1 + P 2 "Coke's demand" Q 2 = 100 - 2P 2 + P 1 "Pepsi's demand" MC 1 = MC 2 = 5 Q 1 = 45 + P 2 /2 Continue Solving for the reaction function Q 1 = Q 1 100 - 2P 1 + P 2 = 45 + P 2 /2 P 1 = 27.5 + P 2 /4 Likewise, P 2 = 27.5 + P 1 /4

11 P 1 = 27.5 + P 2 /4, P 2 = 27.5 + P 1 /4 Q 1 = 100 - 2P 1 + P 2 "Coke's demand" Q 2 = 100 - 2P 2 + P 1 "Pepsi's demand" Solving for price and quantity: P 1 = 27.5 + P 2 /4 P 1 = 27.5 + (27.5 + P 1 /4 )/4 4P 1 = 110 + 27.5 + P 1 /4 3.75P 1 =137.5 P 1 * = 110/3 = P 2 * (Due to symmetry) Q 1 = 100 - 2P 1 + P 2 Q 1 = 100 - 110/3 Q 1 * = 190/3 = Q 2 * (by symmetry) Equilibrium

12 P 1 * = 110/3 = P 2 * Q 1 * = 190/3 = Q 2 * MC 1 = MC 2 = 5 Calculating Profits.  1 * = TR-TC  1 * = (P 1 * - MC 1 ) Q 1 *  1 * = (110/3 - 5) 190/3  1 * = 2005.55 =  2 * (By symmetry) Equilibrium Both Coke and Pepsi make profits of 2005.55 when they produce 63.3 each at a price of \$36.67 each.

13 P 2 = 110/3 Bertrand Equilibrium 27.5 Chapter Thirteen Pepsi’s Price (P 2 ) Coke’s Price (P 1 ) P 2 = 27.5 + P 1 /4 (Pepsi’s R.F.) P 1 = 27.5 + P 2 /4 (Coke’s R.F.) Equilibrium and Reaction Functions P 1 = 110/3 27.5

14 Equilibrium Notes  Equilibrium occurs when all firms simultaneously choose their best response to each others' actions.  Graphically, this amounts to the point where the best response functions cross.  Profits are positive in equilibrium since both prices are above marginal cost!  Even if we have no capacity constraints, and constant marginal cost, a firm cannot capture all demand by cutting price.

15 Chapter Thirteen Horizontal Differentiation Solving Steps 1)Use Residual Demand (given) 2)Calculate (residual) MR 3)MR=MC and demand to find reaction functions (in terms of Prices) 4)Use reaction functions to solve for P’s 5)Use P’s to solve for Q`s 6)Solve for  `s 7)Summarize

16 13.5 Monopolistic Competition Assumptions: Firms set price Differentiated products Many buyers and sellers Free entry and exit Products are ASSUMED to be imperfect substitutes for each other. Due to differentiated products, each firm has its own residual demand curve and optimizes like a monopoly:

17 Average Cost Quantity Price Short-Run Profit q* P* MR Chapter Thirteen 13.5 Short Run Monopolistic Competition D Marginal Cost

18 Monopolistic Competition Example P = 100 - Q TC = 10+Q 2 Calculate Equilibrium price and Quantity TR = PQ = 100Q – Q 2 MR = ∂TR/ ∂Q = 100 - 2Q MC = ∂TC/ ∂Q =2Q MR = MC  100 - 2Q = 2Q Q* = 25 P = 100 – Q P = 100 – 25 P* = 75

19 Monopolistic Competition Example P = 100 - Q Q* = 25 TC = 10+Q 2 P* = 75 Calculate Profits AC = TC/Q = 10/Q+Q  * = TR – TC = (P-AC)Q* = (32.5-10)45 = 1,012.5  * = (75- [10/25+25])25  * = \$1240 This firm will charge a price of \$75 and sell 25 units for profits of \$1240

20 Average Cost Quantity Price Short-Run Profit 25 75 MR Chapter Thirteen 13.5 Short Run Monopolistic Competition Example D Marginal Cost 25.4

21 Chapter Thirteen Monopolistic Competition, Short-Run Solving Steps 1)Use Residual Demand (given) 2)Calculate (residual) MR 3)MR=MC to solve for P 4)No Step (Take a bread, eat a sandwich) 5)Use P to solve for Q 6)Solve for  `s 7)Summarize

22 Long-Run Monopolistic Competition  In the short run, profit is available  There is free entry and exit THEREFORE  Firms will enter, decreasing individual residual demand until: P=AC (profits=0) Note: P≠MC since MC ≠ AC in these examples

23 Average Cost Quantity Price Marginal Cost q* P*=AC MR Chapter Thirteen Monopolistic Competition Long Run Equilibrium D new D old

24 Chapter 13 Conclusions 1)Market structure is determined by: a)Number of Firms b)Product Differentiation 2)Market structure can be measured using the 4-firm concentration ratio (4CR) or the Herfindahl-Hirschman Index (HHI) 3)In a Cournot oligopoly firms choose quantities and make profits

25 Chapter 13 Conclusions 4) In a Bertrand Oligopoly firms choose prices and make no profits (Perfect Competition outcome) 5) In a Stackleberg Oligopoly one firm acts first, for higher output and profits 6) A Dominant Firm works as a monopoly once the fringe has been removed from the demand

26 Chapter 13 Conclusions 7) A Dominant Firm has incentives to keep the competitive fringe small 8) Oligopolies with differentiated products operate with their demand curves SLIGHTLY affected by rivals 9) Monopolistic Competition works like a monopoly, but free entry eliminates profits. 10) Economics is awesome

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