產業組織與廠商策略 Review

0214

The Elasticity Rule

• Optimal Price: MR=MC
• Def of elasticity: \(e=\frac{\Delta q/q}{\Delta p/p}\)
  • \(e < 0\) by law of demand
  • inelastic demand: \(|e|<1\)
    • \(1\%\) increase in price causes \(<1\%\) decrease in demand
  • elastic demand: \(|e|>1\)
• Def of arc elasticity: \(e=\frac{(q_1-q_2)/(q_1+q_2)}{(p_1-p_2)/(p_1+p_2)}\)
• Identification problem: calculation of elasticity should be data points from the same demand curve
• MR and Elasticity: \(\%Rev\approx\%P+\%Q\)
  • \(MR=p\left(1-\frac{1}{|e|}\right)\)
• Elasticity Rule: \(\frac{p-MC}{p}=\frac{1}{|e|}\)
  • Market power=\(\frac{p-MC}{p}\)
• Market Segmentation (Selection by Indicators): different price in different markets, according to their elasticity
  • Ex. Alcoa Metal limited resales by vertically integration

Case - Glaxo's Zantac

HW

0221

Case - Monsanto's Roundup

HW

0307

Coors in the 1970s

Sequential Decision

• Case 1: Incumbent moves first
  • 
  • Potential competition is enough to eat up incumbents profit
• Case 2: Rival moves first
  • 
  • Absense of flexibility improves its outcome
  • First-mover advantage game

Simultaneous Decision

• 
• 
• Case 1:
  • 
• Case 2:
  • 
• Case 2-1: Credible threat by incumbent
  • 
  • Should not enter
• Case 3:
  • 
  • Coordination Game
• Credibility of threat is important

Case - NutraSweet

HW

0314

Entry Deterrence

• Dupont Example
  • 
  • Case 1: Low entry cost
    • EC=500 => Entrant always entry, Incumbent choose 40
    • Entry Accommodation
  • Case 2: Intermediate entry cost
    • EC=600 => Entrant won't entry when Incumbent choose 48
    • Entry Deterrence
  • Case 3: High entry cost
    • EC=700 => Entrant won't entry when Incumbent choose 44 or 48. Will choose monopoly output
    • Blockaded Entry
  • Inverse-U Shaped Relationship w/ EC: 40->48->44
    • No deterrence at Accomodation & Blockaded
• Monsanto Aspartame Example
  • Naked Exclusion: Customers signing exclusive contracts with monopoly, forstalling entry
• Other Examples
  • Cereal Industry: Product Proliferation to deter entry
  • Staples: Store Clustering to deter entry

HW

0321

Judo Economics

• Enter or not -> choose \(N, p_e\) -> choose \(p_i\) -> buyers purchase
• Parameters: \(tot, N, WTP_E, WTP_I, C_E, C_I, p_e, p_i\)
  • \(tot\) for total customers, \(WTP\) for willingness to pay
• Incumbent
  • Accommodate: \((WTP_I - C_I)(tot - N)\)
  • Fight: \((p_e - C_I)tot\)
• Entrant: Make incumbent accommodate
  • \((WTP_I - C_I)(tot - N)\ge (p_e - C_I)tot\)
• Judo entrant add NO value to the market
• What can go wrong for Judo Strategy?
  • credible commitment to stay small
  • incumbent find a way to perform selective matching i.e. price differently
  • incumbent fight today, regain market tomorrow
• Example: Kiwi International Airlines

HW

0328

Experiment: Farmville

Define

• N: # of landlords
• F: # of farmers
• M: # of meadow
• R: # of rocky
• (m, r): (# of M, # of R)

Benchmark: N=1

1. (24, 0): \(P_m=2, \pi=2\times 24=48\)
2. (24, 1): \(E[\pi]=24/17+49\times 16/17 = 47.5\)
   \[ \begin{cases} (p=\frac{1}{17}) F=24 &, P_m=1, P_r=0, \pi=24 \\ (p=\frac{16}{17}) F\ge 25 &, P_m=2, P-r=1, \pi=49 \end{cases} \]
3. We may observe that \(E[\pi] \propto 1/R\)

N=4, endownment=6M+6R

• Monopoly supply: 24 meadows i.e. (6,0) for everyone
  • requires credibility since it is not NE (as follow)
• Consider landlord \(i\) and all other landlord follows agreement: \(M_{-i}=18,R_{-i}=0\). If \(i\) choose \((6,r)\), total supply is \(24+r\)
  \[ \begin{cases} F \ge 24+r &, \pi_i=12+r \\ F < 24+r &, \pi_i=6 \\ \end{cases} \]
  Thus \(E[\pi]=6\times r/17 + (12+r)\times (17-r)/17 = \frac{1}{17}(-r^2-12r+210)\). FOC implies \(r=6\).
  • Firms have incentive to deviate

0411

Oligopoly

• Assumptions
  • No FC, MC=c, P(Q)=a-bQ, a>c
• Bertrand model: Set price simultaneously
  • 
  • NE: P=MC => No profit i.e. Bertrand paradox
  • Key assumptions for zero profit:
    • No capacity contraints, product homogeneity, static competition
• Cournot model: Set quantity simultaneously
  • Firm 1 solve
    • \(max_{q_1\ge 0}P(q_1+q_2)-cq_1\) and
    • get BR function \(BR_1(q_2)=\frac{a-c}{2b}-\frac{q_2}{2}\)
  • Similarily
    • \(BR_2(q_1)=\frac{a-c}{2b}-\frac{q_1}{2}\)
  • Then,
    • \(q_1=q_2=\frac{a-c}{3b}, P=\frac{a+2c}{3}\)
  • Observe that \(q_M < q_1+q_2 < q_C\) i.e. \(p_M > P > p_C\)
• Cournot model with more firms (symmetric Nash Equilibrium)
  • Firm \(i\) solve \(max_{q_i\ge 0}q_iP(q_i+(n-1)q^\#)-cq_i\)
  • in equlibrium,
    • \(q^\#=\frac{a-c}{(n+1)b}, p^\#=\frac{a+nc}{n+1}\)
    • \(p^\#>p_C\) since \(a>c\)
    • as \(N\to\infty\), \(p\to p_C=MC=c\)
• Bertrand or Cournot?
  * Bertand: Two firms are enough to achieve the perfect competition price.
  * Cournot: The price under oligopoly is lower than monopoly price but greater than the perfect competition price.
  • Short-run decisions vs Long-run decisions
  • Case 1: Cannot adjust Q fast - (Capacity is long-run, Price is short run)
    • decide q first => Cournot
    • i.e. adjust price to fit P(q)
    • Ex: PlayStation vs Nintendo
  • Case 2: Can adjust Q fast - (Price is long run, Capacity is short run)
    • decide p first => Bertrend
    • i.e. can adjust capacity fast to fit Q§
    • Ex: Encyclopedia Britannica vs Microsoft Encarta

Oligopoly Competition with (Exogenous) Product Differentiation

• Ex. Linear City
  • Case 1: Same location
    • No product differentiation => Bertrand
  • Case 2: Different location
    • Build the demand function by finding the critical customer i.e indifferent to buy from both store
      • \(x^*=\frac{1}{2}+\frac{1}{2t}(p_2-p_1)\)
    • BR function: max profit wrt demand function
    • Then, intersect of BR implies NE
    • ex. if store is at 0 & 1, \(p_1=p_2=c+t\), \(t\) for transportation cost
• The "Differentiation" here is convenience caused by transportation cost
  • Higher differentation => more like monopoly

(Endogenous) Product Positioning, Search Cost & Switch Cost

• Product positioning
  • Direct effect: closer => higher demand
  • Strategic effect: closer => higher competition
• search cost & switch cost creates sellers' market power

Example (past final exam question)

Two firms are engaged in Bertrand competition. There are 10000 people in the population, each of whom is willing to pay at most $10 for at most one unit of the product. Both firms have a constant marginal cost of $5.

Each firm is originally allocated half the market. Customers know what prices are being charged. It costs a customer \(k\) to switch from one firm to the other. Law or custom restricts the firm to charging whole-dollar amounts.

1. Suppose \(k=0\). What are the NE of this model?
2. Why does whole-dollar pricing result in more equilibria than continuous pricing?
3. Suppose \(k=2\). What are the NE of this model?
4. Suppose \(k=4\). What are the NE of this model?
5. What is the value of raising customers' switching costs from $2 to $4?

sol

1. BR function for firm 1 is

Similarly

Thus NE are (5,5), (6,6), (7,7)

2. Since the minimum price adjust is large, firms will be better off not to make the price minimum

3. Customers will switch if
   \[ 10 - p_2 \le 10 - p_1 - k \Rightarrow p_1 \le p_2 - 2 \]

Price difference need \(\ge 2\). The BR function for firm 1 becomes

Another solution?

When price difference equals to 2, customers will not swtich. Since both price are the same to customers. That is, price of firm2 plus switch cost equals to price of firm1.

The BR function for firm 2 becomes

The NE is (10,10)

4. Customers will switch if
   \[ 10 - p_2 < 10 - p_1 - k \Rightarrow p_1 < p_2 - 4 \]
   Price difference need \(\ge 5\). The NE is (10,10).

5. No value???

HW

0418

HW

0425

Repeated Games and Tacit Collusion

• Maximize present value of all future profit
• Act according to history => contingent plan
• Case 1: opponent always set P=MC
  • SPNE: set P=MC
• Case 2: Grim Trigger Strategy (GTS)
  • first period: \(P=p_M, \pi=\pi_M/2\)
  • Later: set \(P=C\) if opponent deviate
• Not deviating discount payoff: \(V=\frac{1}{2}\left(\frac{1}{1-\delta}\right)\pi_M\)
• Deviating: \(V'=\pi^M\) (only first period)
• Not deviating require \(V\ge V'\Rightarrow \delta\ge \frac{1}{2}\) => future is important if discount factor is large
• discount factor \(\delta=\left(\frac{1}{1+r/f}\right)h(1+g)\)
  • \(f\): frequency of firm changing price (related to firm interaction)
  • \(h\): survival prob
  • \(g\): demand growth rate
  • \(r\): risk-free interest rate
• Extensions
  1. Finite time horizon: always deviate
  2. More firms: hard for collusion
     • deviate gain \(\frac{N-1}{N}\pi_M\) becomes larger while profit for dicipline \(\frac{1}{N}\pi_M\)
  3. Asymmetric cost structures
  4. Multimarket contacts: collusions are easier to maintain when firms have different cost in different markets
• Why don't firms collude more often?
  • not large enough discount factor
  • too many firms
  • secret price cuts lower demands, however not sure if it is because of secret price cuts or demand shocks
    • Ex. Ready-Mixed Concrete in Denmark

HW

0502

Perfect (and Almost Perfect) Competitions

Perfect competitions

• Key assumptions for Perfect competitions
  • large number of small firms
  • free entry
  • product homogeneity
  • equal access to technologies
  • perfect information about prices set by all firms
  • no transaction costs and externality
• Theory vs Reality
  • Either "Entry or Exit" vs High Gross Entry and Exit, small net entry rate
    • Mainly young and small firms that entry and exit
  • Zero profit vs different profit rate for each firms

Competitve Selection

• Assumptions for Competitve Selection Theory
  • Those above +
  • Pay sunk cost to entry
  • Different firm have different degree of efficiency => different technology
  • Uncertain about its own effiency
• Result: long run P=MC(q)=min AC(q)
• Can explain reality above
• Results from Competitive Selection
  • Efficiency level is the KEY

Monopolist competition via product differentiation

• demand elasticity is not infinity, p > MC
• long run zero profit: p = min AC(q)
• 

Case: Cola Wars