oligopoly_plots.Rmd

# Monopolistic Competition Model: Short Run


```{r, fig.retina=3}
MC=function(x){3*x^2-8*x+9}
AC=function(x){x^2-4*x+10+10/x}
AVC=function(x){10*x+200}
Demand=function(x){20-2.5*x}
MR=function(x){20-5*x}


mc_plot<-ggplot(data.frame(x=c(0,12)), aes(x=x))+
  stat_function(fun=MC, geom="line", color="red", size=2)+
  geom_label(x=3.5,y=MC(3.5), color = "red", label="MC(q)")+
  stat_function(fun=AC, geom="line", color="orange", size=2)+
  geom_label(x=4.5,y=AC(4.5), color = "orange", label="AC(q)")+
  stat_function(fun=Demand, geom="line", color="blue", size=2)+
  geom_label(x=4.5,y=Demand(4.5), color = "blue", label="Demand")+
  stat_function(fun=MR, geom="line", color="purple", size=2)+
  geom_label(x=3.5,y=MR(3.5), color = "purple", label="MR(q)")+
  geom_segment(aes(x=10,y=0),xend=10,yend=450,linetype=3, size=2)+
  geom_segment(aes(x=0,y=450),xend=10,yend=450, linetype=3, size=2)+
  labs(x = "Quantity (q)",
       y = "Price (p)")+
  theme_classic(base_family = "Fira Sans Condensed", base_size=18)

mc_plot+
  scale_x_continuous(breaks=NULL,
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=NULL,
                     limits=c(0,20),
                     expand=c(0,0))
```

# Monopolistic Competition Model: Short Run

```{r, fig.retina=3}
mc_plot+
  geom_segment(x=2.48, xend=2.48, y=0, yend=8, size = 1, linetype="dotted")+
  scale_x_continuous(breaks=c(0,2.48),
                     labels=c(0,expression(q*degree)),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=NULL,
                     limits=c(0,20),
                     expand=c(0,0))
```

```{r, fig.retina=3}
mc_plot+
  geom_segment(x=2.48, xend=2.48, y=0, yend=Demand(2.48), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.48, y=Demand(2.48), yend=Demand(2.48), size = 1, linetype="dotted")+
  scale_x_continuous(breaks=c(0,2.48),
                     labels=c(0,expression(q*degree)),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=c(0,Demand(2.48)),
                     labels=c(0,expression(p*degree)),
                     limits=c(0,20),
                     expand=c(0,0))
```


```{r, fig.retina=3}
mc_plot+
  geom_rect(xmin=0, xmax=2.48, ymin=AC(2.48), ymax=Demand(2.48), fill="green", alpha=0.4)+
  geom_segment(x=2.48, xend=2.48, y=0, yend=Demand(2.48), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.48, y=Demand(2.48), yend=Demand(2.48), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.48, y=AC(2.48), yend=AC(2.48), size = 1, linetype="dotted")+
  scale_x_continuous(breaks=c(0,2.48),
                     labels=c(0,expression(q*degree)),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=c(0,AC(2.48),Demand(2.48)),
                     labels=c(0,expression(AC(q*degree)),expression(p*degree)),
                     limits=c(0,20),
                     expand=c(0,0))
```
```{r, fig.retina=3}
mc_plot+
  geom_rect(xmin=0, xmax=2.48, ymin=AC(2.48), ymax=Demand(2.48), fill="green", alpha=0.4)+
  geom_segment(x=2.48, xend=2.48, y=0, yend=Demand(2.48), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.48, y=Demand(2.48), yend=Demand(2.48), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.48, y=AC(2.48), yend=AC(2.48), size = 1, linetype="dotted")+
  scale_x_continuous(breaks=c(0,2.48),
                     labels=c(0,expression(q*degree)),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=c(0,AC(2.48),Demand(2.48)),
                     labels=c(0,expression(AC(q*degree)),expression(p*degree)),
                     limits=c(0,20),
                     expand=c(0,0))
```
#long run

```{r, fig.retina=3}
Demand2=function(x){15-2*x}
MR2=function(x){15-4.5*x}


mc_plot2<-ggplot(data.frame(x=c(0,12)), aes(x=x))+
  stat_function(fun=MC, geom="line", color="red", size=2)+
  geom_label(x=3.5,y=MC(3.5), color = "red", label="MC(q)")+
  stat_function(fun=AC, geom="line", color="orange", size=2)+
  geom_label(x=4.5,y=AC(4.5), color = "orange", label="AC(q)")+
  stat_function(fun=Demand2, geom="line", color="blue", size=2)+
  geom_label(x=4.5,y=Demand2(4.5), color = "blue", label="Demand (LR)")+
  stat_function(fun=MR2, geom="line", color="purple", size=2)+
  geom_label(x=3.25,y=MR2(3.25), color = "purple", label="MR(q) (LR)")+
  geom_segment(aes(x=10,y=0),xend=10,yend=450,linetype=3, size=2)+
  geom_segment(aes(x=0,y=450),xend=10,yend=450, linetype=3, size=2)+
  labs(x = "Quantity (q)",
       y = "Price (p)")+
  theme_classic(base_family = "Fira Sans Condensed", base_size=18)

mc_plot2+
  
  # old 
  stat_function(fun=Demand, geom="line", color="blue", size=2, alpha=0.25)+
  stat_function(fun=MR, geom="line", color="purple", size=2, alpha=0.25)+

  geom_segment(x=2.125, xend=2.125, y=0, yend=Demand2(2.125), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.125, y=Demand2(2.125), yend=Demand2(2.125), size = 1, linetype="dotted")+
  scale_x_continuous(breaks=c(0,2.125),
                     labels=c(0,expression(q[LR])),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=c(0,Demand2(2.125)),
                     labels=c(0,expression(p[LR]==AC(q[LR]))),
                     limits=c(0,20),
                     expand=c(0,0))

```


# Monopolistic Competition vs. Perfect Competition

```{r, fig.retina=3}
cs_pc<-tribble(
  ~x, ~y,
  0, Demand2(0),
  0, Demand2(2.75),
  2.75, Demand2(2.75)
)

mc_plot2+
  # pc
  geom_polygon(data=cs_pc, aes(x=x,y=y), fill="blue",alpha=0.5)+
  geom_segment(x=2.75, xend=2.75, y=0, yend=Demand2(2.75), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.75, y=Demand2(2.75), yend=Demand2(2.75), size = 1, linetype="dotted")+
  scale_x_continuous(breaks=c(0,2.75),
                     labels=c(0,expression(q[c])),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=c(0,Demand2(2.75)),
                     labels=c(0,expression(p[c])),
                     limits=c(0,20),
                     expand=c(0,0))

```

```{r, fig.retina=3}
cs_mc<-tribble(
  ~x, ~y,
  0, Demand2(0),
  0, Demand2(2.125),
  2.125, Demand2(2.125)
)

dwl<-tribble(
  ~x, ~y,
  2.125, Demand2(2.125),
  2.125, MC(2.125),
  2.75, Demand2(2.75)
)

mc_plot2+
  geom_polygon(data=cs_mc, aes(x=x,y=y), fill="blue",alpha=0.5)+
  geom_polygon(data=dwl, aes(x=x,y=y), fill="black",alpha=0.5)+
  geom_segment(x=2.125, xend=2.125, y=0, yend=Demand2(2.125), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.125, y=Demand2(2.125), yend=Demand2(2.125), size = 1, linetype="dotted")+
  
  # pc
  geom_segment(x=2.75, xend=2.75, y=0, yend=Demand2(2.75), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.75, y=Demand2(2.75), yend=Demand2(2.75), size = 1, linetype="dotted")+
  
  scale_x_continuous(breaks=c(0,2.125, 2.75),
                     labels=c(0,expression(q[m]), expression(q[c])),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=c(0,Demand2(2.125), Demand2(2.75)),
                     labels=c(0,expression(p[m]), expression(p[c])),
                     limits=c(0,20),
                     expand=c(0,0))

```

```{r, fig.retina=3}
cs_mc<-tribble(
  ~x, ~y,
  0, Demand2(0),
  0, Demand2(2.125),
  2.125, Demand2(2.125)
)

dwl<-tribble(
  ~x, ~y,
  2.125, Demand2(2.125),
  2.125, MC(2.125),
  2.75, Demand2(2.75)
)

mc_plot2+
  geom_polygon(data=cs_mc, aes(x=x,y=y), fill="blue",alpha=0.5)+
  geom_polygon(data=dwl, aes(x=x,y=y), fill="black",alpha=0.5)+
  geom_segment(x=2.125, xend=2.125, y=0, yend=Demand2(2.125), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.125, y=Demand2(2.125), yend=Demand2(2.125), size = 1, linetype="dotted")+
  
  # pc
  geom_segment(x=2.75, xend=2.75, y=0, yend=Demand2(2.75), size = 1, linetype="dotted")+
  geom_segment(x=0, xend=2.75, y=Demand2(2.75), yend=Demand2(2.75), size = 1, linetype="dotted")+
  
  scale_x_continuous(breaks=c(0,2.125, 2.75),
                     labels=c(0,expression(q[m]), expression(q[c])),
                     limits=c(0,5),
                     expand=c(0,0))+
  scale_y_continuous(breaks=c(0,Demand2(2.125), Demand2(2.75)),
                     labels=c(0,expression(p[m]), expression(p[c])),
                     limits=c(0,20),
                     expand=c(0,0))

```




# Game Theory

.pull-left[
.center[
![:scale 100%](https://www.dropbox.com/s/93gtv9xei0q5fik/gametheory.jpg?raw=1)
]
]

.pull-right[

- .hi[Game theory]: a set of tools that model strategic interactions ("games") between rational players, 3 elements:
    1. **Players**
    2. **Strategies** that players can choose from
    3. **Payoffs** to each player that are *jointly-determined* from combination of all players' strategies 

]


---

# Game Theory vs. Decision Theory Models I

.pull-left[
.center[
![](https://www.dropbox.com/s/kjm2fzw4o3p0sk3/optimize.jpg?raw=1)
]
]

.pull-right[

- Traditional economic models are often called .hi[Decision theory]:

- .hi-purple[Optimization models] **ignore all other agents** and just focus on how can **you** maximize **your** objective within **your** constraints
  - Consumers max utility; firms max profit, etc.

- **Outcome**: .hi-purple[optimum]: decision where *you* have no better alternatives

]


---

# Game Theory vs. Decision Theory Models I

.pull-left[

.center[
![](https://www.dropbox.com/s/9d2bkesu20g5fj7/crowdartistic.jpg?raw=1)
]
]

.pull-right[

- Traditional economic models are often called .hi[Decision theory]:

- .hi-purple[Equilibrium models] assume that there are **so many agents** that **no agent's decision can affect the outcome**
  - Firms are price-takers or the *only* buyer or seller
  - **Ignores all other agents' decisions**!

- **Outcome**: .hi-purple[equilibrium]: where *nobody* has no better alternatives

]


---

# Game Theory vs. Decision Theory Models III

.pull-left[
.center[
![](https://www.dropbox.com/s/tymdsxbqaq2scxq/chessknights.jpg?raw=1)
]
]

.pull-right[

- .hi[Game theory models] directly confront **strategic interactions** between players
  - How each player would respond to a strategy chosen by other player(s)
  - Lead to a stable outcome where everyone has considered and chosen their best responses

- **Outcome**: .hi-purple[Nash equilibrium]: where *nobody* has a better strategy *given the strategies everyone else is playing*

]


---

# Equilibrium in Oligopoly


.pull-left[
.center[
![:scale 100%](https://www.dropbox.com/s/j7xenkgo3p71vke/equilibriumbalance.png?raw=1)
]
]

.pull-right[

- What does .hi-purple["equilibrium"] mean in an *oligopoly*?

- In competition or monopoly, a unique $(q^*,p^*)$ for whole market such that **no firms/consumers have incentives to change price**

]

---

# Equilibrium in Oligopoly

.pull-left[
.center[
![:scale 100%](https://www.dropbox.com/s/tymdsxbqaq2scxq/chessknights.jpg?raw=1)
]
]

.pull-right[

- Oligopoly: use game-theoretic .hi-purple[Nash Equilibrium]: 
  - no player wants to change their strategy **given all other player' strategies**
  - each player is playing a **best response** against other players' strategies

]

---

# As a Prisoner's Dilemma I

.pull-left[
.center[

![:scale 100%](https://www.dropbox.com/s/uj1jxo2s1dr8yeb/applevsgoogle.jpg?raw=1)
]
]

.pull-right[

- Suppose we have a **duopoly** between Apple and Google

- Each is planning to launch a new tablet, and choose to sell it at a **High Price** or a **Low Price**

]


---

# As a Prisoner's Dilemma I

.pull-left[

- Payoff matrix represents profits to each firm
  - First number in each box goes to .hi-red[Row player (Apple)]
  - Second number in each box goes to .hi-blue[Column player (Google)]
]

.pull-right[
.center[
![](https://www.dropbox.com/s/7z7okbojvajbfmq/pdapplegoogle.png?raw=1)
]
]
---

# As a Prisoner's Dilemma II

.pull-left[

- From .hi-red[Apple]'s perspective:
  - .hi-red[Low Price] is a .hi-purple[dominant strategy] for .hi-red[Apple]

]

.pull-right[
.center[
![](https://www.dropbox.com/s/223j924yyaph1sk/pdapple1.png?raw=1)
]
]

---

# As a Prisoner's Dilemma II

.pull-left[

- From Google's perspective:
  - .hi-blue[Low Price] is a .hi-purple[dominant strategy] for .hi-blue[Google]

]

.pull-right[
.center[
![](https://www.dropbox.com/s/5vzsainx3h556ke/pdgoogle1.png?raw=1)
]
]

---

# As a Prisoner's Dilemma II

.pull-left[

- .hi[Nash equilibrium]: (.hi-red[Low Price], .hi-blue[Low Price])
  - neither player has an incentive to change price, *given the other's price*

]

.pull-right[
.center[

![](https://www.dropbox.com/s/9xram8ppumhfuoq/pdapplegooglenash.png?raw=1)

]
]

---

# As a Prisoner's Dilemma III

.pull-left[

- .hi[Nash equilibrium]: (.hi-red[Low Price], .hi-blue[Low Price])
  - neither player has an incentive to change price, *given the other's price*
  
- A possible **Pareto improvement**: (.hi-red[High Price], .hi-blue[High Price])
  - Both players are better off, nobody worse off!
  - Is it a Nash Equilibrium?

]

.pull-right[
.center[

![](https://www.dropbox.com/s/y2903cwtikr31e4/pdapplegooglecartel.png?raw=1)

]
]

---

class: inverse, center, middle

# Cartels

---

# As a Prisoner's Dilemma IV

.pull-left[

- Google and Apple could .hi-purple[collude] with one another and agree to both raise prices

- .hi[Cartel]: group of sellers coordinate to raise prices to act like a collective monopoly and split the profits	

]

.pull-right[

.center[
![](https://www.dropbox.com/s/nxgqbud4hgatv2s/backroomdeal.png?raw=1)
]
]

---

# Instability of Cartels

.pull-left[

- Cartels often **unstable**:

- Incentive for each member to cheat is too strong

- Entrants (non-cartel members) can threaten lower prices

- Difficult to monitor whether firms are upholding agreement

- Cartels are illegal, must be discrete 

]

.pull-right[
.center[
![:scale 100%](https://www.dropbox.com/s/x1voms5mqjtqw7p/businesslie.png?raw=1)
]
]

---

# Attempts to Sustain Collusion I

.pull-left[
.center[
![](https://www.dropbox.com/s/z9g7dikfm4uvk4w/lysinecartel.jpg?raw=1)
]
]

.pull-right[

Archer Daniels Midland (USA), Ajinomoto (Japan), Koywa Hakko Kogyo (Japan), Sewon American Inc (South Korea) held secret meetings to fix the price of lysine, a food additive to animal feed in the 1990s.


]

---

# Attempts to Sustain Collusion I 

.pull-left[
.center[
![:scale 70%](https://www.dropbox.com/s/9j0m2shzpd8g261/theinformant.jpg?raw=1)
]
]

.pull-right[

Archer Daniels Midland (USA), Ajinomoto (Japan), Koywa Hakko Kogyo (Japan), Sewon American Inc (South Korea) held secret meetings to fix the price of lysine, a food additive to animal feed in the 1990s.

An internal FBI informant brought the cartel down.

]

---


# Attempts to Sustain Collusion II

.pull-left[
.center[
![](https://www.dropbox.com/s/rjki2si8ylvt2ov/turbine.jpg?raw=1)
]
]

.pull-right[

- 1950s market for turbines (for electric utility companies)

- A triopoly by market share:
  - GE: 60%
  - Westinghouse: 30%
  - Allied-Chalmers: 10%

- Maintained this equilibrium with clever coordination
]

---

# Attempts to Sustain Collusion II

.pull-left[
.center[
![](https://www.dropbox.com/s/rjki2si8ylvt2ov/turbine.jpg?raw=1)
]
]

.pull-right[

- Utility companies solicit bids to build turbines:

- If bid comes on day 1-17 on *lunar* calendar
  - Westinghouse & A-C bid prohibitively high
  - Ensures GE won
]

---

# Attempts to Sustain Collusion II

.pull-left[
.center[
![](https://www.dropbox.com/s/rjki2si8ylvt2ov/turbine.jpg?raw=1)
]
]

.pull-right[

- Utility companies solicit bids to build turbines:

- If bid comes on day 18-25 on *lunar* calendar
  - GE & A-C bid prohibitively high
  - Ensures Westinghouse won
]

---

# Attempts to Sustain Collusion II

.pull-left[
.center[
![](https://www.dropbox.com/s/rjki2si8ylvt2ov/turbine.jpg?raw=1)
]
]

.pull-right[

- Utility companies solicit bids to build turbines:

- If bid comes on day 26-28 on *lunar* calendar
  - GE & Westinghouse bid prohibitively high
  - Ensures Allied-Chalmers won
]

---

# Attempts to Sustain Collusion II

.pull-left[
.center[
![](https://www.dropbox.com/s/rjki2si8ylvt2ov/turbine.jpg?raw=1)
]
]

.pull-right[

- Utility companies released their bids randomly, not according to lunar calendar
  - Ensures the 60%-30%-10% distribution

- Cheating by one of the 3 firms easily monitored by other 2

- Nobody thought about the lunar calendar, until antitrust authorities caught on
]

---

# Attempts to Sustain Collusion III

.pull-left[
.center[
![:scale 80%](https://www.dropbox.com/s/fxds9egwshfdczg/signal.png?raw=1)
]
]

.pull-right[

- FCC Spectrum License auctions 1996-1997

- Firm seeking a license in particular location (and willing to fight for it) signals to other firms via ending its bid in the **telephone area code** digits
  - e.g. $50,100,**202** for Washington DC (area code 202)

- Other firms let it win (in exchange for tacit agreement to do the same)
]

---

# Government-Sanctioned Cartels I

.pull-left[

- Like monopolies, some cartels exist because they are *supported* by governments or regulators, possibly by rent-seeking

- National Recovery Administration (1933-1935)
  - cartelized most industries to artificially raise prices of goods
  - found unconstitutional in *Schechter Poultry Corp. v. United States* (1935)

]

.pull-right[
.center[
![:scale 80%](https://www.dropbox.com/s/9fvp8zl5iswxqa3/nra.png?raw=1)
]
]

---

# Government-Sanctioned Cartels II

.center[
![:scale 80%](https://www.dropbox.com/s/ild2a28u99mui7b/robberbarons.png?raw=1)
]

---

# Government-Sanctioned Cartels II

.left-column[
.center[
![](https://www.dropbox.com/s/kx6bt3w2oc4liiv/icc.png?raw=1)

]
]

.right-column[

 "[B]ecause of their inability to maintain their cartels [prior to the ICC], railroads were big supporters of the [Interstate Commerce Act] because the newly-formed ICC could coordinate cartel prices...Using the new law as authority, the railroads revamped their freight classification, raised rates, eliminated passes and fare reductions, and revised less than carload rates on all types of goods, including groceries." 

.source[Kolko, Gabriel, 1963, *The Triumph of Conservatism: A Reinterpretation of American History, 1900-1916*]
]

---

# Government-Sanctioned Cartels III

.pull-left[
.center[
![:scale 75%](https://www.dropbox.com/s/q42p83xk669261j/raisinoutlaw.png?raw=1)

Source: [NPR Planet Money](https://www.npr.org/sections/money/2015/06/24/417187957/episode-478-the-raisin-outlaw)
]
]

.pull-right[

> "Marvin Horne was known as the raisin outlaw. His crime: Selling 100% of his raisin crop, against the wishes of the Raisin Administrative Committee, a group of farmers that regulates the national raisin supply.
> He took the case all the way to the Supreme Court, which issued its final ruling this week."

]

---

# Government-Sanctioned Cartels IV

.pull-left[
.center[
![:scale 100%](https://www.dropbox.com/s/1ljfb3cupxpnt4e/opeccountries.png?raw=1)
]
]

.pull-right[
.center[
![:scale 100%](https://www.dropbox.com/s/nx515e7whtet9i6/opecflag.png?raw=1)
]
]

---

# Cartels: In Fiction I

.center[
<iframe width="560" height="315" src="https://www.youtube.com/embed/hGo5bxWy21g" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
]

---

# Cartels: In Fiction II

.center[
<iframe width="560" height="315" src="https://www.youtube.com/embed/aT7TxMaZ4eM" frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

]

---

# Comparing Industries

| Industry | Firms | Entry | Price (LR Eq.) | Output | Profits (LR) | Cons. Surplus | DWL |
|----------|-------|-------|--------|--------|--------------|---------------|-----|
| **Perfect competition** | Very many | Free | Lowest $(MC)$ | Highest | 0 | Highest | None |
| **Monopolistic competition** | Many | Free | Higher $(p>MC)$ | Lower | 0 | Lower | Some |
| **Oligopoly** (non-cooperative) | Few | Barriers? | Higher | Lower | Some | Lower | Some |
| **Monopoly**<sup>.red[1]</sup> (or cartel) | 1 | Barriers | Highest | Lowest | Highest | Lowest | Largest |

.footnote[<sup>.red[1]</sup> *Without* price-discrimination. Price-discrimination will increase output, increase profits, decrease consumer surplus, decrease deadweight loss]