Professor: Zhen Lei (Sabbatical at PKU)

## Silicon Valley

- Culture (informal, tolerant of failures)
- People
- University (especially Stanford)
- VC (Sand Hill)
## Innovation Ecosystem (Rainforest)

- Universities
Story: USPTO(Patent & Trademark Office) Most of patens owned by Steve Jobs were Design Patent rather than Innovation Patent.

- Knowledge Goods
- Knowledge Goods vs Normal Goods
- Non-Rivalry: Knowledge can be shared
- Non-Excludable: Cannot prevent from people using knowledge Goods

- Public Goods
- Defense
- Public Radio
The cost of marginal consumption of drug is close to zero but the price is high.

- Knowledge Goods vs Normal Goods
*Ex-post Social Welfare Maximization*vs*Ex-ante Incentives*- Patent:
- Force the knowledge to be excludable for a limit period of time
- Protect knowledge, give incentives to the producers, …
After 1st generation of iPhone, other companies

**invent around**

- Patent:

## Microeconomics Fundamentals

### Demand

Competitive Market: price-taker, take the market price as given

- Consumer:
- Benefit/Utility Function:
`B(Q)`

,`B'(Q)>0`

,`B'(Q)<0`

`B(Q)`

**concave function**(rather than convex)- Consumer’s Problem:
**Net Benefit**`Max B(Q)-PQ`

- Take derivative
- F.O.C
`B'(Q)-P=0`

=>`P=B'(Q*)`

- This is how we derive the market demand.
- Intuition: if
`B'(Q*)>P`

consumer would buy more

- S.O.C
`B''(Q)<0`

- Intuition: Demand curve is decreasing curve. When the price goes up, the consumption goes down.

- F.O.C

- Benefit/Utility Function:

### Supply

Also competitive market

- Company/Producer:
- Cost Function:
`C(Q)`

,`C'(Q)>0`

,`C''(Q)>0`

(*increasing MC*) `C(Q)`

**convex function**- Producer’s Problem:
**Revenue-Cost**`Max PQ-C(Q)`

- Take derivative
- F.O.C
`P-C'(Q)=0`

=>`P=C'(Q)`

- Supply Curve(Given a price we can get how much producer want to produce)
- Intuition: if
`P>C'(Q)`

producer would produce more, if`P<C'(Q)`

producer would cut back the production.

- S.O.C
`-C''(Q)<0`

=>`C''(Q)>0`

- Intuition: Supply curve is increasing curve.

- F.O.C

- Cost Function:

### Equilibrium

- Invisible hand
- The social welfare reaches the maximum at the equilibrium.
- Dead Weight Lost: The sum the differences between Q and Q-star that you should’ve had.

### Monopoly

- Cost Function: $C(Q)$, $C’(Q)>0$, $C’’(Q)>0$
- Not price-taker but
*price-setter* - Faced with
**demand curve**$P(Q)$: downwards sloping - Monopoly’s Problem: still profit $Max P(Q)Q-C(Q)$ where $R(Q)=P(Q)Q$
- $P$ is a function of $Q$
- $F.O.C: P’(Q)P + P(Q) - C’(Q) = 0$
- Marginal Revenue: $MR(Q) = P’(Q)P + P(Q) < P(Q)$
- $P’(Q)P + P(Q) => P’(Q)P + P(Q)*1$
- $P(Q)*1$ revenue from the additional unit
- $P’(Q)P <0$ reduction of revenue from previous units

- $P’(Q)P + P(Q) => P’(Q)P + P(Q)*1$
- Marginal Cost: $MR(Q) = C’(Q)$
- $MR(Q)=MC(Q)$

- Marginal Revenue: $MR(Q) = P’(Q)P + P(Q) < P(Q)$

- Demand: linear demand curve $P=a-bQ$
- $R(Q) = (a-bQ) * Q = aQ - bQ^{2}$
- $MR = a - 2bQ$

- DWL: Consumers’ Marginal Benefit > Producers’ Marginal Cost
- Rectangle below: Total Revenue
- Producer Surplus / Profit: Part of Total Revenue above MC

## Discounting

Time value of money: The money of today is worth more than that of tomorrow.

- Discounting factor $\dfrac {1}{1+r} < 1$
- Present value(PV)
- The present value of money x at t=1: $\dfrac {1}{1+r} < 1$
- The present value of money x at t=2: $\dfrac {1}{(1+r)^2} < 1$

- Effective Patent Life $T = 1/(1+r) + 1/(1+r)^2 + … + 1/(1+r)^{20} < 20$
- Patent Protection (forever)
- Profit: $x[\dfrac {1}{1+r} + \dfrac {1}{(1+r)^2} + … ] = x[\dfrac {1}{1+r}]$

- Social value of this invention does not stop at t=20. When the patent expires, the DWL would be gone.

## Cobb-Douglas Production Function

- $y=Ak^{\alpha}n^{1-\alpha}$
- The growth rate $\dfrac {dy}{y}=\dfrac {dA}{A} + \alpha \dfrac {dk}{k} + (1-\alpha) \dfrac {dn}{n}$
- Growth in A accounted for more than half of growth(k:$\dfrac {1}{8}$ to $\dfrac {1}{4}$)
- TFP(Total Factor Productivity)

## Causal Links from Research to Growth: Agricultural

- Investment in R&D
- Agricultural Productivity
- Nutrition
- Physiological Capital
- People’s capacity for work & Less disease & Infant mortality & Life expectancy …

## Knowledge is public good

- Non-rivalry
- Non-excludable

Rivalry | Non-Rivalry | |
---|---|---|

Excludable |
Teachers, Cable TVs, Patents | |

Non-Excludable |
Public Park(in holidays) | Defence, Knowledge, Public Radio/TV |

## Intellectual Property Protection As Incentives

Once the invention was made, marginal cost becomes zero.

The social optimal point: $MC = MR = 0$

Consumer surplus is the whole triangle and $PS = 0$

No company has incentives to invent in the first place.

Once the inventor has patent, the owner of the patent becomes monopoly.

Patent is one of intellectual property protections.

Any other method? Set some kind of prize?

Government does not know much information of the value/cost of an invention so they want to let market figure it out.

### PV of an invention

Then the value of an invention is $\dfrac {v}{r} - dvT$

Hint: $(mv+\pi v)[\dfrac {1}{1+r} + \dfrac {1}{(1+r)^2} + …+ \dfrac {1}{(1+r)^{20}}] = (mv+\pi v)T = (v-dv)T$

Patent: $\dfrac {v}{r} - dvT$

Prize: $\dfrac {v}{r} - Prize$

### Invention(V,C)

Suppose the government knows $C$, then $prize=C$

Suppose the government doesn’t know $C$ but $V$, then $prize=\pi vT$

There are two ideas $(v_{1}, c_{1})$ and $(v_{2}, c_{2})$

- Suppose the government can observe $v_{i}$ and $c_{i}$
- Ex-ante: $s_{1}=\dfrac {v_{1}}{r}-c_{1} > s_{2}= \dfrac {v_{2}}{r}-c_{2}$

- Suppose the government can observe $v_{i}$ but not $c_{i}$
- Second-Price Auction (
*Vickery Auction*)- Ask the inventors to report the surplus $s_{1}$ and $s_{2}$
- Choose the invention with larger surplus and give the prize $\dfrac {v_{1}}{r}-s_{2}$ (suppose $s_{1} > s_{2}$)
- If both tell the truth, for the first inventor $\dfrac {v_{1}}{r}-s_{2} - c_{1} = (\dfrac {v_{1}}{r} - c_{1} )-s_{2} = s_{1} -s_{2} > 0$
- Both telling the truth is the
**Nash Equilibrium**in this game.

- Second-Price Auction (

## Innovation

- Uncertainty
- Need to move quickly
- Resistance to change
- Entrepreneurs v.s social inertia

### Types

- New products
- Sources of supply (shale gas/oil)
- Exploitation of new markets(Viagra)
- New ways to organize businesses(Corporation v.s Partnership)
- Corporation: separate the management and ownership; limited liability; principle-agent problem(disadvantage)
- Partnership: Most accounting firms, investment banks

### Classical of innovation

- Incremental
- Radical
- Revolutionary clusters of innovations

## Incentive mechanisms

- Intellectual property rights
- patent, copyright, trademarks, trade secrecy

- Prizes and Rewards
- Patronage
- Grants

Q1: Patent v.s. Prize? Patronage v.s. Grant?

Q2: Incentives for a university professor?

## Institutions of Innovation

- Government
- Education
- In house: National labs
- Sponsorship: NSF/NIH grants, SBIR grants

- Firms
- Self-funded
- Venture Capital funded
- Government-funded

- Foundations
- Ford, Rockefeller, Gates

- Universities

# Institutional history of innovation

- Government
- Firm
- The rich

# Economics of process innovation

Process innovation: cost-reducing $c \rightarrow c’$

single stage innovation

Non-Drastic vs Drastic (Competitive Market)

- Non-Drastic Innovation: monopoly price is higher than $c$
- So set the price $p = c - \epsilon$
- $\pi ^{Before}=0$, $\Delta\pi = S_{triangle} = (c - \epsilon - c’)Q> 0$

- Drastic Innovation: monopoly price $c^{m}$ is still lower than $c$
- $Q^{m}$ is determined by $c’$
- $\pi ^{Before}=0$, $\Delta\pi = S_{triangle} = (p^{m} - c’)Q> 0$ d33

- Non-Drastic Innovation: monopoly price is higher than $c$

- Non-Drastic vs Drastic (Monopoly)
- Non-Drastic Innovation:
- $\Delta\pi > 0$

- Drastic Innovation:
- $\Delta\pi > 0$

- Non-Drastic Innovation:

## Nordhans Model (1969)

Patent length as a policy lever

- Tradeoff: incentive(ex-ante) vs deadweight loss(ex-post)

Model

- Competitive market
- Single innovation
- No uncertainty
- Non-drastic process innovations
- Demand: $P=a-bQ$
- Resources
- $R$: put in R&D
- $s$: cost per unit
- Cost for R&D: $Rs$

$$c-c’=R^{\alpha}, 0<\alpha<1$$

$0<\alpha<1$ means diminishing return in production

$$\dfrac{\Delta c}{dR}>0$$

$$\dfrac{\Delta^2 c}{dR^2}=\alpha(\alpha-1)R^{\alpha-2}<0$$

$$Q = \dfrac{a-c}{b}$$

$$\pi = Q \Delta c = \dfrac{a-c}{b} R^{\alpha}$$

Net profit: $$\pi T - Rs$$

Difference/Increase of Social welfare: $$\dfrac{\pi + DWL}{r}$$

Gain of Social welfare:

$$[\dfrac{\pi}{1+r} + \dots + \dfrac{\pi}{(1+r)^t}] + \dfrac{\pi+DWL}{(1+r)^{t+1}} +\dfrac{\pi+DWL}{(1+r)^{t+2}}+ \dots$$

$$=[\dfrac{\pi+DWL}{1+r} + \dots + \dfrac{\pi+DWL}{(1+r)^t} - \dfrac{DWL}{1+r} - \dots - \dfrac{DWL}{(1+r)^t}] + \dfrac{\pi+DWL}{(1+r)^{t+1}} + \dfrac{\pi+DWL}{(1+r)^{t+2}}+ \dots$$

$$=[\dfrac{\pi+DWL}{1+r} + \dots + \dfrac{\pi+DWL}{(1+r)^t} + \dfrac{\pi+DWL}{(1+r)^{t+1}} + \dfrac{\pi+DWL}{(1+r)^{t+2}}+ \dots ] - [\dfrac{DWL}{1+r} + \dots +\dfrac{DWL}{(1+r)^t}] $$

$$=\dfrac{\pi + DWL}{r}-DWL*T$$

$$\pi T + \dfrac{\pi + DWL}{r} - \pi T - DWL*T = \dfrac{\pi + DWL}{r}-DWL*T$$

Deadweight Loss: $$DWL=\dfrac{\Delta c}{2b} \Delta c = \dfrac{R^{2 \alpha}}{2b}$$

Government set $T$, then innovators decide $R$ given $T$.

Suppose $T$ is given, innovators would maximize $\pi T - Rs$

$$\max\limits_{R} Q_0R^{\alpha}T-Rs$$

F.O.C: $$ R^*=(\dfrac{\alpha Q_0 T}{s})^{\frac{1}{1-\alpha}}$$

$$\dfrac{\partial R^{*}}{\partial T} > 0$$

$$\dfrac{\partial R^{*}}{\partial s} < 0$$

For government:

$$\max\limits_{T} (\dfrac{\pi + DWL}{r}-DWL*T)-Rs$$

$$s.t. R=(\dfrac{\alpha Q_0 T}{s})^{\frac{1}{1-\alpha}}$$

## Patent Race

- Idea: Known by >1 firms
- Open Resource Problem

### Fishery Problem

- Lake (property)
- Production function $$F(L)$$ $$F’(L)>0, F’’(L)<0$$
- Price $P$
- Cost $c$

$$\max\limits_{L} F(L)P-cL$$

F.O.C: $$F’(L^{*})P=c$$

Suppose Open Access

$$P\dfrac{F(L^{**})}{L^{**}}=c$$

$$L^{*} < L^{**}$$

### Patent Race

- Multiple Innovators
- Compete to get a patent
- Each innovator take single independet approach
- Each innovator invests $c$
- Value of the innovation is $v$

#### For social planner

- no patent needed
- decides $n^*$ firms to invest in R&D

$$\max\limits_{n} (1-\rho ^n)\dfrac{v}{r}-cn$$

$$P’(n^*)\dfrac{v}{r}=c$$

$P(n)$ is success rate

#### Patent Race

$$\dfrac{1}{n^{**}}P(n^{**}) \cdot \pi v T = c$$

## Cumulative Innovation

### Three types of cumulative innovation

- Basic research into application
- Laser
- Theroy of Laser by Einstein
- 1954 Maser by Tommas(patent)
- 1960 Laser by Tommas at Bell’s Lab(patent)
- Gould improved Tommas’ Laser(patent)

- Laser
- Tool + Tool -> ApplicationL: GMO(embodied) Drag(Dis-embodied)
- Quality ladder

#### Solution

**Type1: Basic research into application**- Innovator 1 at stage 1 decides whether to invest to make the first innovation. Cost is $c_1$
- Innovator 2’s cost is $c_2$, social value is $y$
- If $\pi yT-c_1-c_2<0$, government would like to make this innovation happen
- The timing of license does not matter

**Type2: Tool + Tool -> Application**Case1: Two tools are owned by two owners

Patent 1: $p_1$ given $p_2$

$$\max\limits_{p_1} (\frac{1}{2}-p_1-p_2)p_1$$

$BRF_1$ (best response function for $p_1$)

$$p_1=\frac{1}{4}-\frac{p_2}{2}$$

Patent 2: $p_2$ given $p_1$

$$\max\limits_{p_2} (\frac{1}{2}-p_2-p_1)p_2$$

$BRF_2$

$$p_2=\frac{1}{4}-\frac{p_1}{2}$$

$$p_1=p_2=\frac{1}{6}$$

$$\pi_1=\pi_2=\frac{1}{36}$$

Case2: Both tools are owned by one patentee

$$\max\limits_{p_1,p_2} p_1(\frac{1}{2}-p_1-p_2) + p_2(\frac{1}{2}-p_2-p_1)$$$$p_1=p_2=\frac{1}{8}$$

$$\pi_1=\pi_2=\frac{1}{32}$$

Patent thicket -> Solution: Patent Pool

- Transaction cost hold-up
- Efficiency

**Type3: Quality ladder**A sequence of product with impoving quality

- Quality improvement = $\Delta$ ($q, q+\Delta, q+2\Delta …$)
- MC of production = 0
Consumers are willing to pay a higher price of a higher quality $\Delta p=\Delta q$

Patentability vs Patent Scale

- Patentability = $\Delta$
Scale = at most $\Delta$

Suppose Patentability = $\Delta$, Scale = 2$\Delta$

### Licensing of Technology

Market for technology

- USA
- About 17.6% of patents are licensed
- 1/8 of the respondents(firms)
- Licensing because of litigation

#### Types of licensing

- Exclusive licensing v.s Non-exclusive licensing
- Exclusive by region / application / uses

- Payment (licensee v.s licensor)
- Upfront (risk is on licensee)
- Lump-sum payment

- Running royalty (risk is on licensor)
~~Profit~~- Units
- Revenue

- Upfront (risk is on licensee)
- Details about licensing contracts
- Grant-back of license on licensee’s future inventions
- Restricitons on sub-licensing

#### Advantages & Disadvantages

Advantages

- Enable specialization of research & firms
A patent on a product

Example

- One factory (monopoly)
- Two factories
- MC becomes smaller
- price becomes lower
- CS1 < CS2
- PS1 < PS2

- Demand $P(Q)=A-BQ$
- For one factory:

$$TC(Q)=F+KQ+CQ^2$$ $$MC(Q)=K+2CQ$$

$$R(Q) = P(Q)Q = AQ-BQ^2$$

$$MR(Q)=A-2BQ$$

$$Q^m = \frac{A-K}{2B+2C}$$ For two factories:

$$TC(Q)=2\times [F+K \frac{Q}{2}+C(\frac{Q}{2})^2]\=2F+KQ+C\frac{Q^2}{2}$$

$$MC(Q)=K+CQ=A-2BQ$$

$$Q^{m’} =\frac{A-K}{2B+C}>Q^m$$Situation: two factories

$$Q^m = \frac{A-K}{2B+C}$$

$$\frac{Q^m}{2}$$For the licensee:

$$P = A - B(Q+\frac{Q^m}{2})$$

$$MR = A-B \frac{Q^m}{2}-2BQ$$

$$MC=K+2CQ+\delta$$

$$A-B\frac{Q^m}{2}-2BQ=K+2CQ+\delta$$

```
$$\max\limits_{Q} \ [A-B(Q+\frac{Q^m}{2})]Q - (F+KQ+CQ^2+\delta Q)$$
```