R&D (Time Of Discovery)

Question 1

Patent requirements (3)

Answer 1

Novel
Non-trivial
Useful

Question 2

Model for patents:

Investment x reduces unit cost c to c-x.
Assume small/minor innovation

What happens to market price?

Answer 2

Recall we said monopoly price is higher, however homogenous goods so cannot charge above, so decide to instead undercut arbitrarily.

So for simplicity keep P=C

Question 3

Assume P=a-Q.

Identify innovators gain, and DWL pg42

B) answers for M and DWL

Answer 3

See a fall in costs to c-x.

M is innovator now earning monopoly profit since costs fall.

Price remains at c, hence why DWL as optimal is now if P=c-x, but innovator does not charge this price, it keeps prices at P=C to get profit.

V) M = (a-c)x
DWL = x²/2

Question 4

So assume they earn these monopoly profit M for t periods. After they earn 0, why?

Answer 4

Patent expires, as CS takes over M and DL as now as people can enter market.

Question 5

How to model the patent lasting till T then earning 0 profits

By using Lemma, finite series
Final equation for lemma

Answer 5

1- p to the t / 1-p

P is discount factor

Question 6

Using our monopoly profits is (a-c)x and DWL x²/2

How can we find our choice of R&D level x.

B) final equation we get for x
C) using equation what does our choice of R&D levels increase with (4)

Answer 6

Maximise profit
Maxπ(x, T) =

, then FOC and rearrange to find X (optimal R&D level!

B) X = [1-p to the t/ 1-p] (a-c)
So lemma equation x (a-c)

C) as T increases (duration of patent)
As demand a increases
As cost c falls
As discount factor p increases (value future profits, thus invest more)

Question 7

So that is a firm’s choice of R&D level.

What is the optimal length (t) of patent for society?

First regulator chooses T

So what is total welfare for T years
B) welfare onwards

Answer 7

W = CS+M for T year

B) CS+M+DWL

Fuck this too hard

Question 11

Why would firm invested in R&D license its tech to rival that hasn’t invested?

Answer 11

Since the rivals quantity and profits do not change, firm 1 just extracts additional rent

Question 12

R&D subsidising - assume 2 countries

Airbus and Boeing
Game theory - look at the diagram pg 53

What is the nash equilibrium

Answer 12

There are 2

Either [producer, don’t produce] or don’t [produce, produce]. At each of these points there is no incentive to deviate for either firm

(Whereas for [produce produce] and [don’t,dont], there is incentive to deviate thus no nash equilirbium)

Question 13

What if EU gives airbus subsidy of £15

Draw new game theory now

B) what is the new nash equilibrim,

Answer 13

Payoff for Airbus is now 65 for [don’t produce, produce]

Since Airbus will always want to produce as always profitable now given the subsidy.

Question 14

Effect on social welfare

Answer 14

Unclear, Airbus has monopoly, however funded by taxes.

Question 15

So that was subsidising a new product.

Now consider subsdising a process innovation.
P=a-Q
Subsidy xi reduces cost c to c-xi
Gov cost TC = x²i/2

2 stage game. Firms take subsidy and max profits
What is firm i’s profit max problem then and steps to get final profit (in terms of subsidy Xi and Xj)

Answer 15

Max πi = (a-qi-qj-c+xi)qi
(Don’t need to include TC into firm I’s problem, since TC is a government cost, so used for society welfare not this) PTO

FOC, rearrange to find qi, by symmetry qj. Then sub qj into qi to get final qi and qj. Add together to get Q, then sub into find P=a-Q. Then can find πi.

Question 16

Then find welfare of country i; expression

b)Then differentiate to find level of subsidy for R&D
c) intuition of result
d) using equation, what does subsidy R&D level increase with (2)

Answer 16

Profit - TC
so just answer from previous FC - TC X²i/2

b) xi=xj= 4(a-c) /5

c) beneficial for at least one firm to subsidise R&D (return from export sales>costs of R&D)

d) subsidy size, increases with demand, decreases with cost c