Assume that firm 1 performs R&D that benefits firm 2. Firm 1\'s marginal benefit
ID: 1248733 • Letter: A
Question
Assume that firm 1 performs R&D that benefits firm 2. Firm 1's marginal benefits and marginal costs from a quantity x of R&D are given byMB1(x)= 20 - 10x; MC1(x)=5
Firm 2's benefits from firm 1's R&D are given by MB2 (x) = 2 - x
(i) What is firm 1's optimal choice of R&D if it does not take into account the external benefit to firm 2?
(ii) What is the socially optimal amount of R&D?
(iii) Compute the value of a unit subsidy s that would induce firm 1 to choose the optimal amount of R&D.
Explanation / Answer
Assume that firm 1 performs R&D that benefits firm 2. Firm 1's marginal benefits and marginal costs from a quantity x of R&D are given byMB1(x)= 20 - 10x; MC1(x)=5
Firm 2's benefits from firm 1's R&D are given by MB2 (x) = 2 - x
(i) What is firm 1's optimal choice of R&D if it does not take into account the external benefit to firm 2?
Optimal choice of R&D is where MC= MB
20 - 10x =5
10x= 15
x= 1.5 units
(ii) What is the socially optimal amount of R&D?
With this positive externality of 2-x, the marginal benifit curve will shift towards its right.
For the new curve we have to add the MB of frim 1 and externality due to firm 1, MB= 2-x
MB curve 2= 20 - 10x + 2 - x
= 22 - 11x.
Socially optimum level:
MB2= MC
22- 11x= 5
11x= 17
x= 17/11
x = 1.54
(iii) Compute the value of a unit subsidy s that would induce firm 1 to choose the optimal amount of R&D.
Difference in the the quantity 1.54 - 1.5= 0.04 worth subsidy should be given.
Marginal benifit derived from 0.04 quantity is
MB= 20 - 10(0.04)
= 20 - 0.4
= $19.6
should be given in order to produce the socially optimum output.