1.Suppose several R&D labs are considering whether to invest in the development of a new invention, which will require each lab to make an outlay of $1,000,000. Suppose the revenue if the invention were successfully produced and patented is $10,000,000 and that this is the total benefit from the invention (ignoring any other benefits). Each additional lab’s investment in R&D increases the probability that the invention is successfully produced, but does so at a diminishing rate. The table below shows how the probability of making the invention, and hence the expected revenue (probability of success times the revenue of $10,000,000 from the invention) changes with the number of labs making the investment.

Number of labs	Probability of successfully making invention	Expected Revenue = prob*revenue from invention
0	0	0
1	.3	3,000,000
2	.5	5,000,000
3	.5667	5,667,000
4	.61	6,100,000
5	.61	6,100,000
6	.61	6,100,000

(a)    What is the efficient number of labs investing in the development of the invention, where efficiency is defined in terms of marginal revenue and marginal cost?

(b)   Suppose at the outset that each lab which invests has an equal chance of being the first lab to come up with the invention. Due to patenting, only the first lab to successfully produce the invention will get the entire revenue of $10,000,000. Looking at the labs’ incentives to invest, each lab will consider how its investment will affect the probability of successful invention (given the number of other labs which have already invested), and its probability of being the first among these labs to come up with the invention. For example, if there are 2 labs investing, the probability of successful invention is .5 but each lab has a 50% chance of being the first so each lab’s probability of being the first successful inventor (who gets the patent) is 50% (.5) = .25.  Given this patent system, how many labs will invest in the development of the invention?

(c)    Based on your answers in (a) and (b), what can you conclude about the effects of a patent system on the amount of R&D investment?

2.
Suppose the government of an open economy suddenly decides to implement protectionist policies by sharply increasing import taxes on consumer good imports.

(a)    Sketch the effects on GDP (you may ignore the revenue effects of taxes).

(b)   What is the likely effect on the open economy’s trade partners?

(c)    If the countries from which the open economy imports are also the major markets for its own exports, will it make any difference in the long run? Why or why not?

 3.
After a small Asian country suffers a currency crisis, it consults two experts.  Dr Know-it-All says that the government should cut down on its spending because not running a budget deficit is critical for growth. Prof Too Smart says that if the country switches from its current system of a pegged exchange rate to a fully flexible exchange rate, it can insure itself against future speculative attacks.  Are either or both of these experts correct? Explain their reasoning.