Since ideas can sometimes be copied quite easily, many people think that we should put more effort into creating new ideas. Let€™s see if there is trade-offs to having more people creating new ideas. To keep things simple, let€™s assume that the growth rate of the economy depends on how many people search for ideas, whether in laboratories, or huddled over laptops in coffee shops, or while listening to €œStairway to Heaven€ at three in the morning. People either produces stuff or produce ideas. Here€™s how this economy works:
Yt = (1 €“ R) × AtL (GDP production function)
At+1 = (1 + R) 00D7 At (Technology production function)
There are a total of L people in the society, and a fraction (1 €“ R) of them work in factories and offices making stuff (remember, people working in offices help create output, too!), while the remaining fraction R try to come up with good ideas all day long. To keep the story simple, there are no diminishing returns.
a. What€™s the trade-off here? If 100% of the people work to make new ideas (R = 1), won€™t that create a prosperous world?
b. In this society, if people are willing to wait a long time for a reward, should they choose a large R or a small R?
c. Plot out GDP in this society for 5 years if A starts off at 100, L starts off at 100, and R is 10%.

d. Plot out GDP in this society if the society instead chose R = 20%.

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Year Y/L 2 100 110 9,000 90