## (Solved) Exercise 5 In the Romer model, it is assumed that the production function for new technology (ideas) was given by: A = L A A . a) Suppose > 0.

Exercise 5

In the Romer model, it is assumed that the production function for new technology (ideas) was given by: A Ì‡ = Î´ L Î»A A Ï† .

a) Suppose Ï† > 0. What does this imply about the relationship between the current level of technology and the difficulty of discovering new ideas? Give an explanation about why this could be a reasonable assumption.

b) Suppose Ï† < 0. What does this imply about the relationship between the current level of technology and the difficulty of discovering new ideas? Give an explanation about why this could be a reasonable assumption.

c) Suppose Î» = 1. What does this imply about the productivity of labor in the research sector?

d) Suppose that Ï† âˆˆ (0, 1), Î» âˆˆ (0, 1) and that the share of labor devoted to research is constant.

Calculate the growth rate of output per capita in the Romer model.

e) According to the equation you derived in part d, what does the model imply for the relationship between population growth and growth in output per capita in the balanced growth path?

f) If you could choose the parameters of the model, could you generate long-run growth of output per capita in the balanced growth path with zero population growth? Using the appropriate equation(s) explain your reasoning.

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