Consider the model Suppose labor is supplied exogenously at . In addition, ideas are produced using the production function where is labor productivity, and is the fraction of the population that is researching ideas. Workers either produce output or ideas which implies. In addition, the number of workers producing ideas is determined by the equation .
a) Solve for the growth rate of ideas on a balanced growth path.
b) Derive the equation for output per person at any point in time on a balanced growth path as a function of the initial stock of ideas and other known parameters.
c) Suppose at time t0 there is a fall in . Draw a time path for output per person.
d) Suppose we compare the output per person in two countries, Country A and Country B. Countries A and B currently have the same output per person. Both countries have the same initial stock of ideas, and dedicate the same fraction of their population to research. However, both the population and labor productivity are higher in Country A. Assuming nothing else changes, what can you say about output per person in Country A compared to output per person in Country B in 100 years? Briefly explain.
e) Define rivalrous. Are ideeas rivalrous?
f) Explain in a few sentences how this model differs from the Solow Model in the setup and the results of the model.