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Consider the two-sector edogenous growth model Y = F[K, (1− u)LE] = K0.3[(1 − u)LE]0.7 Output...

Consider the two-sector edogenous growth model

Y = F[K, (1− u)LE] = K0.3[(1 − u)LE]0.7

Output per effective worker is

y = f(k, 1 − u) = k0.3(1 − u)0.7

  1. (3 points) In this economy, with a depreciation rate of 13%, a population growth rate of 2%, and technological growth rate of g(u), what is the break-even investment (the amount of investment needed to keep capital per effective worker constant)?
  2. (7 points) Write down the equation of motion for k which shows Δk as savings minus break-even investment. Use this equation to draw a graph (nothing precise - just a sketch) showing the determination of steady-state k.
  3. (5 points) In this economy, what is the steady-state growth rate of output per worker Y/L? How do the savings rate s and the fraction of labor force in research u affect the steady-state growth rate?
  4. (7 points) Using your graph, show the impact on capital and output of an increase in u. Describe both the immediate and the steady-state effects.
  5. (3 points) Based on your analysis, is an increase in u an unambiguously good thing for the economy? Explain.
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