Assume that output per unit of labor is related to the

Question

Assume that output per unit of labor is related to the capital-labor ratio by y_t = r log(k_t); and that saving is a fixed proportion, s, of output.

a. What is the capital accumulation condition?

b. Derive the equation characterizing the steady-state capital-labor ratio.

c. For the parameter values k0 = 0:5, s = 0:1, d = 0:05, n = 0, and r = 2, plot the capital-labor ratio and the consumption-labor ratio as functions of time.

d. What is the effect of an increase in r on the capital-labor ratio?

e. Repeat part c, starting the economy above the steady-state capital-labor ratio. Explain the observed growth path.