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Assume that output per unit of labor is related to the capital–labor ratio by yt = r log(kt); 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.