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Consider a numerical example using the Solow growth model: The production technology is Y=F(K,N)=K0.5N0.5 and people...

Consider a numerical example using the Solow growth model: The production technology is Y=F(K,N)=K0.5N0.5 and people consume after saving a proportion of income, C=(1-s)Y. The capital per worker, k=K/N, evolves by (1+n)k’=szf(k)+(1-d)k.

(a) Describe the steady state k* as a function of other variables.

(b) Suppose that there are two countries with the same steady state capital per worker k* and zero growth rate of population(n=0), but differ by saving rate, s and depreciation rate, d. So we assume that s1/d1=s2/d2 where s2>s1 and d2>d1. Compare two countries’ consumption per worker(C/N). Is it different? Why?

(c) Now we learn that that d=0.1, s=0.1, z=1, and n=0. Calculate the steady state k*. Suppose that the saving rate, s, is doubled into s=0.2. Find out the new steady state k**.  

(d) Now suppose that d=0. Can you describe the steady state? If not, explain why.

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