6. Consider the basic Solow model of chapters 10 and 11 in which both technology

Question

6.   Consider the basic Solow model of chapters 10 and 11 in which both technology (A) and the units of labor input (N) are fixed.

a)Show how the steady state equilibrium values of Y/N and K/N are determined. Given that N is fixed by assumption, are Y and K changing in this steady-state equilibrium? Explain.

b)What is the optimal, or golden rule, value of K/N, and how is this determined?

c)Illustrate the case in which the steady-state value of K/N (i.e., K*/N) exceeds the golden rule value of K/N (i.e., K*gold/N).

d)Show that there exists a saving rate such that K*/N = k*gold/N. Is this saving rate higher or lower than the saving rate implicit in part c?

e)Why would it be difficult to attain K*gold/N in the case in which K*/N < K*gold/N?

Explanation / Answer

Let Y/N = y, K/N= k

y = f(k)

change in k = sf(k) - dk

where s= savings rate

d= depreciation rate

In steady state, change in k =0

sf'(k*) = d

b) Golden rul level of capital is determined by when consumption is highest

i.e. when MPK = f'(k*gold) = s

c) k*gold<k*

then it means that MPK at k*gold is higher.

d) Here savings rate will be lower than part (c)

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