Question

Suppose the production function is given by ? = ?^a?'^1-a, where Y is output; K is capital

stock and N is Labor (look Appendix in Chapter 16).

a. Is this production function characterized by constant return to scale? How? Show the

work.

b. Write this production function as a relationship between output per worker and capital

per worker.

c. If saving (S) equals investment (I), and S = sY, where s is saving rate, what is the

corresponding investment per worker equation?

d. Write down the dynamic capital accumulation equation per worker.

e. For saving rate (s) and a depreciation rate (?), given an expression for capital per

worker in the steady state in terms of s and ?.

f. Show the steady state equilibrium in the diagram.

g. What is the equation for output per worker in the steady state?

h. Solve the steady state level of output per worker when ? = 0.5 s = 0.10 and ? = 0.10.

i. If saving rate doubles (s = 0.20), what happens to the steady state level of output per

worker?

j. Show this equilibrium in (h) and (j) in the diagram.

Answer 1

DO Y = kwa Increade both inputs by d. dy = (dk)a (AN) - jak na Ni-a 19 -a. Ko Nl-a ja - Kania Incrence in both Kand a byd leads to increase in Y by a It mand production function exhibit constant return to scale OLY = kanla Divide both sides by N. ka Nia (output per worker production fod y • k - o IS I= sy Des Divide both & des by N. 4 . (*)" (see put b)

> I ek_Closet ment per wurkeregunten). @ capital accumulaten Guetiu. DR 3y - SR (calohl accumulaton egrention par les has per chang puling, I ansurred first four part.