Considering the following labour augmented version of the Neoclassical (Solow) growth model, where the production function is given by: Y_t=K_t^0.5(A_tN_t)^0.5

Where K_t is the aggregate capital stock, Y_t is the aggregate output, A_t is the total factor productivity, N_t is the number of workers within the economy. The labour force grows at rate n, households save fraction s of their income, capital depreciates at a rate d. Additionally, total factor productivity (TFP) grows at a constant rate g.

1) Determine the production function expression in per effective worker terms or in intensive terms.

a) y=k^-0.5

b)y=k^0.5

c)y=A^0.5k^0.5

d) Y= A^0.5k^0.5

2) The steady state is described as k=0.

Capital accumulates according to k_t+1=I_t+(1-d)K_t and the effective labour the following period, A_t+1N_t+1 grows at a rate g+n. What is the steady state (break-even) investement per effective worker.

a) i=(n+g+d)k

b) i=(1+n+d)k

c) i=(1+n+g+d)k

d)i=(n+d)k

3)Using the steady state expression found in question 2, as well as the goods market equilibrium condition, determine the steady state condition that dictates the level of steady state capital stock per effective worker, k*, given that the expression for y indicates output per effective worker.

a) sk^0.5=(n+g+d)k

b)sA^0.5k^0.5=(1+n+g+d)k

c)sk^0.5=(1+n+g+d)k

d)sA^0.5k^0.5=(n+g+d)k

4) Determine the steady state level of capital per effective worker, in terms of s, n, g, and d. Suppose that A=9 s=0.3, g=0.01, n=0.02 and d=0.2, determine k*

a) k*=[(1+n+g+d)/A^0.5s]^-2 & k*=0.535

b)k*=[(1+n+g+d)/s]^-2 & k*=0.0595

c)k*=[(n+g+d)/A^0.5s]^-2 & k*=15.312

d) k*=[(n+g+d)/s]^-2 & k*=1.701

5) Using the values of k* from question 4, determine the steady state output per worker ,y*

a) y*=1.304

b) y*=0.731

c) y*=0.244

d) y*=3.913

6) c*, the value of consumption per effective worker is closest to:

a) 2.739

b)0.171

c)0.913

d)0.512

7) Assume the population growth rate, n, rises from 0.02 to 0.03. The new steady state output per effective worker, y*, the new level of capital per effective worker, k*, and consumption per effective worker, c*, are closest to:

a) k*=1.563, y*=1.25, c*=0.825

b) k*=1.563, y*=1.25, c*=1.625

c) k*=0.0585, y*=0.242, c*=0.315

d) k*=0.0585, y*=0.242, c*=0.169

8) Given the values acquired in question 7, determine the effect on the economy's living standards.

a) Risen

b) Fallen

c) Unchanged

d) The effect cannot be determined