Topic 10: Piketty and Inequality Dynamics

Question 1

What are the counterpoints to the argument that physical capital has lost its importance and that the new economy will be based on human capital and talent?

Answer 1

Human capital and talent isn’t equitably distributed either.

Capital takes an almost infinite number of forms and each remains useful.

Question 2

What are the initial equations to set up the solow model with human capital?

Answer 2

(L_t+1 - L) / L = n

K_t+1 - K_t = I_t - δK_t

Y=AK^α(θ_LL)^1-α

We consider technoligical change as augmenting workers, increaseing the number of efefective works for each actual worker.

where L_e=θL

Question 3

Show how the effective labour force changes with growth in the Solow model.

Answer 3

(L^e_t+1 - L^e_t)/L_t^e = ( θ_t(1+g)L_t(1+n) - θ_tL_t ) / θ_tL_t

= (1+g)(1+n) = n + g + ng

we can ignore ng since it is small.

Question 4

Show the Solow equations in per effective worker terms

Answer 4

y_e = AK^αL_e^1-α / L_e = A(K/L_e)^α

k_e = K/L_e

y_e = Ak^α_e

Question 5

Determine the steady state in the Solow model.

Answer 5

The equation of motion is

Kt+1 = K_t - δK_t + I_t = K_t(1- δ) + sY_t

But with population rising continually, there is no stready state of Y or K. But there is a steady state per effective worker.

k_et+1 - k_et = (i_et - (δ + n + g)k_et) / (1 + n + g)

Stedy state where

sy_e = sf(k_e) = i_be = (δ+n+g)k_e

Question 6

What are the factor rewards in the Solow model?

Answer 6

y_e = Ak_e^α

MPK = δY/δK = δy_e/δk_e=αA/k_e^1-α

So this is constant in the steady state.

w_e=δY/δL_e=A(1-α)(K/L_e)^α = A(1-α)k_e^α

So in the steady state, the real wave of effective workers is constant – which means growth the wage of real workers! (at g)

Question 7

What is the ratio of capital stock to income in the steady state?

Answer 7

s/(δ+n+g)

Question 8

What reason does pikkety argue might cause the capital stock / rent to change?

Answer 8

Substitution in between capital and labour.