The Uzawa-Lucas Model

The Uzawa-Lucas Model

In this model, The production of Human capital involves no physical capital. Thus this model is different from the one sector AK model in a way that in one sector model Human capital accumulation needed physical capital accumulation.

So in case of one sector model we had the production function in Cobb-Douglas form as

So in Uzawa-Lucas framework η=0, implies v=1, since K is not productive in the education sector, all of it is used in goods sector. So the production function is:

Now we specify the dynamic analysis as

ω=K/H and χ=C/K. by using these expression in equation 3 and 4 we get expression for the growth rate of K and H as

 The FOC shows that the growth rate of consumption is given by

 

Steady state Analysis

At steady state μ, ω and χ are constant in a steady state.

Φ ≡ ρ+δ(1-θ)/Bθ

The steady state value , which corresponds to  are given as

And the rate of return and the common growth rate of C,K,H,Y and Q in the steady state is given as

r* = B- δ ……….(14)

y* =1/θ (B-δ-ρ) …..(15)

Further we can find the transitional dynamics from equation 7,9and 10.