Difficult# Solow Model with Growing Labor and Technology

MACRO-L5CELS

Consider a Solow growth model with the following Cobb-Douglas production function for GDP:

$$Y = K^\alpha (\bar A L)^{1-\alpha}$$

...where $Y$ is GDP, $A$ is the level of (labor-augmenting) technology, $K$ is the capital stock and $L$ is the labor force. Let the savings rate by households be denoted $s$, and the rate of capital depreciation be denoted $\delta$. Also assume that the labor force grows at the fixed rate of $n$ each period and technology grows at rate $g$.

In the steady state, the level of GDP and the capital stock both

, while the level of GDP and capital *per capita* both

.