Question

Using Romer's growth/production model, derive the expressions for: the level of per capita output in time t, as a function of the growth rate.

Answer 1

Formula/Equation:

The formula for basic production function, according to Romer is as:

Y_i = AK_i^α L_i^1-α K^-ß

For the sake of simplicity, he considers all the industries alike. As a result, each industry will employ similar amount of capital and labor. Accordingly, the aggregate production will be as:

Y = AK^α+ß L^1-α

In the beginning, we assume that the value of A does not increase with the passage of time, rather it remains fixed. It means that for the time being it has been assumed that no technical progress takes place. As we take the total differential of the general production function and divide it by dt as:

Where g shows the rate of growth of output and n represents growth of population. As Solow model assumes constant returns to scale, therefore, in that model ß = 0. Hence, in the absence of technical progress the per capita growth rate will be zero.

All the three factors described by Romer which also include the externalities of capital, will make ß = 0. As a result, the per capita growth rate, i.e., g - n > 0, and Y/L , i.e., per capita output will be increasing. Again, we have introduced the endogenous growth in the model which depends upon savings and investment, not on the productivity like exogenous factor. Thus, the notable property of Romer's model is this that because of investment or technical spillover, the diminishing return's of the capital can be checked.