Q1. Consider the Harrod-Domar model as discussed in the lecture for this question.
a. Draw the isoquants of the production function. Derive expressions for Y/K, Y/L, and K/L
under the assumption that both production factors are fully employed. What happens if the
actual K/L is less than $v/a$? What if it is larger than $v/a$?
b. Show that in order to maintain full employment of capital in the model, output and
investment must grow at the so-called \"warranted rate of growth\" .
c. Show that in order to maintain full employment of labor in the model, output and investment
must grow at the so-called \"natural rate of growth\", which is equal to $n$.
d. Derive the condition under which the economy grows with full employment of both factors
of production. What happens if the condition that you derived does not hold?
e. Compare what the Solow model predicts about the long-term growth rate in an economy
with what Harrod-Domar model predicts. (For the Harrod-Domar model restrict your
analysis to the full-employment case.) What aspect of (or assumption in) the Solow model
sets it apart from the Harrod-Domar model and allows us to get these different predictions?
Which one of these assumptions make more sense in a long-run growth setting?
