In a standard Solow growth model without technological progress, if the savings rate (s) increases, what is the long-run effect on the per capita capital stock (k) and the per capita output (y)?

Solution: The Solow Model makes key distinctions between the level and the growth rate of per capita variables: · Long-Run Steady State: In the Solow model without technological progress, the long-run growth rate of per capita variables (k and y) is determined solely by the rate of exogenous technological progress (g), which is assumed to be zero here. Thus, the long-run growth rate of y remains zero. · Effect of Increased Savings Rate: An increase in the savings rate (s) shifts the actual investment curve (s⋅f(k)) upward. This causes a new, higher steady-state per capita capital stock (k∗) to be established where the new investment curve intersects the depreciation line ((δ+n)k). · New Level: The increase in k∗ leads to a permanent, higher level of per capita output (y∗=f(k∗)). The economy experiences a temporary period of positive growth as it transitions to the new steady state, but the long-run growth rate returns to zero.