Answer to Question #283727 in Macroeconomics for ABEX

Question

28. Consider the Solow model with technology. Suppose that saving rate increases from s to s'. Demonstrate using graphs and quantitative methods how this shock affects

(a) Level of per capita income.

(b) Growth rate in per capita income.

Answer 1

The term "technological progress" in economic growth models is understood in a very broad sense, namely, in the sense of all factors that, given amounts of labor L and capital K, allow an increase in national income, or output Y.

The main thing we should pay attention to is the shift of the production function Y = f(K,L), which turns into a function that depends on the variable t, i.e. on time: Y = f(K,L,t). As a result of technological progress, the production function per employee shifts from y1 = f(k) to y2 = f(k). The shift of the production function can occur under the influence of a variety of factors: improvement of the quality of physical capital, quality of the labor force (growth of workers' qualification), improvement of the production structure, improvement of management, etc.

Along with the shift of the production function graph from position y1 = f(k) to position y2 = f(k), the savings (actual investment) graph also shifts from position s1f(k) to position s2f(k). Technological progress causes the steady-state level of capital formation to shift from point k1* to point k2*. The equilibrium level of required investment and savings moves from point E1 to point E2. Accordingly, the sustainable level of output per capita rises from the level of y1* to the level of y2*.