Answer to Question #290900 in Macroeconomics for lisa

Question

With the help of the Solow growth model diagram, explain the effects of shocks on steady state per worker capital and output.

Answer 1

Impulses (technological shocks)

In order to understand the root cause and mechanism of the spread of the technological cycle, we modify the production function in the Solow model by introducing the variable At, which takes into account the unevenness in the development of scientific and technological progress:

The immutability of the technology is reflected At = 1, during the period of technological improvements At > 1. The period of technological regression corresponds to At < 1.

Taking into account the modification, the basic dynamic equation of the Solow model becomes more complicated and takes the form

k = sAf(k) (n + g + b)k

If there has been a positive technological shift, i.e. At > 1, then in the initial equilibrium state, the actual investments exceed the necessary ones, therefore the level of capital-to-weight ratio will begin to increase. The economy will move to a new equilibrium state corresponding to a higher level of capital-to-weight ratio k2*. Therefore, output will grow at a faster rate than in the initial equilibrium state (than the trend growth rate).

Let's say the initial positive technological impulse disappeared, i.e. the technology improvement was temporary. Obviously, although the initial k1* will again be the new stable level of capital-to-weight ratio, the output, nevertheless, will not immediately return to its original equilibrium trajectory. Therefore, as long as kt > k1*, the output will continue to be more than potential, although the technological level during this period corresponds to the initial one. Hence, the technological shift causes the beginning of the cycle and contains a built-in mechanism for its propagation

The consequence of a positive technological shift is an increase in output, and hence the amount of savings. Consequently, the capital stock will be larger than it could be in the absence of a technological shift. Therefore, the effect of technology improvement will be effective even when the level of technology returns to the original, since a higher capital stock will lead to higher savings and higher output.