Question

Hello tutor, could you solve part e of this question for me ASAP

thank you.

Suppose the economy is producing output with the CRS production function F) below where At is some measure of labor augmenting technological progress, Kt is some measure of physical capital, Nt is the size of the labor force. A constant fraction (s) of the income Yt is saved, and savings in the economy finance the investment in physical capital (It). Each period a certain share (d) of the physical capital stock depreciates and new additions to the physical capital stock are realized with (It) Assume that the population grows at a constant rate (n) and the technology grows at a constant rate (g). Let Yt ,Ct, /t and Kt denote the aggregate variables, yt ,Ct, it and kt denote the per capita variables and Vt, Ct, ît, kt denote the per effective unit of labor variables (ie. yt-t/AN, and others are also defined similarly) a. Write down the income expenditure identity in terms of all three types of b. Derive the fundamental law of motion for the capital stock again for the three c. Derive the equation that equates savings to the desired level of investment in variables (aggregate, per capita ans per effective labor). types of variables the economy in terms of per effective unit of labor (^ variables) (In the model we discussed in class it was sf(k) - (n + d)k) and solve for the steady state level of capital stock k d. Derive the steady state level of t and find the golden rule level of capital per effective unit of labor k" which maximizes consumption per effective unit of labor at steady state. Consider the impact of a rise in the growth rate of technology g. Analyze the impacts of this change on the steady state levels of steady state growth rates of yt and kt. Use a graph in your analysis e. t Vt .Vt ,kt and the

Answer 1

The initial steady state equilibrium occurs at point E_1 in the below model diagram A rise in the growth rate of technology will shift the curve upwards to delta + n + g_2 k and thus new steady state equilibrium occurs at point E_2 where both capital per effective worker and output per effective worker has fallen in the economy steady state growth rate of capital and output per effective worker is equal to zero because both are constant in the steady state However, since efficiency of each worker is growing at the rate g, output per worker is also growing at the rate g total output grows at the rate of n + g