Answer to Question #143953 in Macroeconomics for Tanvir Alam

Question

Describe how, if at all, each of the following developments
affects the actual investment and the break-even investment (this is the linear line) lines
in the basic diagram for the Solow model:
(a) The rate of depreciation falls
(b) The rate of technological progress falls
(c) The production function is Cobb-Douglas, f(k) = kα, and capital’s share, α falls.
(d) Workers exert more effort, so that output per unit of effective labor for a given level
of capital per unit of effective labor is higher than before.

Answer 1

a) If the rate of depreciation falls, the slope of the line representing break-even-investment decreases ,that is it becomes less steep. This is because fall in rate of depreciation will increase capital accumulation and higher levels of output since investment exceeds the rate of depreciation.

b) If the rate of technological progress falls, the slope of break-even-investment decreases, the line becomes gentle. This is because the economy will grow slower. This means less investment is needed to keep pace with the growth rate.

c) When the production function of Cobb-Douglass f(k)=ka, and capital's share, a fall, the line representing actual investment moves downward. This is because the capital share decline, less investment is needed at any value of capital per effective worker.

d) When workers exert less effort, the line representing actual investment moves upward while break-even-investment remains unchanged. The output level will fall because the output growth rate lies on the steady -state path of output per worker.