Suppose output, investment, and depreciation are given by the following formulas: Output: Y = √ K Investment: I = 0.3 √ K Depreciation: D = 0.02 K What is the new steady-state levels of capital stock and the new steady-state level of output if we increase the depreciation rate from 0.02 to 0.03?

The new steady state of capital stock = 10

Explanation:

At steady state change in capital stock is equal to zero . As well as depreciation is equal to investment.

So, investment = Depreciation

0.3\sqrt{}K = 0.02 K

0.3 / 0.02 = k / \sqrt{}K

15 = \sqrt{}K

Thus K = 15*15 = 225 and Y = \sqrt{}K = \sqrt{}225 = 15

However when depreciation will increase from 0.02 to 0.03 then new steady state will be as follows

Investment = Depreciation

0.3 \sqrt{}K = 0.03 K

0.3 / 0.03 = k / \sqrt{}K

10 = \sqrt{}K

K = 10*10 = 100

Thus new steady state of capital stock ( K s s ) = 100 and new steady state of output ( Y s s) will be = \sqrt{}K = \sqrt{}100 = 10

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