Question

Problern Consider the following Graph Deprecation vement a. Show on the graph where is the steady state level of Capital per worker (k*). Explain why b. Suppose the savings rate decreased. Which curve shifts and which way? Suppose we have a savings rate of 0.2 (20% of income is saved). Our Depreciation rate is 0.15 (15%). Calculate the steady state level of Capital stock per worker. Show your work c.

Answer 1

Answer 1

(a) Steady State occurs when

$\Delta$ k = sf(k) - d*k = 0

=> sf(k) = d*k

where s = saving rate, k = Capital per worker

y = f(k) = output per worker and d = depreciation rate(Note instead of delta I used d to represent depreciation rate)

hence according to figure steady state occurs when Investment curve intersect depreciation.

Hence k* is that level of capital per worker at which Blue curve intersect Purple curve.

(b)

Suppose saving rate decreases then Investment = sf(k) decreases. Hence Decrease in saving rate will result in Investment(Purple Curve) to shift and it will shift downward. Note it will shift downward but still it will pass through the origin.Hence decrease in saving rate will result in Investment curve to rotate right or downward.

(c)

Steady State occurs when

$\Delta$ k = sf(k) - d*k = 0

=> sf(k) = d*k

where s = saving rate = 0.2, k = Capital per worker

y = f(k) = output per worker and d = depreciation rate = 0.15 (Note instead of delta I used d to represent depreciation rate)

Hence, $\Delta$ k = sf(k) - d*k = 0

=> 0.2f(k) = 0.15k

=> f(k)/k = 0.75

Steady state level of capital per worker = k*

=> f(k*)/k* = 0.75

(Note this is the equation we have to solve for steady state level of Capital per worker(k*))