Question

Suppose that the aggregate production is given by , where Y is real GDP, K is the total capital stock and L is the (constant) labour force. Assume that aggregate investment is equal to aggregate savings and that the depreciation rate is 0.05, hence the total capital stock evolves according to K=sY − 0.05K, where s is the savings rate.

Y = 0.5VKVL

1) Under the stated assumptions for this question, what is the steady-state level of capital per worker when the saving rate is given by s = 0.1?

2) Consumption is determined by (1 − s)Y. Under the stated assumptions for this question, what is the steady-state level of consumption per worker when the saving rate is given by s = 0.1?

Answer 1

6- 5 Jkve 0.5 uk UI 1 = 0.5X ool = 0.05 0.5 = 0.5+14) .5 c=(1- sy = 0.9 X0-05 = 10.045 = 0.58 K sy = o.ook 0.1X0.5 x 15 = 0.5k 0.05ks = o.sk 0.5 0.05 = 0.1 co.ut K = 0.01