Question

3) [20 points] Consider the Solow growth model without population growth or technological change. The parameters of the model are given by s = 0.2 (savings rate) and d=0.05 (depreciation rate). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. a. Rewrite production function below in per worker terms: 1 2 Y = K3L3 b. Find the steady-state level of the capital stock, c. What is the golden rule level of k for this economy? Report your answer to two decimal places. d. Let's say that a benevolent social planner wishes to obtain k = kg in steady-state. What is the associated savings rate Sgr that must be imposed by the social planner to support kgr? e. What are the implications of the planner's policy on consumer in short- run and long-run? f. Identify two economic policies that could help the social planner implement Sgr in a real-world situation.

Answer 1

As per the HOMEWORKLIB POLICY, answering the first four parts

L Y = k\34213 a. production function in per-worker terms – y = 1 = k"3,213=() "3 - pils So, y= k'z o An where k = Capital pro Worker = ķ b. at steady state, Ak=0 → $fCk) – (d+n) k = 0 1. f(k)= y & n=o So, $y = 0.05% sk'3 = 0.05 k S = 0.05623 → → X100 - $23 => (208)8/2 = K - Put & = 0.2 . k*= (+)/2 . k* = (22) 312 [k* = 8) Aomo 1. c. at Golden Rule level of Capital Stock, MPx = 0 > 3643 = 0.05 ('4 = k3 de 318455 MPa = 443 - 1. Rgr = (6.67 312 = 17,23 And d. Put Rgr in equation ② 208 = (17.233943 $ $gr = 0.33 = ☆ Ana

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