[ 考題 106 年政大商學院 ]

Consider an economy in which production is characterized by the neoclassical function Ｙ＝Ｋ0.5Ｎ0.5, where Y , K and N denote the output, capital stock and quantity of labor, respectively.

Suppose that it has a saving rate of 0.1, a population growth rate of 0.02, and an average depreciation rate of 0.03.

(1) Write this production function in per capita form in which y=Y/N and k=K/N, and find the steady-state value of y and k.

(2) At the steady-state value of k , is there more or less capital than at the golden-rule level?

(3) Determine what saving rate would yield the golden-rule level of capital in this model.

(4)In the context of this neoclassical growth model, can a country have too much saving?

[ 解答 ] 經濟成長的考題基本上是總體經濟學的必考題，穩定均衡與黃金法則成長，兩者則是同學必須要會求解的兩種解題技巧。

(1) 由生產函數Ｙ＝Ｋ0.5Ｎ0.5同除以人口 N ，可求得人均的生產函數 Ｙ＝Ｋ0.5，而 steady-state 條件為 ，則0.1．ｋ0.5=(0.02+0.03)．k，可求得

(2) 求黃金法則下的資本存量，其條件為 ，則 0.5．ｋ0.5=(0.02+0.03)，可求得

(3) 承上題，求黃金法則下對應的儲蓄率，將 代入 steady-state 條件 ，可得

(4) 在本題中初始的儲蓄率 0.1 低於黃金法則下的儲蓄率 0.5 ，故並非儲蓄過多，而是儲蓄過少。