本文中，我們建立一個小型開放經濟體的貨幣內生成長模型，在購 買力平價說成立下，我們試圖透過生產函數，引入政府支出具有生產的外 部性引進經濟體系；考量政府藉發行本國名目貨幣融通政府提供具有生產 性功能的公共基礎建設。在此架構下，當央行以名目貨幣供給成長率指標 作為貨幣政策時，央行調整貨幣供給成長率對產出成長率的關係不再只是 單一方向的影響，貨幣供給成長率存在一個最適水準可達成產出成長率的 極大。在低於此貨幣供給水準下，央行提高貨幣供給成長率將提升經濟體 系的產出成長率；反之，兩者之間存在著負向變動關係。再者，我們的分 析進一步發現，貨幣供給成長率存在一個較高的門檻水準以及一個較低的 門檻水準，準此，我們可以發現到通貨膨脹率與經濟成長率兩者之間存在 著非線性(non-linear)的關係；且當貨幣供給成長率在兩個門檻之間時，通 貨膨脹率與經濟成長率之間存在著正向變動關係。除此之外，兩者之間存 在著負向變動關係。再者，本文中，貨幣供給成長率改變時，對消費成長 率並未產生任何影響。準此，我們發現到當產出成長率高於消費成長率的 情況下，將會與Barro(1990)命題 - 「成長極大即是福利極大」的結論相 符。
附錄 A
將(B5)代入終端條件(9.a)式可得：
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