: 3 ( 100820 :,,,,,,,;,,,,,, :,,,,,, (Barro,1990, (Barro and Sala2I2Martin,1992,(Arrow and Kurz,1970,,, ( Glomm and Ravikumar,1994,,,, (Solow,1957 3, 10
2004 3,,,,,,,,,,,, :,,, ( Inada,1963,,,,,;, ;, ;,,,,,(Ramsey,1928,,,, ;,, (, c ( t u [ c ( t ] (,t : : ga = ( r - : lim { a. exp [ - t t 0 maxu = 0 e - ( - n t c1- - 1 dt (1 1 - n a + w - c ; : a (0 = 1 ; [ r( v - n ] dv ]} 0, a, r, w, n,> 0,> n u[ c ( t ] (,,,, ( i K i L i -, ; i 11
: Y i = A K i L (1- i ( G (1- (2, Y i, K i,l i, G, K, G,= GΠK,,K i Π L i = k i = k = KΠL,(2 y = Ak ( G (1- (3, y, k,0 << 1, 1, = 1, k, (3 y = AL 1 - k, A K (, w r, (2 (3, max[ A K a i L 1- a i ( G (1- a - wl i - ( r + K i ] (4,k i = k,, w = f ( k, G - kf ( k, G = A (1 - k ( G 1- (5 r + = f ( k, G = A k - 1 ( G 1- (6 (6, : 11 = 0,,,; 21 0 << 1,,,, ; 31 1, = 1,,, K,G = K = Lk, r += A L 1 -, L (, r w,,,,, a = k (5 (6, (1, : : gk = f ( k, G - c - (+ n k (7 : k (0 = 1 (8 - gr ( t : lim[ k e t ] 0 (9 t,gr ( t, : gr ( t = (1Πt t r( v dv 0,,, : H( c, k, = e - (- n t c1- - 1 + [ f ( k, G - c - (+ n k ] 1 - : 5 H 5 c = e - (- n t c - - = 0 (10 : 5 H 5 k 12 = [ A k- 1 ( G 1- - - n ] = - g (11
: lim t { k exp ( t 0 2004 3 [ f ( k, G - - n ] dv } = 0 (12 (10 (11 (7 gc ( t gk ( t,(8 (12, (10 : - gπ= - n +gcπc, (11 c : c = gc c = 1 [ A k- 1 ( G 1- - (+ ] (13 (13,,: 11 = 0,,, ;0 << 1,, 1,,,,, 21 G, = 1,G = K = Lk, (13 c = [ A L 1- - (+ ]Π,,,,( ; ( Kaldor,1961 GDP,,,, GΠK 1,,,, ( c k y 11, = 1, (7 gk = Ak ( G 1- - c - (+ n k (14 - ( A (13, lim [ k e L1- - - n t ] = 0, t,,, y k c (,,, (15, 3 y = 3 k = 3 c = 1 ( A L 1- - - (15 21, < 1, (14, (13, lim k exp{ - t t [ f ( k, G - n - ] dv} = 0 0, k c y, 13
:, 3 y = 3 k = 3 c = 0, ( c 3, k 3,, k y c, K Y C n,, (14 (13 c = f ( k, G - ( n + k (16 f ( k 3, G = + (17, k,,k gold,k gold : f ( k gold, G = n + f ( k gold, G - n, (17, f ( k gold, G - 1 31 k c (1, (16 gk = 0,,,k = 0,f ( k, G = n +; c k 0 (17 gc = 0, 0 << 1,1 gc = 0 gk = 0 4,,c ( k k, c (0,(,1, 2,gc 1 = 0 gc 2 = 0 gc 3 = 0,,,gc = 0,, k 3 c 3 ; 3,1, gk = 0, k 3,, 1,(13, gk = 0,k,,,,, 14
2004 3 2 3 ( c ( t u[ c ( t ], ( i K i L i,,,,t,, Y i = A K 1- i L i ( G 1- (18 (18 (2,G (18,, G i,k = k i = K i / L i = K/ L,: y = Ak ( G 1-, y, k { w, r, },,max[ (1 - A K i L i 1- ( G (1- - wl i - ( r + K i ],, r, ( w = (1 - A (1 - k ( G 1- ( r + = (1 - A k - 1 ( G 1- (19 G,,G = Y Y = A K L 1 - ( G 1 - : (20 (19 : r + = (1 - A k - 1 ( ALk G = A K L 1- ( G 1- = ( ALk (1-1- (1-1 1- (1- = (1 - A( AL (20 (1- - 1+(1-1- (1- k 1- (1- (21 (21,, 0 < < 1, k, - 1 + (1 - < 0 1 - (1 -, - 1 + (1 -, > - 1, 1 - (1 -, - 1 + (1 -, = 1, : = 1 - (1-0 15
: (21 r + = (1 - A( AL 1,,L, ( (1 gk = (1 - f ( k, G - c - (+ n k (22, c = gc c = 1 [ (1 - A k1- - (+ ] (23 (20 (23, c = 1 [ (1 - A( (1- AL - 1+(1-1- (1- k 1- (1- - (+ ] (24 (24,,, (1 -,,, (24 : 11= 0, 210 << 1, k - 1,,, 31= 1,k, (24 c = 1 [ (1 - A( 1- AL - (+ ] (25,,,,,,,,,,,, = 1,(25 : 5 c 5 = 1 A 1 L 1-1- ( - 1 + A 1 1- L 1 -, = 1 -, 4,,, c,,, c,,(barro,1992 16 1-2 (1-4
2004 3 0 < < 1,(24 : 5 c 5 = 1 A 1 (1-1- (1 - L - 1+(1-1- (1- k 1- (1- ( - 1 + A 1 1- (1- L (1- - 1+(1-1- (1- k 1- (1 - (1-1- (1 - (1 - (1-1 - (1-2(1- - 1 1- (1 - = (1 -, 4, c,,,, =(1 - < 1 -,< 1 c, (1 -, c ;, c, (,,, (1, : Y = C + gg + g G + gk + K (26 Y = gg + g G (27 Y, C, gg (, g, K, (26, (27,, G =Y, g = 0, G = gg,(26 Y = C + G + gk +K, : gk = (1 - Ak ( G 1- - c - (+ n k (28 : c = 1 (1 - A ( (1- AL 1- (1 - k 1 - (1 -, = 1, - 1+(1-1- (1 - - (+ (29 c ( = 1 [ (1 - A ( 1- AL - (+ ] (30 (30 (25,,< 1, c ( c (,, c ( c (,,,,,,,= 1 - ;,=(1 -, ( 11,gk = (1 - f ( k, G - c - (+ n k, c (25,,(1-17
: 1- A( AL > +> 1 - (1-1- L 1- L A ( 1 - (+ +, 3 c = 3 k = 3 y = (1 - A ( 1 - (+ Π, c k y,, (28 (30,,(1 - A( 1 1- L > + > 1 - (1 - A ( 1 1- L - (+ + > 0, c k y, 3 c ( = 3 k ( = 3 y ( = 1 (1-1- L A ( 1 - (+,,,, 21,(22, c (24,,, 3 c = 3 k = 3 y = 0, ( c 3, k 3,,k c, 1, 2 3 0 << 1,,gk = 0,k 3,,(28, (29, 3 c = 3 k = 3 y = 0,,k 3 k 3,,,,,,,,,,,,,, ( Greiner,1996, (,1960 1992 0141 ; 1960 1990 0144 ;1978 1998 0127,,,, 18
2004 3 Arrow, Kenneth J., Kurz, Mordecai, 1970, Public Investment, the Rate of Return, and Optimal Fiscal Policy, John Hopkins Press. Arrow, Kenneth J., 1962, The Economic Implications of Learning by Doing, Review of Economies Studies, Vol. 29 : 155 73. Aschauer, David A., 1989,Is Public Expenditure Productive?, Journal of Monetary Economics, Vol. 23 : 177 200. Barro, Robert J., 1990,Government Spending in a Simple Model of Endogenous Growth, Journal of Political Economy, Vol. 98, No. 5. Barro, Robert J., Sala2I2Martin, Xavier, 1992a,Convergence, Journal of Political Economy, Vol. 100, No. 2 : 223 51. Barro, Robert J., Sala2I2Martin, Xavier, 1992b,Public Finance in Models of Economic Growth, Review of Economic Studies, Vol. 59. Cass, David, 1965,Optimum Growth in an Aggregative Model of Capital Accoumulation, Review of Ecomonic Studies, Vol. 32 : 233 40. Glomm, Gerhard, Ravikumar, B., 1994,Public Investment in Infrastructure in a Simple Growth Model, Journal of Economic Dynamics and Control, Vol. 18 : 1173 87. Greiner,Alfred, 1996, Fiscal Policy and Economic Growth. Inada Ken2Ichi, 1963,On a Two2sector Model of Economic Growth : Comments and a Generalization, Review of Economic Studies, 30 (June, 119 127. Kaldor, Nicholas, 1961,Capital Accumulation and Economic Growth, in Friedrich A. Luts and Douglas C. Hague (eds., The Theory of Capital. Proceedings of A Conference Held by the International Economics Association, pp. 177 222. St. Martin s Press, New York. Lucas, Robert E., 1988,On the Mechanics of Economic Development, Journal of Monetary Economics, Vol. 2 : 3 42. Ramsey, Frank P., 1928,A Mathematical Theory of Saving, Economic Journal, Vol. 38 : 543 59. Rebelo, Sergio, 1991,Long2run Policy Analysis and Long2Run Growth, Journal of Political Economy, Vol. 99, No. 3 : 500 21. Romer, Paul M., 1986,Increasing Returns and Long2Run Growth, Jounal of Political Economy, Vol. 94, No. 5 : 1002 37. Romer, Paul M., 1990,Endogenous Technological Change, Journal of Political Economy, Vol. 98, No. 5, pt. 2 : S71 102. Solow, Robert M., 1957,Technical Change and the Aggregate Production Function, Review of Economics and Statistics, Vol. 39. Swan, Trevor W., 1956,Econnomic Growth and Capital Accumulation, Economic Record, Vol. 32 : 334 61. Public Investment Policy in Long2run Economic Gro wth General Congestion Public Infrastructure in Long2run Growth Model Lou Hong (Department of Treasury,Ministry of Finance,P. R. C Abstract : Generally, infrastructure is of congestion and pure public infrastructure is an extreme example. The investment in infrastructure can be both of exogenous and endogenous. To take the general congestion into account, the paper sets up an exogenous growth model as well as an endogenous model. This paper reached the following conclusion : when the exogenous infrastructure is of pure public,it can generate long run and sustainable growth rate. And when the infrastructure is of congestion it can also increase the long run growth rate. If the endogenous infrasturcture is of pure public,it can lead to constant endogenous growth and if the infrastructure is of congestion,it can also increase the long run growth rate which varies according to the degree of congestion. Key Words : Growth ; Public Infrastructure ; Investment Policy JEL Classification : H410,O410,O110 ( : ( : 19