١ﻉ١ﻡ Badal Mukherjiﻣﻮﻛﺮﺟﻰ ﺑﺎﺩﺍﻝ :ﻣﻘﺪﻣﺔ M. Manzar A. Ahmad Model ∗ Indian A Macro Model of the Islamic Tax System Economics Review, vol. XV, No. 1. Delhi School of Economics ∗ ﺃﻭﻻﹰ ﺎﺛﺎﻧﻴ ﺛﺎﻟﺜﹰﺎ m y yymin y ymax Wage Subsidy ﺍﻟﻨﻤﻮﺫﺝ ﺍﻷﻭﻝ Wage Subsidy Equilibrium KW Cambridge Aggregative Per Capita Micro Models W(O) >= Wmin :ﻓﺮﻭﺽ ﻧﻈﺎﻡ ﺍﻟﺰﻛﺎﺓ ﺍﻹﺳﻼﻣﻲ ﰲ ﺍﻟﺘﺤﻠﻴﻞ ﺍﻻﻗﺘﺼﺎﺩﻱ ﺍﻟﻜﻠﻰ Proportional Growing wealth Production instruments Optimizing system λ :ﺍﻟﻨﻤﺎﺫﺝ ﺍﻻﻗﺘﺼﺎﺩﻳﺔ ﻟﻨﻈﺎﻡ ﺍﻟﺰﻛﺎﺓ ﺍﻟﻀﺮﻳﱯ :ﺍﻟﻨﻤﻮﺫﺝ ﺍﻷﻭﻝ K λnkkn λ n = K n K kn=λn k tn k - kn= (1 - λn)k T1 T1 = tn (1 - λn)k .......................................................................................(1) k (1 − λ n ) K ≥ k λ λ = λ = λn 1− λ = n K n K − K K n K − K = n n λ nK λ nK λn = = K − λ nK K (1 − λ n ) 1− λ n λnλ Ykkn Yk = K n = bK n .......... .......... .....( 2 ) v knb W W W ≥ W Y Y = Yk + W = bkn + W..........................................................(3) C = cY c S = (1 - c)Y = s(bkn + W)...............................................................(4) s ty T2 T2=tys (bkn + W) T T = T1 + T2 = t n (1 − λ n ) K + tys (bλ n K + W ) = [t n (1 − λ n ) + tysb λ n ]K + tysW 1 − λn + tysb λ n K + tysW = t n λn 1 − λn + tysb K + tysW .......... .......... .(5) = t n λn Ts5 λn Gross surplus 1− λn + tysb K n + t y sW + W ) − t n λn 1 − λ n + s (1 − t y ) W GS = K n sb (1 − t y ) − t n λ n t 1 − λ n + s (1 − t y ) W .......... .......... .( 6 ) = K n sb (1 − t y ) − n λ λ n GS = S − T = s ( bK n λ = λn 1 − λn GS6 λns ty,tn 6 W = 0 GS 1 − λn sb(1 − t y ) > t n λn sb > t n 1 − λ n ................................(6.a ) (1 − t ) λ y n λn6-a *gw6-a λ g w λ = sbλ ≥ tn ..............................(6.b) (1 − t y ) 6-b2 2Concave indifference curves Iso-utility Proposition 1 g K K > 0 ↔ g < 0 :ﺍﳋﻄﻮﺓ ﺍﻷﻭﱃ λn λ = K n n K = K K λ n n ∆k ∆K = ∆K n λ n S - T > 0 6tg ∆K = ∆K n t = (1 − t g )sb(1 − t y ) − n K n + (1 − t g )(1 − t y )sW λn λ t ∆K n = λ n (1 − t g )sb(1 − t y ) − n K n + λ n (1 − t g )(1 − t y )sW....(7) λ 7 g g= ∆K n t = λ n (1 − t g )sb(1 − t y ) − n ......................(8) λ Kn s,λg dg > O, dg > O dλ ds 8 tg, ty, tng tg = tn ≠ ty tg = tn = ty :ﺍﳋﻄﻮﺓ ﺍﻟﺜﺎﻧﻴﺔ tg = tn ≠ ty 8tg = tn t g = λ n (1 − t g )sb(1 − t y ) − n λ g= λn 2 1 t n − λ n + sb(1 − t y ) t n + λ n sb(1 − t y ) λ λ tng dg 2λ n 1 = t n − λ n + sb(1 − t y ) λ λ dt n d 2 g 2λ n = dt 2n λ tng d 2 g 2λ n >O = dt 2n λ tn dg = O g dt tn = λsb(1 − t y ) + 1 2 g = 0 tn = sb(1 - t y) tn=1 3.3, 3.2, 3.1 ∆k 9 t O = λ n (1 − t g )sb(1 − t y ) n + K n + λn (1 − t g )(1 − t y )sW λ Kn = λ(1 − t y )sW t n − λsb (1 − t y ) .......... .......... ......( 9) Rectangular hyparbola 9 tn t n = λsb(1 − t y ) 494 3.4, 453.3, 3.2 6.2tn6.1 g < 0 k K > 0 ↔ g < 0 tg = tn = ty :ﺍﳋﻄﻮﺓ ﺍﻟﺜﺎﻟﺜﺔ 108 1 g = λ n (t n − 1) t n sb + − sb .................... .(10) λ tng tn=1tn tn t n = sbλ < 1 sbλ + 1 λ 10 1 1 g = λ n sb + t 2n − λ n 2sb + t n + λ n sb. λ λ dg 1 1 = 2λ n sb + t n − λ n 2sb + dt n λ λ d 2g 1 = 2λ n sb + > O dt 2n λ tn = 2sbλ + 1 dg g =O 2sbλ + 2 dt n λsW Kn = tn − sb 1− tn tn = λsb 1 + λsb K g ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺜﺎﱐ Wage subsidies ty GrowingStock KW Proposition 2 tg = tn = ty ﺩﻋﻢ ﺍﻷﺟﻮﺭ ﻣﻦ ﺍﻟﻀﺮﻳﺒﺔ ﻋﻠﻰ ﺍﻟﺜﺮﻭﺓ ﺍﻟﻨﺎﻣﻴﺔ:ﺍﳊﺎﻟﺔ ﺍﻷﻭﱃ h h = sb(1 − t y ) − t n λ t K n = sb(1 − t y ) − n t g = t g hK n λ W dK n • = K = λ n (1 − t g ) hK n + λ n sW (1 − t y ) dt dW • = W = t g hK n .....................................(11) dt Stationary Kn = W = 0 µ λ n (1 − t g )h − µ λ ns(1 − t y ) -µ tg h =0 u 2 − uλ n (1 − t g ) h − t g hλ n s(1 − t y ) = 0......................(12) u= [ 1 λ n (1 − t g )h ± 2 (λ h ) (1 − t ) 2 n 2 g ] + 4λ n t g hs (1 − t y ) ........(13) λn, tg, s, h > 0; tg < 1 λn(1 - tg)h λn(1 - tg)h > 0 W, K K W S(1 - ty) = 1, λn h = 1 Stable arcW = - hknCharacteristic Vectors Unstable W = Ktg +1arc µ = 1K0, W0 ﺩﻋﻢ ﺍﻷﺟﻮﺭ ﻣﻦ ﺍﻟﻀﺮﻳﺒﺔ ﻋﻠﻰ ﺍﻟﺜﺮﻭﺓ ﺍﻟﻘﺎﺋﻤﺔ ﻭﺍﻟﻨﺎﻣﻴﺔ:ﺍﳊﺎﻟﺔ ﺍﻟﺜﺎﻧﻴﺔ t, W, K • K = λ n (1 − t g )hK n + λ nsW (1 − t y ) • t W = t g h + n K n ...........................(14) λ 1 u = λ n (1 − t g )h ± 2 (λ h ) (1 − t ) 2 n 2 g t + 4sλ n (1 − t y ) ht g + n ........(13) λ g W, K Proposition 2 ﺍﳋﻼﺻﺔ
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