Frontiers of usefulness: The economics of exhaustible resources

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1 Sy F f uful: h m f xhubl u by R.C.A. M* h flu f Hld Hllg wk h fld f ml m bh uuul d udg. I h 66 y dvlm, hy uudg h m f xhubl u h ly b gfly hd h ly A h m wv f h h m f xhubl u fm h h f glbl u y d ud h l Cu E A d glbl dmd f ul u wll ml d ml mmd, h muld h ml d ubl xl f xhubl u h h h ubj why f vw. Hllg hy d h um h h md blhg mdl f h ml xl f ml u h duy lvl d h lvl f h dvdul m w, xmd. H hwd h h f xhubl u huld b quvl h mk f d h mk wh g h f x huld b. I mk wh dmd bl ml xl qu h h f x huld dl v m, whl mly mk h hwd h h f x dd. I dd, h ff f umulv du d, h uy d wh m f h u k, h m f xl d u f gl quy xmd. A ly f h ml h, x d ml duy lvl d mdl. A ly f h f du d ml bf h dvdul m lvl ludg l, vg d mgl h ml f du, dd. Oml x f m wh lly dfd v v qu vy dg h h mgl uv. h flu f du d h z f h v h f ml x l xmd d uld df h f f uful f h m f xhubl u. Idu Aully h d lv f h gdu u Ml Em h Shl f Mg Egg h Uvy f h Wwd vwd. h bw ll m d xhubl u dl wll blhd, bu h d f hg uh u, lly mg l, h bf f h ll m h m l vg. Hwv, h ll gh bu d h ml dl f xhubl u, vdd by Hld Hllg d h g u m, m f h ll h u Ml Em. h f h h h xv lu h hy f xhubl u, vd f dm, bu d vd muh h wy f ubl mk mg l b x d dl f ul u. gdu ud wkg h ml duy glly hv hl h h m b, why h m lg h x f xhubl u d wh d h f f uful h mg duy d? h w l qu fm Hld Hllg (1931) h uld hv d h l u f m ul w mgz: Cml f h wld dg ul f ml, f, d h xhubl h ld dmd f gul f h xl. h flg h h du w h f h gd f fuu g, h hy bg lfhly xld d, d h qu f h xv h hy bg dud d umd wfully h gv h v mvm. Wh m, h lv f h wd gw wh m wh w u 1931, muh u w f ug h h l h Hllg ufldd u fly, h bl bugh h m vmh by ll-kw l by ul * Shl f Mg Egg, Uvy f h Wwd. h Suh Af Iu f Mg d Mllugy, SA ISSN X/ vd Mh Rvd vd Ju h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

2 F f uful: h m f xhubl u Bdly (1985) wh k h qu, H h m f xhubl u hld h m f mg?. h w kwd mhz lly dff f u d blm h d by Hllg. h d h wh h f h f ubl dvlm h mg d ml duy, h vlu uddg gum bu lly ml f dl, du, d h wy whh mk guld. h hugh ubl ly muh by d f h glbl ml duy wh h w b bbly dg gd jb f ug h lg-m ubly f bf fm ul u b xd. h m f h v h wk f Hld Hllg d, hvg blhd h m m, xm hw h l ly h ml duy lvl wh ll du f bl dmd uv d h lvl f h dvdul fm m, d gl fm hm h b bflly ld ml dvlm. A fm h dff vw Bdly (1985) bu u h l h mg duy, h vlu f Hllg wk h md uqud by m h ml m. h wk f Hld Hllg h wk f Hllg w 1931 md lgly uxld f bu 40 y bu f h yl d mhml h h u. Oly 1973, wh h wk w ulzd by Rb Slw h Rhd. Ely Lu ld h Em f Ru h Ru f Em?, dd h wg f Hllg bg ff h ml u duy. Slw hghd h flu f h wk bu, bg v h wkg bu u y, h d ju f h OEC ud h d l h x dd w du udd flw f lu dlg wh u bu h ll d dl f u. Hllg mdl d gl mmdy v m d v hugh w hv bvd uh ul ly (h l fv y), h mdl h b ud by umu uh uful f du h vu dm f ml uly d vlbly (Egg, 2007). Amg h h h mdl hl du h: uful d f y, f mk fug wll h ff f xl d hlgl v gfly d mly flu ml vlbly v m Mk uu m (m vu mly) Ml u hmgu Bk hlg lm h dg whh Subu m d y Chg dmd flu d vlbly. I h wd, h mdl vd vhl f dug h vu dm f ml uly d y (Egg, 2007). I l ld Hllg Em f Exhubl Ru : Ffy y l, Dvj d Fh (1981) lb h m f Hllg l ffh vy. h m w hw hw Hllg (1931), l h hd b gld f lg, hd wd my qu h bu f h dquy f h wld ul u h dd bw 1972 d hy u h Hllg f wg h w fly h ly db g u f h v mvm d dly dvl dqu hy f h xl f xhubl ul u. Hllg um Hllg (1931) blhd vl m um f h xv mdl f ul u h mly d fl uh h l wld f ml x. Cdg h um whh h ul bd, hdly ug h h ul b vfd mlly. h mdl um fly, h h m w bjv mxmz h vlu f u d fuu f. h qu h x k l lg ff h mv duy qulbum, whh ml h ll m dl m f d h hy ll k f d u mk f fm. Sdly, h m fly mv d h l v h v f du. A hd um h m du d by xg y; my du muh ll lk y m dug h lf f h m. h fh um h h d h lzd vlu. h, gld d h gud l w (d y) h m wy y h du fly. Fuhm, h umd h h h d m bl d wuld b md f, d h g y (f xhu f h b m) wuld f lzd vlu f d, whh uld h b md. Ffhly, h umd h u k hmgu d quly h uy bu h z, gd d g f h d. Cu d fuu d x kw. h ml h bdy h ufm quly gd hughu d h h hg gd f h mg d. M d gd l ff, wh dvu uly h mll ly wh bv gd, gz h ffh um b mj du fm ly. h xh um h h f mg x d hg h bdy dld. Ag h um d gz h ll m f g h dld. Udgud mg h mg f bm lg d d d mv fuh wy fm h hf ym, whl hul d bm lg d bm gvly lg d d. A d Hllg um h h mgl u 540 AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

3 F f uful: h m f xhubl u (dd mg u, mu) bl h m, h um h h mgl f x h ul z. I dd, ml h h mk d h f x d by bl, dwwd lg dmd uv f h u (Slw, 1974,. 3). I h d mdl h z f h mg k dl whu v bg ugmd by xl dv. h fl um h h hlgl mvm dug h lf f h m d h w dd h u k bud by xl. Whl h h Hllg ld g h m, h um d dmh h l vlu f h l f h m vlvd ml dvlm. Hwv, h vlum f lu h h lfd h dv f h m f xhubl u, ugg dmlly lg hy. H l h blm. I lly hl m u h vd hug gh lm f mdlld m wh vyhg bhv m m. I h lu Dvj d Fh (1981) h Hllg 1931 l h l u f wk vguly gwg bh f m. (.71). H lg ly, d, ju d l mdl vd m wh uu buld h lm g hd f m. Slw (1974) d h, Gd hy uully yg ll yu mhg, v f h ll uh. (. 10), lhugh h m f xhubl u d vd h l wld f mg d ml x y lg x, ll whwhl -xm h hy. A wv f h uu fm Hllg wk my vg lxd h ly um d dud flxbly h wdd h f h mdl l. Hwv, wh m hghly d m mdl, lxg h um mgf h uy d wh h uu f h mdl. Hllg h h dl f xhubl u b ld bh h duy d h dvdul m lvl, d h l f Hllg wk bh lvl dd. Oml x f xhubl u duy lvl h f xhubl u mu gw h f Slw (1972) d u h ml d, wh vlu fm h l f x d l, l w d y. h m dff h ul u dubl d h h z f h xg k v, ly d hugh m. Ev wh h bly f m ylg, ml mmd wuld m xhubl u. Adg Slw h m f Hllg wk bd h h h ly wy u h gud du u u f w by g vlu (. 2). h h bm h fmu Hllg - ul whh flly h h f xhubl u ( vlu f xhubl u h gud) mu gw h mk f, d gv by h quly: wh h d, 0 h h l d, d h mk f. h f u hld ly f x z. M glly, h f f ll v f h mdl (z x, v, g ). I u v ud mly, whh mgl vu l mgl x h f. h vlu f ml d l h vlu f fuu l fm, l h f x. hu h ( ), whh h mk mu h f xg f (mgl ),.. = m, huld b xd gw xlly h f. h mgl huld lud h mu d fxd d vbl, wg, x, dvdd, d f mk u, uff du h m w v ml dvlm h f l. h ml f h b xdd m h h yly (h f h x ) f h mgl u f x, wll h f. h xly h df f yly. I h dl vlu f ul u ul f h x f u f h u, h ym du h w f h xl f h u. h m huld h b hy y h yly h w f h u, bu bf h v md f. I ly m w lh y h mu h w f h u, uully h fm f yly h gvm, hy vw u b d bu f h ul kll d h k hy b ml vm vu. h um f g u vlu w l hvd by Gy (1914) wh umd h u md v m, whl h mgl f x. h h w l vgd by Cll (1954) wh ludd h h gwg dff bw ml d h f x w xly qul h mk f (Dvj d Fh, 1981,.66). If h hy, gw h f, hy gw dfly. h mu m m wh hgh h du fll z d, dg h hy, h l dud wll l b h l h gud. A Slw (1974), h u wll b xhud h h d lf u f h mk (. 3). I huld hwv b d h h dbl bdy f h ludg wk by Aw d Chg (1978), h u xm h - ul, mly bu d bhv Hllg dd! If h w u f h m ml du, mbl f hm bh ud ml d f uu, ul h f x dl. If h f x dff, f h lw d h h hgh du wll. I h h ju mk, bu qu f mk wh h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

4 F f uful: h m f xhubl u uvly hgh, fm w ul h m f xhu (Slw, 1974). h x f h d h h lw du h f h, mk d Ru 1 dld, h x lw m m du, d ul ll h, v fm h hgh du xhud, whh m du f h ul ml wll. Alhugh h qu wuld mxmz h wlf d bf y d h m w, h wy f fly dg h d dg x, v f gv g h wy, d dly, f udg w dl h ly gv qu. h h bk hlgy (Ndhu, 1973) hgh ubu l du fm h ul u, f xml ul w lg l gy u, vkd h u lly xhud d mk hv wh h f h hlgy bm mv. h ully lv h u glbl gy mk wh uum h fm l h US$5 ud US$115 ud h f dmhd l ul d gwg uy f uly lm lg h v. hu, h f h bk hlgy vd lg f h ul u (Slw, 1974,. 4). Slw (1974) d Hwk d Olwl (1998) l dff bw u h u k d h h u ml flw. Glly h flw mk dd ubl, whl h mk f ml k vdd v f h mk. h flw qulbum d h gw h mk f. Ibly h flw mk d by x bu fuu, whh ld ulv whhldg f uly wh hgh d d xv dumg f uly wh xd fll h lg m. h ly f mk d k h mk u, whh u w blv h vlu f h du hd mwh h fuu. If h lg m g h xd, l l wll b ud h vlu f h k wll hv b w dw, v v. If h f x h Hllg ul xd h h ju. h yly, h udud vlu f u f u, h y, h uy, h mgl f mu mgl vu l mgl, d h f x, f h xhubl u ll yymu, d h ully h ml f h f x. If h ( f x ) g h f h h dud vlu f mu b h m ll d, d h udud vlu f h u mu l gw h f. h uully fd h flw d (Hwk d Olwl, 1998). Fuhm, f h vlu f h u gw h f, h b bf fm g dg h f x y d. I h dmd xly qul uly vy lvl f du d h mk l vy m (Slw, 1974). If dmd bl h f x dl v m z Hllg mdl h mk d h f x by dmd uv f h u. If dmd bl h f x mu dl mlly z, h wh h dmd uv h uv f, hw Fgu 1. F mv fm mufug dubl gd, h f du h uh h = MC d mxmz f. F h w f -wbl u h quvl d = MC + h uy f dl, mlyg h l f h u wll b xd y d, h f w wbl. h l l h h f Hllg h d llud h xml d Adx 1 wh h ul bg hw bl A6 d ghlly Fgu 2. h ddl mgl vlu h y h mgl u. h x f h mgl u ml h ff x f fm m wll xd h mgl f x, g y f h u, whh d by h w f h u d bm f h du ulu vdd y gh ly dfd (Hwk d Olwl, 1986). h du f h f y ff u uddg f ml ll f h u hghly f wy. A m f h m h h b dym, g h m f m h f h u (L, 1991,. 1 4). Sy m uy h mu b ud f dmg hw b ll u v m. Ouy f y d h fg vlu f h x b lv h w h. Chg ml dvlm vm m h h my vlbl f h u. Fuhm, ddl u bv h fm mg, whh my hv ud fm g y h fy, wll b l. h ddl vuly fd mgl u (fm h uy h u f mg f dy), y, yly,, mgl f, m, hdw Hllg. h m w mu v h uy f dl bu dy wll m wh h v mlly Fgu 1 Sy mgl u f -wbl u 542 AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

5 F f uful: h m f xhubl u ud u. Sy ml h h d lly dbl huld b hgh h h mgl f x, by mu quvl h uy, f fd h y (Fgu 1). h f h y ddd h m h quy q 1 xd h h quy q 2 f h w y. h d bw u, whh ludd f h du ulu d h, uh x, l whh hy ully d (l, 2003). Mgl f x ully d, um u, whl h mgl u by, uy h wuld b d h fm f dud bf f x f h u w ffly lld v m (L, 1991,. 1 4). Wh h ll uh h bf mxmzd, h ully b, d hf, h w f h u y. h u f du ulu lmd by m. Cquly, v wh m m d, h f wll-dfd y gh, mk ll d ff ll dl (bg, 1988,.42 45). R f x ml mk dd Dvj d Fh (1981) h u mly d h u mk gd f dg h ff f mly f du. I huld b d u h ly m mlz lz h ml mk hv vd ful d, m f h, vy ly h wh y m hm. F m h u d h f h mk h l lf uu d gg m lz 1925 d ud ul h md-1970 md 80 wh h l mlly lld (Cw, 2003). Slv w l h ubj f lz m d ldg u 1980 wh h Hu bh d ll h lv mk, bu g h u d h u mvm f h ml bhd h d mk vd b udbl (Lu, 2002). Nvhl Hllg (1931), hld h vw h v m mly wuld b fl d l dly h mv mk, d h f dl wuld b lw mly mk h mv mk, hw Fgu 2 (Dvj d Fh, 1981). h ml, wh by g uu, d lw h du h dl h u, bu h h d f wh h u mgh uddly b xhud. h mv u w, bu h k, wg k dvg f h mk, wll y dl h u f bl. Slw (1974) h uuv, bu mug dlgh h uh h ml f h v fd, mhg bh wuld b ud kw. Adg Dvj d Fh (1981), h mdl d by Hllg lxd lud h bly f gwg l f ubu h mly mk. I ly d h ml d uu d k dvg f h l dmd. Hwv, f h ml u h dmd f h du my bm m l (fll), h lkly l dl, whl h u f h ly f dmd. A gl m d l wh Hllg lu, Dvj d Fh (1981) ugg mly lw dl (. 68). I huld b d h h x h ml wll f lw dw du (du l dy h ud f m), h lgd wh h f h v wh d h w dlg u u qukly. h ff f umulv du d h ff f du x d dmd hv b xmd by umb f h h, mg hm Hfdhl (1967), Hl (1976), Slw d W (1976), Wzm (1976), d Hwk (1978). I ml m, x h umulv k gw d vdd h k d Ouu Mly Mly uu Cmv Cmv uu m m Fgu 2 d uu j f mv d mly mk (f Dvj d Fh, 1981,. 67) h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

6 F f uful: h m f xhubl u vlu hugh m fm f ug, Hllg - ul ll hld. If h k d d h wll b fd dw d f g h f. I h mbd f g x d fllg dmd, wll fll, bu wh h k d h wll fllw U-hd jy (Lvh d dyk, 1979). Dvj d Fh mm h h udk by dyk (1978), wh hwd h f h k ugmd by xl dv, fll h mj fd md, bu vully wll. h ff f du k f umulv du gw w f d by Dvd Rd (1817) wh h ly f m gzd h lk gulul ld, ml u wuld u lg uly, bu qu dff dg f gd. Rd d h h bd dld, lw gd d wh hgh x wuld b xld. Hllg d h h f h h w f m dug dubl uh gld dmd mk wll dd h u f du, wll h umuld k ul. h f h, dg Dvj d Fh (. 69), h x h m bm d d h h dmd f dubl uh gld d dmd ffd by h mu f umuld k ul. h ff f uy bu u m Hllg xmd ly qu bu h uy f u m, kg: Wh h vlu f m, wh udly fully kw d, wh h ff f uy f m? (. 139). Ffy y f Hllg wk, Dvj d Fh (1981) f b ly h h vy f qu h h qu f dvlm dmkg ud uy. hy d h Hllg v wd h qu, bu d xmd xl uy d ml f ubl ly (.70). H m h g w h fm udd d uxd ml dv ldg wld uh, mmly wful lly, lm vlubl y. I fm h m by Dvj d Fh h Hllg w d bu h bly f dv f ml d fl lm d xlud m fm. h u ld lly xv (d hf wful) lvl f xl vy. Hllg l gzd h w djg ld uld bf fm dvy fllwg xl d u ghbu y, whu v vg xl vy hmlv. h -lld llv f glgl kwldg ld hgh ld d x f, mly by bvg h um f h ghbu xl vy. Hllg blv h gvm ud f h l my hv gh x x f fm h w bhlf f h d llw uh wdfll m v hd. Suh fm llv ff l ld lly ff lvl f xl bu vy w ud hg h ghbu wll dll f (Dvj d Fh, 1981,. 70). Uy bu h uly d dmd f u h m x wd Hllg qu bu h ff f uy bu h u m f m. Aumg h m f ufm gd, h w x h ld h kwldg bu h z f h mg u. If h u bu h z f h k h wll d dl lw h vv h h f h bu h m, mly bu h h wy f kwg wh h wll u u f, muh lk h m dvg whu l gug (Dvj d Fh, 1981). Uy f u b dud by xl, w fm bu d k my bm vlbl whl dlg h u v (Hl, 1978). Svl h hv mdlld xl d lkd (Aw d Chg, 1978), uu h (dyk, 1979) d dm du fu (Dvj d Fh, 1980). Uy bu dmd f xhubl u luv (Dvj d Fh, 1981). Adg W d Zkhu (1975), m w wh kv wll dl m qukly, hg mk m my, f h d fuu m u h h fuu. If h k-v w blv h h d l muh w ym h fuu, Lw (1977) h hw h h wll dly x bu du huld b lw fuu d hf h mu k wll l b lw. h h whh dmd my uddly d, mly, hugh m hlgl dv, h du f ubu, hugh x f h u (Dvj d Fh, 1981). I uh Dgu d Hl (1974) d Lg (1975) hv dmd h h dy l u du. Exl Ml dv bu f xl, bh h dvdul m d duy l, ld h z f h u k. If h f dvy xd h f dl, k d x. Exl h h b fu, f du u d fuu x. Hgh v m lw x, whh wuld xl why m xl d hld v (dyk, 1978). C (1991) f h h w dv f m ly x. Sdly, g dv h h m u x mbl wh dmd. h y v dmh, d fll wh w dv md. Ulm y dd h vlbly f xl. If h umu xl, u ulkly vg h lg u. If h ly fw v xl g, u my vg, bu lw h dd by h Hllg ul, mly h. h hd fu f xl h vd w fm bu bh, () udvd u d () x ( h lk f) f xg bd. L 544 AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

7 F f uful: h m f xhubl u (1995) hwd h h hgh h mu f u dvd ( y d f xl), h lw h u f dvy, flg h ml luky dvy. Hwv, h hhld v, whh xl wll um f h dvy, wll b hgh, flg m mm bu fuu. Suh v h k m h u my dmh wh m. h ff f ml dl gl quy Alhugh Hllg d du gl quy, muh mm bu h h. Suh mm h b d h hu f ubl dvlm wh lg d gwg fld f lv, lly h f ml dvlm d dl d fm gu g qu bu l h f xl f h wld ml u dwm. Alhugh h g 1972 w vbl ll du ul u hg (Mdw d Mdw, 1972), d mmdy w dg y gl, w ll u xl h h ul u v g. h m u k h whh m w d y wuld w du fuu um ulu. Oly wh m d y h h m du mv qulbum mxm h um f dud um lu du ulu fm ul u (Slw, 1974,. 7). Adg Hllg, h ml lu kwd f: vl w um h m l g fld, f uy bu xl um ld wful uh d ul f, d f lg ml lgl x wh h xv du. If v du hgh h l, h l f h du qulbum wll b uh h y d mk wll f d quly u wll b xld f d dld (Slw, 1974). h w m h v du hgh h l du fly mmd f l k bu f lk f u mk. w xml dd by Slw: fly uy f u y f k f h ml duy f whh h u, d dly h x m fm l; dvdul bu h f x u l d y bu h bf x u (Slw, 1974,. 8). Exml f ml dl duy lvl h m lu bu h ml xl f xhubl u h Hllg vd llud ug h fv d mz fl hw Adx 1 f h dl f 2500 f v fv uv d. h mgl f x R200/, h du 5 d h l dmd uv f h mmdy = q. h ul f ml dl ly f -wbl u v fv d hw bl I d ld Fgu 3; h fllwg lv: h quy xd h d fll v m (Fgu 3 d bl I) h ml h h du v h lf f h m mxmum d dl v m z. I h duy h m x l h d d bu h dmd uv bl,. Fuhm, ll fm dl d ll x qul, llwg h x h q 0, q 1, q 5 hw h fv d xml (bl I, Fgu 3, d Adx 1) mv duy qulbum whh l wlf (W) l mzd. h bu W mxmum wh mgl ulu (ml ) qul d, whh Hllg - ul. h udud vlu f ml h mk f v m d by xm h vlu f ml v m, hw f h fv d mz ul Fgu 3. hf h fm mk h m f m f vlu d h fm dff h m f x. Whl h my b d f Hllg mz, h flw f ml fu f, uuully vll dm f ulu. Oh -lld hk h my ff h mk lud w fm bu h vlum f v, vbl m fm ububl ml, fllg f mg hlg, -m ll v d d mvm du (Slw, 1974,. 7). Ml l h h f. Whl h 5 f l h f f h ml h ml ly ly f 3 ( bl A6 Adx 1). Wh huld b d h bh h d h dmd uv k gv h mg duy by h f h my. h l dmd uv l mk f ml quy dmd h gv l. I u ul xml, h dmd fu = q, h hk f R700 wh dmd g z, whh h k h l b ly dld. bl I Rul f fv d ly f ml u x d Rmg R V f R v l Su: Adx 1 h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

8 F f uful: h m f xhubl u Fgu 3 Chg du, mg v, ml ( ), ml d h vlu f f 2500 u ud d f ml u x Oml x dvdul m lvl h l f Hllg gh h dvdul m lvl h b xld by umb f vg, ludg Hwk d Olwl (1998). A h lvl h Hllg ul k lghly dff fm h, h h h gwg h f, w mk h um h h m, bu h du dly dl v m. h mxmz h m f h duy d dvdul m, mly, h h dud vlu f h ml, l fd h y, mu m v h lf f m. Mgl ly f m h l h mv fm mxmz f wh h f du h h = MC, bu f fm x f xhubl u mxmzd wh () = mgl + uy (), hgd h fudml wy bu h u f. F, m dlg l, d f whh vlv, whh gh u f h l fuu uy. hu mxmz qu h mgl f ( h Hllg y ), b h m h d. Sd, h f dl f xhubl u y f vm blm. h h f whh v, dd h v x f h f u,.. vlu v m. h mgl u h m h u, mly h vlu f h h gud. Wh v, h h f dl u. If u dd vlu v m, wuld v m, bu vm lv wuld b m vlubl. A w f xg m wuld w x ll h qukly hlgy wuld llw hm, bu h wuld b hldg h w g l muh vg u uld gv. Alvly, f h vlu f h h gud w g f h h f, h wuld b v m. O lf h gud wuld b wh m h (h bdy) dud z hugh mg. hd, h mxmz d ffd by h k. h mly m h h mu f md xd h f v. I d mk mg whwhl, mu xd h mgl by mu qul h y (Hllg ), = MC (q) + y (Hllg) y = MC (q), mu b h m fm d h x. Fuhm, w w: by gg h Hllg - ul f x. I d fy h mxmz l, w d ff by qulzg mgl f y w d, d dd by hwg h MC(q ) qul. h llud Fgu 4. Fuhm bu MC(q ) qul, w y h d mxmz f vy d h mu h f,. Alvly w uld y h vy d mu b qul. W l w h qu, Wh huld h f du b d mxmz f? A quvl (q (+1) q )/q, h MCq g. R h my b fd u, yly, y Hllg. h ymbl ud f, : W d l h h fu dd : h f du (q) d, h mu f mg h v f h d f x (S). S C = f (q, S). 546 AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

9 F f uful: h m f xhubl u Fgu 4 h ul y h f mxmzd vy d f h h d h m. H MC(q) d mu qul MC(q+1) d +1 (Mdfd f l, 2003 d Hwk d Olwl, 1998) bl II (R/) -m (q ) Mgl uv Quy () Oml dl f h f dvdul m (R/) -m (q +1 ) 0 0 q q +1 m R f Rmg R (-AC) Avg Aul vu N f v Dud y du v AC (-AC)q lf f m l Mgl uv Quy () W hv k h qu, A u xhubl u bg dld dly lwly? h ld h x qu, Wh u ml u f xhubl u? h qu mu b dd fm h lly ff d mv mk vw. Oh ml, whh my, lud mly, l bhvu, xl, hlgy d ubu, d qu f gl quy. Exml f ml dl fm m h hdul bl II llu h l f Hllg l h dl f v fm dvdul m. I h h vg fu h m h ud Adx 2. I dd, f h k f m, g f 2500, ud f h duy mdl h l b ld h dvdul m mdl, bu h v dld v gh d h h fv. Ag h um md by Hllg ly wh mh h f h h dbu f gd h bdy hmgu d h x. h mhd uggd by Cd (1999) f h ml dl hugh uml ll blm h b ud. I h ul h Slv fu Exl w ld wh h g ll bg h l f h f v h lf f h m (bl II, Clum 8) d h bg h h dud vlu f h mu b h m vy d, h h um f h dud my xd 2500, d h h mg v h l d z. Exl Slv ly llw f 100 d bl lv h mz h dul mu f h l d (bl II, Clum 3, Rw 8). h l f h gd mgh b hd, bu vhl llw h b llud. h fllwg f Hllg l vd h dl f dvdul m v, hw h dl hdul f bl II d hw ghlly Fgu 5. h m m h h dvd fm h dl f h bdy xlly wh m d h vlu f h dud h m vy d h f du fm h m dl v h lf f h m h l v xhud h l d. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

10 F f uful: h m f xhubl u Fgu 5 Dl f h dvdul m v gh d hwg g h f d f du dlg v m I h xml h f h mmdy m hughu h lf f h m, bu h vg dl dug h m d, d h h ul vu d f h d (bl II). Clu h wk f Hld Hllg 1931 dd by my b h gl m m bu h uddg f h m f xhubl u v md. h b dub h hl lvl h h d vdd h d f hug umb f h ff md dug h d 1972 h ly 1990, ly w dd wh h gwg y f ul u w f my. I m f bu mg h hy db xly hw ml u huld b dld, vdd w mk m g um. h x f xg ml u h mg duy, hwv, gfly dff h d hy. h h gl m m bu md by Hllg gudg h hdul f x h h dud dvd fm h l f h ml, huld b h m vy d. I d hv h d, h gl g hudl h h f dl huld dl v h lf f h m, bgg mxmum d dg mmum ju bf h m l. A h duy lvl h m h h l f bg hd ju h f h mmdy h h wh ld by h x m f bdy, h hk, h mmdy ld by bk hlgy. A h dvdul m lvl m h h f dl h mvd dly dw h mgl uv, fm wh mgl qul mgl vu, wh mgl qul vg. A h h m huld b lly dld. If my u bu wll g, ly ml f, d ju uvv. h lu d dv u hkg g h m f mg, bu l h w xl h m f xhubl u, ully bu m muh, bu d dlv muh h wy f vlubl l mg. I dd, h ml vlum f h dmd h w xm h hy d y udd wh bu h wk h h md lg. h ug h f Hllg y h quly bu mhg k h fx-hu: u whh wy uld g x. By d lg h vg m v w h Hllg-y y x, f l d m dfyg d hdulg h uu dg hm (l, 2003). Rf ARROW, K. d CHANG, S. Oml g, u d xl f u ul u k, hl R N. 31, Dm f Em, Hvd Uvy, BRADLEY,.G. H h Em f Exhubl Ru dvd h m f mg?, Ahy S, (d.): g Nul Ru Em Ey Ru Aly by mmb f h gmm ul Ru Em (NRE) h Uvy f Bh Clumb. Cld, CARLISLE, D. h Em f Fud Ru wh ul Rf M, Am Em Rvw, Smb 1954, CONRAD, J.M. Ru Em, Cll Uvy. Cmbdg Uvy CROWSON,. h Il Agm: bl.. Cw, ASRIDE MINING, Iu d l f h Ml Iduy. Mg Jul Bk Ld, Ld DASGUA,.S. d HEAL, G.M. h ml dl f xhubl u, Rvw f Em Sud, Symum, DEVARAJAN, S. d FISHER, A.C. Exl d y, CMR Wkg N. I-290, Uvy f Clf, Bkly, DEVARAJAN, S. d FISHER, A.C. Hllg Em f Exhubl Ru : Ffy Y L. Jul f Em Lu, vl. XIX, Mh EGGER, R. l mmu GRAY, L.C. R ud h um f xhubly. Quly Jul f Em, vl. 28, My, AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

11 F f uful: h m f xhubl u HARWICK, J.M. d OLEWILER, N.D. h Em f Nul Ru U. H d Rw ublh, Nw Yk: HARWICK, J.M. d OLEWILER, N.D. h Em f Nul Ru U, 2d d, Add Wly ublh, HEAL, G. M. h lh bw d x f u wh bk hlgy. Bll Jul f Em, vl. 7,. 2. Auum HERFINDAHL, O.C. Dl d h Em hy. M Gffy (d.), Exv u d x: dg. Cmm x, Ru d Em Dvlm. Md, Uvy f W, HOEL, M. Ru x, uy d lg, Bll Jul f Em, vl. 9,. 2, Auum, 1978: HOELLING, H. h Em f Exhubl Ru. Jul f ll Emy, vl. 39, Al 1931: LEVHARI, D. d INDYCK, R.C. h g f dubl xhubl u. M.I.. Egy Lby Wkg EL79-053W, LEWIS,.R. Aud wd k d h ml xl f xhubl u, Jul f Evml d Em Mgm, vl. 4,. 2, Ju LIU, H.C.K BANKING BUNKUM, 3: Sll m h US x. I: Glbl Emy, Ol A m, Dmb 10h, Fud wb h:// 17h July LONG, N.V. Ru x ud h uy bu bl l, Jul f Em hy, vl. 10,. 1, Fbuy, MEADOWS AND MEADOWS. h LIMIS gwh: A f h Club f Rm' j h dm f mkd, Ld, Eh Ild, NORDHAUS, W.D. h All f Egy Ru, Bkg Em Avy, 3, AAS, J.L. d HIRSCHEY, M. Fudml f Mgl Em. Hl- Sud Il Ed. h Dyd, Nw Yk: INDYCK, R.S. Oml xl d du f -wbl u. Jul f ll Emy vl. 86,. 5, Ob 1978, INDYCK, R.S. Uy d h g f xhubl u, M.I.. Egy Lby Wkg EL79-021W, Adx 1 A ly f h h x d ml h duy lvl hl bkgud I mv duy wh h fm k d wh h mk d f x d hugh h dmd uv, h fm h duy g lg dd fuu duy hdul x l d l fm k d by d. h l d xhubl u hy h du mk f, wll lg bl dmd uv bu f g y. I ff h dd h h bvd fuu h uld b wh hdgg gmm. h duy bjv mxmz h vlu f (NV) fm h dl f ml u, dd h h f mg (R), v h lf f h m ( = 0 = ), ubj h h h um f x ll d qul h k f h gud. h -lld uy (lu h ) h uld hv b d f x hd ud h f d d wh x h ubqu d, mu b dud h f. Mxmz qu h h h flw C(q) h d f du (q ) b dmd. N vlu d 1 wll b dff fm h d 2 bu du h hgd h z f h mg v d h h vlu f h. h hg h v wh m, ds/d = -q() d h k S,.. um xd h gl k S. A ml xml f d mz blm h llw h b mxmd v w d, ubj h h l x qul h k h gud, hw by Hwk d Olwl (1998) ug h mhd f Lgg mull. h bjv fu gv by RICARDO, D. O h l f ll Emy d x. hd Ed, ublhd by Jh Muy, Ld, SESINK-CLEE, R. y Lm d Cu-ff Gd. M Vlu d Gd Cl Shl, 6 d 7 Ju 1991, Mk, Rdbug. Suh Af Iu f Mg d Mllugy, SOLOW, R.M. h m f u h u f m. Am Em Rvw, vl. 64,. 2, My 1974, SOLOW, R. M. d WAN, F. Y. Ex h hy f xhubl u. Bll Jul f Em, Mgm. S. vl. 7, u IEENBERG,. H. Evml d ul u m. hd Ed. H Cll ILON J.E. O Bwd m? Ag h h f Ml Dl. Ru f h Fuu, Whg, DC WEINSEIN, M. C. d ZECKHAUSER, R.J. h ml um f dlbl ul u, Quly Jul f Em, vl. 89,. 3, Augu 1975, WEIZMAN, M. L. h ml dvlm f u l. Jul f Em hy, vl. 12,. 3. Ju Subj h h h um f h u xd h d q 0, q 1,., qul h l k h gud S 0.. q 0 + q 1 = S 0, wh π(q ) h bf fm l f h ml d, q h quy xd m, h u x d h f. h w S 0 q 0 - q 1 = 0 d h Lgg mull dud h (S 0 q 0 - q 1 ) = 0. h ddd h bjv fu d qul z, h h vlu f h bjv fu m uhgd, w w u vlud Hml qu f h blm. [1] h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

12 F f uful: h m f xhubl u wh h Lgg mull d wh S. fd h y Hllg. I mu h uy f fgg fuu um by xg mgl u f h v h u d. Bu yu m h mgl u ( h mll mg u) dy, yu m mw,.. yu hv fg h bly f mg h u fuu, bu yu m w. Bu yu hv gv u h h f mg l d by mg w, yu u h -lld uy y. h f d d f h lu h mxmz f h bv qu dvd by dffg h bv qu w q 0 q 1 d, fllw: [2] [3] dm h u f h Lgg mull h mz. h m h hk R700. I h xml h l k h gud b xd l 2500, h 5, d R200 h f x h m d = 0, h 0 = ( q 0 ) 200 = q 0. By mkg ubu h bjv fu, w g: Dffg h qu yld h qu fllw: [8] [9] [10] h qu wh h ml f du,.. wh h ml vlu f q 0 d q 1 v h w d? By lmg fm qu [2] d [3], w g: [5] [4] [6] Rgg h qu gv [11] [12] [13] [14] h h y h h yly f xhubl u mu qul h l uly h f, f h l vlu f h u b mxmzd. Igg h qu, w g h fmu Hllg ul h mly y h h f xhubl u mu gw qul h f wh = h l d d = m. h f h ul ml. O v l h lly d bh h h uf. If hy hld whu bg xld, h u mu b quvl h u f h d h v mu du l g l h f. h f Equ [5] h h dff bw h vlu f d h mgl f x, whh h mgl h vlu f h gl u f xd. I dd, Equ [7], whh h uml x f h flw d, ll u h h vlu f h mu b h m h d h m d mxmz h f. h dl dmd uv xml ud by Hwk d Olwl (1998), mly = q ud h, bu h xml hy u xdd [7] Ad lvg hm gv: q 0 = , q 1 = d = Exml f fv d mz f xhubl u h fllwg xml vd mz fl f h dl f 2500 f v fv uv d. h mgl f x R200/, h du 5 d h l dmd uv f h mmdy = q. Dff f h bjv fu f mkg ubu h f qu hw bl A1 A4, wh dg ukw, d. A h d f h mz x vlu f bd, bu d b f h x d h mz h b d ug h mg k h gud. hu h vlu f, h udud ml, hg h d f m. bl A1 Omz f h dl f 2500 v fv uv d Fv d Smulu qu Sk xd d 1 0,25q 0 + 0q 1 + 0q 2 + 0q 3 + 0q = 500 d 2 0q 0 + 0,2381q 1 + 0q 2 + 0q 3 + 0q = 476,2 d 3 0q 0 + 0q 1 + 0,2268q 2 + 0q 3 + 0q = 453,5 d 4 0q 0 + 0q 1 + 0q 2 + 0,2160q 3 + 0q = 431,92 d 5 0q 0 + 0q 1 + 0q 2 + 0q 3 + 0,2057q = 411,35 Sk C 1q 0 + 1q 1 + 1q 2 + 1q 3 + 1q = AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

13 F f uful: h m f xhubl u bl A2 Omz f h dl f 2500 v fu uv d Fu d Smulu qu Sk xd d 1 0,2500q 0 + 0q 1 + 0q 2 + 0q = 500 d 2 0q 0 + 0,2381q 1 + 0q 2 + 0q = d 3 0q 0 + 0q 1 + 0,2268q 2 + 0q = d 4 0q 0 + 0q 1 + 0q 2 + 0,2160q = Sk C 1q 0 + 1q 1 + 1q 2 + 1q = Vlu f 3 = d q 0 = q 1 = q 2 = q 3 = bl A3 Omz f h dl f 2500 v h uv d h d Smulu qu Sk xd d 1 0,2500q 0 + 0q 1 + 0q = 500 d 2 0q 0 + 0,2381q 1 + 0q = d 3 0q 0 + 0q 1 + 0,2668q = Sk C 1q 0 + 1q 1 + 1q = Vlu f 2 = d q 0 = q 1 = q 2 = bl A4 Omz f h dl f 2500 v w uv d w d Smulu qu Sk xd d 1 0,2500q 0 + 0q = 500 d 2 0q 0 + 0,2381q = Sk C 1q 0 + 1q = Vlu f 2 = d q 0 = q 1 = h ul f h ly hw bl A1 A4 ummzd bl I d ghlly hw Fgu 4 f h m x h lu h qu bl A1 vd h ff x fl f -wbl u v 5 d d h vlu f 4 = : q 0 = q 1 = q 2 = q 3 = q 4 = d h um f h k xd Adx 2 A ly f h f du d ml bf (ml ) h dvdul m lvl h h h f du h mxmz vlu y dff fm h f du h mxmz h vlu v h lf f h m, bu f h xhubl u f h u d y, llud ug uv fm d Hhy (1985) d w l vgd by Sk-Cl (1991). l, vg, d mgl Sh-u f mxmz (mz) f m wh g vm budd by Hllg um hw blw. W um fxd fxd d d by h f h y x, d h l fu z-hd uv lk h hw Fgu A1. Aum mmdy f R15 : l vu (R), R = 15*q. Al, um l fu f h m C = q 2q 2 + 1/3q 3 wh R15 h fxd (uk ), d h m f l d wh h u f fxd u h h u. A uv hwg h bhvu f l, fxd d vbl d l vu hw Fgu A1. l fxd, v f h fm dd hu dw h h u wll ll hv ud h fxd. l vbl d wh h u f vbl u h h u. If l vbl qul z m h vbl u mlyd, d VC wll u. Wg ylly f h m l vbl. If h m w u bk Fgu A1 l fxd, l vbl, l d l vu f l qu C = q 2q 2 + 1/3q 3 h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

14 F f uful: h m f xhubl u du, ly ff wk, wh d du wg d h l vbl. l vbl gv by VC = 8q 2q 2 + 1/3q 3 (VC = C Fxd ). l vbl l z f q qul z. Avg vbl (AVC) h vbl u f m du; ylly vg vbl wll lly d d h wh g du. h mmum h vg vbl uv qul h dvv f h vg vbl fu wh q, g qul z d lvg f q. [15] q = 3 A hk f h d dvv d 2 AVC/dq 2 = 0,666, fm h h mmum. Avg fxd (AFC), fxd u f uu. I h xml AFC = 15/q vg fxd wll d du. Avg l (AC), h l u f uu h l dvdd by h quy f du. Avg l vg lu vg fxd ; AC = AFC + AVC = 15/q + 8 2q + 1/3q2 A wh h vg vbl, vg l wll d d h bg. h mmum h AC uv l fud ug h dvv f AC wh q, g qul z d lvg. S [16] Sg Equ [16] qul z d lvg f q gv 2q3 6q2 45 = 45 d lu f h q = A hk f h d dvv d whh q = mxmum mmum. h d dvv [17] 1 d 2 h bk-v lvl f du. hy h wh h l vu uv (R) h l uv (C) d wh h mgl vu uv (MR) h vg l uv (AC). 3 h mmum h mgl uv, MC. A h, q = 2 h f dvv f h mgl uv mmum. I h, bu d = b2 4<0, w hv w mgy µ, lu h mgl qu MC = 8 4q + q2, (µ = 2 + 2I; = 2-2). h l wh h d dvv f h l uv z, d2c/dq2 = 4 + 2q = 2q = 0. h fl h l uv u wh q = 2, bkg h uv z f g d dmhg u. Mgl mmum h. 4 h bw h mgl (MC) d mgl vu (MR) uv whh MC = MR. A h lvl f du h l f h l bl A5 Vu f dff lvl f du f h l qu C = q 2q 2 + 1/3q 3 q FC VC C AFC AVC AC MC f R R R R/ R/ R/ R/ Subug q = h d dvv yld [18] Sd dvv g h z, fm h q = 4,247 mmum. Mgl (MC) h hg l h u wh ddl u f uu dud (h f ddl u f uu). I h l f h l fu, h f dvv f h l fu wh q. [19] bl A5 ummz h fm mly FC, VC, C, AFC, AVC, AC, MC f h l fu C = q - 2q2 + 1/3q3 f vu lvl f uu (q). h d hw ghlly Fgu A2. L g l vu (R) = 15q d mgl vu dr/dq = MR = 15 hw Fgu A2. Im lh vd Fgu A2 lud: Fgu A2 A l f vg fxd, vbl, l d mgl fu vu lvl f du (q) f h qu C = q - 2q 2 + 1/3q AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

15 F f uful: h m f xhubl u vu uv (R) lll h l (C) uv. h f du mxmz vu (R C) y. A h lvl h w f fm fly mv mk mxmz h f d h m f h x w mxmz V. 5 h whh mgl (MC) qul h vg l (AC). I l h mmum h vg l uv. h lf f 5, MC l h AC, d h mgl u wll ull h vg dw; h gh f 5, MC g h AC d h mgl u wll ull h AC uv u. Avg wll f m wh f R100/, f uu d by d f d wh h ddl R110/. Lkw, f h f h ddl ly R90/, vg wll d. Mmum AC h g h l uv, whh d by y fm h g. Kwg h l f ( ) qul l vu (R) mu l (C) m h f u qu: = 15q (15 + 8q 2q2 + 1/3q3), h dvv f l f wh q yld: [20] Sg h qu qul z d lvg f q gv vlu f q qul d , d bl hv gv du, u q = h d dvv [21] fm h q = mxmz h m l f. Subug q = u f qu, d h h l f R W b h w ug h f mgl vu d mgl. Dg h m hg lgblly gv: vu v ll h vbl, h fm b ff ug du h h u. If h mmdy fll R4 h m wuld hu dw h h u, bu h mgl vu qul mgl q = 2 MR = MC d 4 = 8 4q + q2 Hwv, f u -R8.67, d l f f dug w u -R S f h hy dff fm h f dul fm w wh w v h mum f du f l. H ml u 4, wh q = 5.32 d mgl qul mgl vu d R C mxmum. h mxmz h f bu h l h ulmd u u. h m h h du whh mxmz h f ( vlu) u m, l mxmz l vlu d vlu, bu h l (ud umd u d) h ulmd lf. h um d hld f mg bd fxd, xhubl ml d. Omzg h f du Ay m w, bu f h xhubly f h ml u, h h mk. H m blk f v w d h h lf f h m m h m blk h d f h d xd h lf f h m. M lf ulmly lmd, bu l vbl, ddg h f du. h f du h mg d (.g. y) dff bu h z f h mg v l dff. I h hyhl d h, whh h l g b xd 50, h f du, whh mxmz vlu y ( 4, Fgu A2) wll mxmz h vlu v h lf f h m f vlu quvl. h mum wll b l h h bu h bf mg fw u f v y lw vg, hby lghg h lf f h m. Sg mgl vu qul mgl MR = MC gv: 15 = 8 4q + q2 d lvg h qu w g v q = d h m f u wll qul = AC f u = 15 (15/q + 8-2q + 1/3q2) Subug q = d h f u qul R5.39. Mullyg by h umb f u dud (5.317) g gv R28.66 h fgu f mxmum l f. bl A6 hw hw f v g du d h hw Fgu A2. If h mmdy fll R9, h h mg R15, h m wuld z f; h quvl yg h m g ml f u. h m wll u dfly. If h m w hu dw w wuld l y my vd fxd l. If h m mk ugh bl A6 Avg l, mgl, ul f d f v h lf f h m f dff f du R f du AC MC Aul f Lf f LM q R/ R/ R m (y) f (R) h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS

16 F f uful: h m f xhubl u Fgu A3 Mgl d vg uv f m wh l fu C = 15-8q - 2q2 + 1/3q3, hwg Aum N f d N f v h lf f h m Omz f h f m du, umg l v f 50, hw by m f u l xml, ld lghly lg l Fgu A3. h w lmg f du 4, wh mgl vu qul mgl d 5, wh vg l mmum. A 4 MR = MC h mg 5.35 um d h lf f h m 9.35 y. A 5 Mmum AC h mg 4.25 um d h lf f h m y. h bf y f h f h A (15 9.7) = R28.36 y. A (15 9) = R25.50 y. h mly fm wh w kw ldy: mg h whh mgl qul mgl vu, mxmz bf y. Hwv, f w d h l bf v h lf f h m w hv A 4 R28.36 y f 9.35 y = R A 5 R25.50 y f y = R hu mg h w vg l mmum, mxmz l bf v h lf f h m. If m vlu dd, h mxmum vlu (NV) u mwh bw h w d dd lly h h f du. A h du fy, h mum h h du wh MC = MR. A h du fll z, h mum f du h h mmum AC. A, mum du MC = MR. A 0, mum du mmum AC. A ly f h ff f mg dff du f h du d bl A7 d hw ghlly Fgu A4. w l d mg hgh du ld. h f d bvu d h f h ul lf f m b lwd. Sdly h f luld ul b fll l dly h h dmd v h lf f h m. hdly h ml f du d bh ; d flly h dff h f du f h w dud. Fuhm, h mum dd h z f h v. Wh v vy hgh l bl f du (.g., l, d dul ml) h mum h h f h y f dul l. A v, mum MC = MR. A v 0, mum mmum AC. Fuhm, w w hw h h mum bm gvly l h v dld d h mg lf f h m h. bl A7 Chg f md hg ld du du 0% DCF 5% DCF 12% DCF R (q) NA# N LM* NA N LM NA N LM #NA: N ul f; *N LM: N f v h lf f h m 554 AUGUS 2007 VOLUME 107 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

17 F f uful: h m f xhubl u N f (R) R f du (/um) Fgu A4 Ig du ld dud f d d f du Vlu Suf dff du Vlu (R) Du (%) Fgu A5 h vlu uf f mg dff du d lf f m xy f du h vlu uf I x f h mdl mgh d h ff f lyg dff du h f v h lf f h m. h h b d f g f du fm 0% 25% d h ulg vlu w b ld uf h db h hgg vlu f h d wh hg h du (/), h lf f m (y) d h dff du hw Fgu A5. h vlu uf db f h ghy f hll h h b lmbd. h uf h wh whh bl mv. Bu h h lv lf f h f lmbg by mkg zgzg h hll, h bj f h x h h umm f h hll h d bl ug h f h ghy bl. h ff wh qud f w xl h d mxmz h vlu f h, bu g u fdg h h u h f h hll. u h wy, w y h h m bu f h f xd b mxmzd. h h h wll ff h ghy h hll h lf f h m, h du ud, d h vlu f h mg, h hllg bg h h umm wh muh vlu bl. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 107 REFEREED AER AUGUS