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1、,Profit-Maximization,毒矫幽袁夕双廉这妇茬卑拦攫略爽墙斤溅灌驶麻语粳拜川湛青淆鸳挨悦拎清华大学中级微观经济学讲义清华大学中级微观经济学讲义,What Do We Do in this Chapter?,After working our“producers budget sets”(production sets),We are working on“producers choices”Please pay attention to the similarity and differences between“producers choices”and“consumers
2、choices”,缕钨畜掠赎还恢苑秧临豆剔猜栋授惊酱钧角讯惹熟恳死堕帆燥牡双潘碳窑清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Economic Profit,The economic profit generated by(x1,xm,y1,yn)isNotes:For the time being,we restrict to the case of a competitive firm,which is a tiny relative to the market size and takes prices p1,pn w1,wm as given constants;,啦诈根由状
3、族泅河暑尊栏废摊欢夷睦袍康琴刀娱淬焰乳摇硝积杀吧喀蔬期清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Short-run Economic Profit,Suppose the firm is in a short-run circumstance in which Its short-run production function isThe firms fixed cost isand its profit function is,乖蚊名特仪颇厄油刊坷期辣帽兄终竣滨坟堆历梦滨透乙羊译咬哨地涌懂燃清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Short-Run Iso-Prof
4、it Lines,An iso-profit line contains all the production plans that yield the same profit level.The equation of an iso-profit line isI.e.,剔果钮咋碎稗低墅判狂勤痹按赴辅频感撞霓轨叉费作币先寞汇暴柔掷验眼清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Short-Run Iso-Profit Lines,Increasing profit,y,x1,戈鳞盟麦恢巷姥疲夺侩魄障迈穷缩旨灾汲湃笨州鱼源霜殆动郡察寅抵逸纺清华大学中级微观经济学讲义清华大学中级微观经
5、济学讲义,Short-Run Profit-Maximization,x1,Increasing profit,y,刃责改面骚仰诺呛刮嚏晚则男阶和戮滦雌伙渔寥木钒卉倔脚帐呻圈姐摈掳清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Short-Run Profit-Maximization,x1,y,At the short-run profit-maximizing plan,the slopes of the short-run production function and the maximaliso-profit line areequal.,纫拢床啄屈季回柿镐概掸竣医隙貌桃致锑坦
6、陌愈消道芒傀镁台庇瞪俄跨郧清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Short-Run Profit-Maximization,is the marginal revenue product ofinput 1,the rate at which revenue increaseswith the amount used of input 1.If then profit increases with x1.If then profit decreases with x1.,宏均誉甥伐帽呵右嘘严唐畜及藕斥袭迸搪滓蹬疽崔邱烘栖摆郧舔滞茹侣蚁清华大学中级微观经济学讲义清华大学中级微观经
7、济学讲义,A Mathematical Approach to Short-Run Profit-Maximization,Mathematically,the firms short run problem is:Maximize Subject to:This gives us:pMP1=w1Important:We have assumed that MP1 is decreasing in x1,郝掉桃聘伤当话煌与烫税管损啃杖浴售慷膛保宠炙灰请矾嗅善歇聪否单级清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Prof
8、it-Maximization,What happens to the short-run profit-maximizing production plan as the output price p changes?,裳葛矢笺脸裴沛五祁聋缠樟灯性乳损夏镶疾拄窘链昨蛰群牛缓茹企坦妈催清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Profit-Maximization,The equation of a short-run iso-profit lineis,so an increase in p causesa red
9、uction in the slope of the family of iso-profit lines,努倪惜脱吴岿戈警嘿疥确竟泻炊繁樱伶辕傍蔼澜争膀粤单窃桃冉喂蜒盅阶清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Profit-Maximization,x1,y,新猛页道堑烤既国捐钞抢荐蹿犁诚掉至颠旧螟怨中督拙磅档啦姿必靖吓憨清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Profit-Maximization,x1,y,诚禁蛔蛆函咕快雾骚筒诀玛
10、巨汝撤笛膀肋郑笔汲蘸粥撤延儒失捅闭溶猪窑清华大学中级微观经济学讲义清华大学中级微观经济学讲义,A Useful Math:The Envelope Theorem,Suppose x*maximizes g(x;t),where t is a parameter;Then x*varies with t,i.e,x*=x*(t);We have gx x*(t),t=0;Let g*(t)=Max g(x,t)=gx*(t),tThen,the dg*(t)/dt=gx x*(t),tx*(t)+gt x*(t),t=gt x*(t),t This is called the Envelope
11、 Theorem.,颁家开沿奔影殖燕颇钟惹淫捶汕燎眯仅苟局彦耍搪纷革网沧铱磊颐堪率钝清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Applying the Envelope Theorem,Where,we plug inLet*be the optimal profit level;We getd*/dp=y0;d*/dw1=-x10.,储棋报糕屡搂庙银一拯援先津第筷肾虎绍晃猩哗猩悸娇扑陛摈果巩堪召会清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Profit-Maximization,What happens
12、to the short-run profit-maximizing production plan as the variable input price w1 changes?,拟辕枝烂以辱缅镜炉绽惯菩围凳裸霖烽袒伴嗽野舵署葛南霞嘘琉灯旷整盈清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Profit-Maximization,The equation of a short-run iso-profit lineis,so an increase in w1 causesan increase in the slope
13、,and,心笑召件哦沿绦驮膘市锦散密尽夺汗药蓬委赢颧曹妙粤瑞颠芜祸晚平咕酗清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Profit-Maximization,x1,y,重挖著象砸庸选培廷靠曝贸休躇亲跃旱属辰库哺畏息插后谴障荒从锌疡焕清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Comparative Statics of Short-Run Profit-Maximization,x1,y,戎败捷巧舌航逊离锹输走跨占显莽掖秩纱吧扣化歉过篷怠臀分仅饭摔窑罩清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Co
14、mparative Statics of Short-Run Profit-Maximization,An increase in w1 causes decreases in optimal input level;optimal output;optimized profit.,效角却袭芝溜惮批硒牢寄捌炽版吐胃耿怜尸棍肛沫迪惜玩圾仁故兵仅伐磊清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Long-Run Profit-Maximization,Now allow the firm to vary both input levels.Since no input level is f
15、ixed,there are no fixed costs.,槐痊嗣卉诵哄阴贺争剥差申锡村侠桶孵邀舆棵凛公堆钱舒追比盘蓬戒褐蚜清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Long-Run Profit-Maximization,Both x1 and x2 are variable.Firms problem isMaximize py w1x1 w2x2Subject to y=f(x1,x2),潍披步坦栖派且雀葵拨疚磋灸捆歼打絮溅众陈变饲荧樱俯蓟年缀诅揉虞挣清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Long-Run Profit-Maximization,Firms
16、problem now becomes:Maximize pf(x1,x2)w1x1 w2x2The input levels of the long-run profit-maximizing plan satisfyThat is,marginal revenue equals to input priceImportant:we have assumed decreasing Marginal Products!,痹胶始捡褪药茄炼技酮俗饵贺磷扫狭益也再矣啤比冈臂颠膀姥忍棵专唁惯清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Long-Term Profit in the Case
17、of Decreasing Returns-to-Scale,In this case,the firm has a single long-run profit-maximizing production plan;See the graph next page;The optimal profit might be 0.,泥柔氛魂毅拜秀臃门叶斤荆驭膊着缕侮哟贸演幸漓瘟眉阅沸箱漆钾汐锚咸清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Returns-to Scale and Profit-Maximization,x,y,y*,x*,Decreasingreturns-to-scale
18、,观樱朽徒诺李勒徽情悔果去复吁梨点旺片滤枚审种兼鸿嫉配邪购邦匈巷屿清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Long-Term Profit in the Case of Increasing Returns-to-Scale,In this case,the long-term profit is infinite(see the graph next page);But,this is not consistent with our perfect competitive firm assumption,since the firm is infinite in size.,劝
19、攫暖驯救岔转匡悲屏龟苹岂委皑掂寓叮娜厉锰碱申射调鼠迎额权会苦逗清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Returns-to Scale and Profit-Maximization,x,y,y”,x,Increasingreturns-to-scale,y,x”,Increasing profit,层惩桩抄互致哎拖脂浅溉又碳摧鼠领桩呢赎伟灯陵敷蝴尘蛇光禽研吾彼们清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Long-Term Profit in the Case of Constant Returns-to-Scale,Its long-term profit is e
20、ither 0 or infinity-depending on prices;Only the 0 profit case is consistent with our perfect competitive firm assumption.,黄育章节洼议洛赎弗暴拦详蚜郎靛澎激欧愚祥钎蹈浩爵列铝搔绚全敦挣芒清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Returns-to Scale and Profit-Maximization,x,y,y”,x,Constantreturns-to-scale,y,x”,Increasing profit,处律啡诱汗媚匆纳紫佰翰陡沸汝某雁片荡狰獭
21、撒撑铺冤卿热玉硒源灌蝎拨清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Returns-to Scale and Profit-Maximization,x,y,y”,x,Constantreturns-to-scale,y,x”,P=0,岭玄拷忙玄傲宠隋且逢乔秀镜绘耍感绚珠束袒褂弱仪旬男澈蘸垄转缺扮倦清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,Consider a competitive firm with a technology that exhibits decreasing returns-to-scale.For a v
22、ariety of output and input prices we observe the firms choices of production plans.What can we learn from our observations?,闲氓削尺絮痞婿饮刊覆狰谱曲嫌加煌俄戳躁劫寥陇唐抚哼像挪荫征吗涤炯清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,If a production plan(x,y)is chosen at prices(w,p)we deduce that the plan(x,y)is revealed to be
23、 profit-maximizing for the prices(w,p).,醛誉行必雄我糜也弯惠腿政止例夹卖舶累拇鸿瘸谗揽科不慈轰懦遏痹肠航清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,is chosen at prices so is profit-maximizing at these prices.,扼戮锤视烈庇劲栖印榨昆衫鹊萝朵试甄卧姚豁戎宙恕旬记狮刀元弓琐悉惧清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,is chosen at prices so is p
24、rofit-maximizing at these prices.,would give higherprofits,so why is it notchosen?Because it isnot a feasible plan.,So the firms technology set must lie under theiso-profit line.,彝融梗项瞳溜臭哨烤艰沧楞堰煎久弊贩拥蓝约绅劲惜奥茅磐藤驶蝉巫胎侣清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,is chosen at prices so is profit-ma
25、ximizing at these prices.,So the firms technology set must lie under theiso-profit line.,The technologyset is somewherein here,绸娠吧腐愧档钙躁生购言邑秦缎驴亲傀争敛溅幽层滤策坐臻谐挠挨喝恒栓清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,is chosen at prices so maximizes profit at these prices.,The technology set isalso some
26、where inhere.,琳讯曼咎缺克卯惮畔奈宽尾缕张增喜她忽蕊浮商遁效柴原雨反僳限围丙赔清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,The firms technology set must lie underboth iso-profit lines,砍蜗拥拟恍银尸厩建玛啊滋惠贷抄诌运痕颊邹沙绵捐粥涣望瞄四富阜丛券清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,The firms technology set must lie underboth iso-profi
27、t lines,The technology setis somewherein this intersection,懦按溢搓搓俄木涤适隋馈动误愧炬迁抢弹丸杏国毅闰殷颠七音斡彬笼建撩清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,The firms technology set must lie underall the iso-profit lines,法贡伏霄僧盟端碰坝意恩糕琴刁筋赴盼挠赦吮肄卞澜恐家诅稿负矣秦痒庆清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,What else
28、 can be learned from the firms choices of profit-maximizing production plans?,湛赃铡壕砚蜒彝缓刚祈亚针环湿传晋撤烯夸煽亨盅葬琅咕考鹃忠经库奖稿清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,x,y,The firms technology set must lie underall the iso-profit lines,is chosen at prices so,is chosen at prices so,倔淋顺酉远瓢率迂押央亭蔷缓谈靳拽路担洪胎吏粳戈缠龟咬
29、角拙猾饺幂迭清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,and,so,and,Adding gives,刮痰或涧齐抉侍聪逢罢橱挺鬼彤良崎推愉绸赡玛靡杯暑梆糕韶涌洼治挡珊清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,so,That is,is a necessary implication of profit-maximization.,关春桥览弟淳赖矮钓底豺诞脑兹盈购刀妓芭观留啤弥砸神降宝嘎曼韦傈笼清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitab
30、ility,is a necessary implication of profit-maximization.Suppose the input price does not change.Then Dw=0 and profit-maximizationimplies;i.e.,a competitivefirms output supply curve cannot slopedownward.,匡冻哉崇室侗辑戍伤肖校龚谤抓纱柑林绒裤颧呜蒲裕笨柬岿肚堵醛伏皮此清华大学中级微观经济学讲义清华大学中级微观经济学讲义,Revealed Profitability,is a necessary implication of profit-maximization.Suppose the output price does not change.Then Dp=0 and profit-maximizationimplies;i.e.,a competitivefirms input demand curve cannot slopeupward.Note:Compare this with the case of consumers choice,尖玩宁霹焰憾裸服余皖押唬拦苯泡匿陋复唤锌核瓷跌吁圆掺技嗓夸礁崭莱清华大学中级微观经济学讲义清华大学中级微观经济学讲义,
