The Firm. The Firm. Maximizing Profits. Decisions. ECON 370: Microeconomic Theory Summer 2004 Rice University Stanley Gilbert

Transcription

1 The Frm The Frm ECON 370: Mcroecoomc Theory Summer 004 Rce Uversty Staley Glbert A Frm s a mechasm for covertg labor, captal ad raw materals to desrable goods A frm s owed by cosumers ad operated for the beeft of ts owers (for ow) We assume that a frm s objectve s to mamze profts Eco The Frm Decsos Frms have three decsos that they must make: How much to produce How to produce t Whether to produce at all We wll eame each of these decsos Proft s: π = Reveue Cost Mamzg Profts We geerally treat all these as flows Profts per week Reveue per week Costs per week Mamzg profts mples: Margal Reveue = Margal Cost MR = MC Ths s the basc rule that apples to all frms Eco The Frm 3 Eco The Frm 4

2 More o Costs We are terested Ecoomc Costs ot Accoutg Costs Ecoomc Cost s the beeft you would get from the best avalable alterate use of the put Eamples: Suk epedtures are suk, they are ot costs Irdum Retal prce of puts Delvery Trucks Ower s tme Eco The Frm 5 Producto Plas Frms use some techology for trasformg puts to valuable outputs Wth a partcular techology, a frm ca trasform a specfc set of puts (,, ) to ot more tha some y amout of output We represet a techology as: y = F(,, ) Where F(,, ) s the producto fucto for ths techology A producto pla s a put budle ad output level: (,,, y) A feasble producto pla wll satsfy y F(,, ) Eco The Frm 6 Techology Set The techology set s the set of all feasble producto plas That s, all producto plas that satsfy y F(,, ) The techology set s also called the Producto Possblty Set Note that a proft mamzg frm wll produce o the Producto Possblty Froter that s, where y F(,, ) Why? We call such producto plas Techcally Effcet Output y Techology Set Graph Oe put ad oe output Producto Possblty Set y = f() s producto fucto y = f( ) s ma output level obtaable from put uts Iput Eco The Frm 7 Eco The Frm 8

3 Isoquats Isoquat Map Oe way of represetg the producto fucto graphcally s by drawg soquats A soquat represets all combatos of puts that wll produce a gve level of output I the two-put case: All, such that c = F(, ) y = 4 y = 3 y = y = Eco The Frm 9 Eco The Frm 0 Commo Utlty Fuctos Cobb-Douglas Techologes: Graph Perfect Substtutes: F() = a + a + + a a > 0 Fed Proportos: F() = m{a, a,, a } a > 0 Cobb-Douglas Prefereces F() = a a a a > 0 All soquats are hyperbolc, asymptotg to, but ever touchg, ay as Eco The Frm Eco The Frm 3

4 Fed-Proportos Techologes: Graph Perfect-Substtuto Techologes: Graph y = m{, } y = = = = m{, } = 4 m{, } = 8 m{, } = = 4 All soquats lear ad parallel 8 4 Eco The Frm 3 Eco The Frm 4 Margal (Physcal) Products Gve a techology: y = F(,,, ) Margal product of put s chage output as put chages, holdg all other put levels fed y MP = Margal Products: Dmshg MP MP s dmshg f t decles as creases That s, f MP y y = = < 0 Cobb-Douglas Eample Cobb-Douglas Eample Typcally, margal product of oe put depeds o amout used of other puts Eco The Frm 5 Eco The Frm 6 4

5 Returs-to-Scale Returs-to-scale Chage output as all puts chage proportoally e.g. all put levels doubled, or halved Costat Returs to Scale: doublg all puts, doubles output F(k, k,, k ) F(,,, ) Decreasg Returs to Scale: doublg all puts, less tha doubles output F(k, k,, k ) < kf(,,, ) Icreasg Returs to Scale: doublg all puts, more tha doubles output F(k, k,, k ) > kf(,,, ) Dfferet Returs to Scale (RTS) A sgle techology ca locally ehbt dfferet returs-to-scale Output y = f() Icreasg returs-to-scale Decreasg returs-to-scale Iput Eco The Frm 7 Eco The Frm 8 Eamples of RTS: Perfect Substtutes The perfect-substtutes producto fucto s y = a + a + L+ a Epad all put levels proportoately by k: = a ( k ) + a ( k ) + L+ a ( k ) ( a + a y + L+ a The perfect-substtutes producto fucto s CRS ) Eamples of RTS: Perfect Complemets Perfect-complemets producto fucto s y = m{ a, a, L, a } Epad all put levels proportoately by k: = m{ a ( k ), a ( k ), L, a ( k )} (m{ a, a, L, a }) y The perfect-complemets producto s CRS Eco The Frm 9 Eco The Frm 0 5

6 Eamples of RTS: Cobb-Douglas Eamples of RTS: Cobb-Douglas The Cobb-Douglas producto fucto s y = a a L Epad all put levels proportoately by k: = ( k ) k Lk a+ a + L+ a a+ L+ a y a a a k a k ( ) L( ) a a a a a a a a L L a a + L+a The Cobb-Douglas techology s RTS: costat f a + + a = creasg f a + + a > decreasg f a + + a < y Eco The Frm Eco The Frm Returs-to-Scale ad Dmshg MP Techcal Rate-of-Substtuto: Graph RTS ad Margal Product (MP) RTS refers to chage all puts MP refers to chage oe put, holdg all others costat Declg MP reflects each ew put havg less of others to work wth ad becomg less productve Wth RTS, each put has same amout of other puts to work wth so RTS eed ot dmsh Illustrato Ca have creasg RTS ad dmshg MP Cobb-Douglas Producto Fucto At what rate ca a frm substtute oe put for aother wthout chagg output? y = 00 Techcal rate-of-substtuto = Slope of soquat = Rate at whch must be gve up as s creased to keep y costat Eco The Frm 3 Eco The Frm 4 6

7 Techcal Rate-of-Substtuto Output y s costat alog soquat Producto fucto y = F(, ) A small chage (d, d ) put budle causes a chage to output level y of: y y dy = d + d d y TRS = = d y = = 0 MP MP Eco The Frm 5 7