BUS 525: Managerial EconomicsLecture 5The Production Process and CostsActivity Schedule:BUS525:2 Originally scheduled classes Makeup classes (Announced by University Makeup classesproposed (!o be "inali#ed in consultation $ith students%lass &ate '(a)s %ases* 2+ May2 , -une. / -une, ** -une %ase *5 20 -uneMid */ 2. -uly1 25 -uly (!hu+ .0 -uly %ase 2 2 2 August (3ri*0 *. August** */ August (3ri)Mid 2*2 20 August %ase .*. !BA 3inalActivity Schedule:BUS525:. Originally scheduled classes Makeup class (Announced by University Makeup classes proposed (!o be "inali#ed in consultation $ith students%lass &ate '(a)s %ases* 22 May2 5 -une. *2 -une, *2 -une %ase *5 2/ -une Mid */ 2, -uly1 2/ -uly (3ri+ .* -uly %ase 2 2 * August (!hu*0 *, August** */ August (3ri Mid 2*2 2* August %ase .*. !BA 3inalOvervie$45 6roduction Analysis7!otal 6roduct8 Marginal 6roduct8 Average 6roduct74so9uants74socosts7%ost Mini)i#ation445 %ost Analysis7!otal %ost8 :ariable %ost8 3i(ed %osts7%ubic %ost 3unction7%ost ;elations4445 Multi units o" capital and L units o" labor5=Short8L A >55 L557 4" the inputs are > A */ and L A */8 then the average product o" labor is A6L A F(*/ 055(*/055GC*/ A *5= Average 6roduct o" %apital= A6> A @C>5= Measures the output o" an DaverageE unit o" capital5='(a)ple: @ A 3(>8L A >55 L557 4" the inputs are > A */ and L A ,8 then the average product o" capital is A6> A F(*/055(,055GC*/ A *C25Measures o" 6roductivity: Marginal 6roduct=Marginal product : !he change in total output attributable to the last unit o" an input= Marginal 6roduct o" Labor: M6L A @CL7 Measures the output produced by the last $orker57 Slope o" the short A @C>7 Measures the output produced by the last unit o" capital57 Hhen capital is allo$ed to vary in the long run8 M6> is the slope o" the production "unction ($ith respect to capital5QLQ=F(K,L)IncreasingMarginalReturnsDiminishingMarginalReturnsNegativeMarginalReturnsMPAPIncreasing, Diminishing and Negative Marginal Returns!6Iuiding the 6roduction 6rocess=6roducing on the production "unction7Aligning incentives to induce )a(i)u) $orker e""ort8 tips8 pro"it sharing5=')ploying the right level o" inputs7Hhen labor or capital vary in the short run8 to )a(i)i#e pro"it a )anager $ill hire=labor until the value o" )arginal product o" labor e9uals the $age: VMPL = w8 $here VMPL = P x MPL5=capital until the value o" )arginal product o" capital e9uals the rental rate: VMPK = r8 $here VMPK = P x MPK .!he 6ro"it Ma(i)i#ing Usage o" 4nputsJ A ;< %8 @ A 3 (>8L8 % A $L K r>J A 65 3(>8L < $L < r>price its equals prouctmarginal o! "alue its #herepointthe to up use $e mustinputeachi%e# & an r P% an rP%LL) F(K,anKL) F(K,'ince( #LL) F(K,P%L)( rKL) F(K,P%K)MP MPMP MPMP MPL KL KL *= == ==== == =L 6 M6L :M6L H:ariable 4nput 6rice o" Output Marginal 6roduct o" Labor6 ( M6lUnit %ost o" Labor0 L. < < L,00* L. 1/ L22+ L,002 L. *12 5*/ L,00. L. 2,, 1.2 L,00, L. 222 +1/ L,005 L. .*/ 2,+ L,00/ L. .*/ 2,+ L,001 L. 222 +1/ L,00+ L. 2,, 1.2 L,002 L. *12 5*/ L,00*0 L. 1/ 22+ L,00** L. K bL= M;!S>L A bCa=Linear iso9uants i)ply that inputs are substituted at a constant rate8 independent o" the input levels e)ployed5Q.Q/Q0Increasing OutputLKLeontie" 4so9uants=%apital and labor are per"ect co)ple)ents5=%apital and labor are used in "i(ed8 cLN=Hhat is the M;!SBQ.Q/Q0KIncreasing OutputL%obbaLb= M;!S>L A M6LCM6>Q0Q/Q.KLIncreasing Output4socost=!he co)binations o" inputs that produce a given level o" output at the sa)e cost:wL + rK = C=;earranging8K= (1/r)C - (w/r)L=3or given input prices8 isocosts "arther "ro) the origin are associated $ith higher costs5=%hanges in input prices change the slope o" the isocost line5KLC1LKNew Isocost Line for a decrease in the wage (price of labor: w

! w"#$%"+r%"+wC0%

+w%

+r%+w

%+w"%+rNew Isocost Line associated with higher costs (%

& %"#$isocost o! 'loper#1 'lope) (r0K 2 rK#L= = = +Lrw%%ost Mini)i#ationQLKPoint of %ost Mini'i(ationSlope of Isocost = Slope of IsoquantAC%ost )ini)i#ationMRTSMPMPKLKLK )(K*L#+L )(K*L#+rw b,di-iding# ( $$$$$$$$ )(K*L# ./0# $$$$$$$$(K)(K*L# /rK0# $$$$$$$$(L)(K*L# /wL01 2.3 )(K*L# rKwL0 Lagrangian= = == == == =+ + == += + =/ 0. %%%%%%% (/ (0 (L) F(K, Q su$3ect to rK#L Minimi4eL) F(K, QrK, #L 2%ost Mini)i#ation=Marginal product per dollar spent should be e9ual "or all inputs:=But8 this is OustrwMPMPrMPwMPKL K L= =rwMRTSKL =Opti)al 4nput Substitution = A "ir) initially produces Q0 by e)ploying the co)bination o" inputs represented by point A at a cost o" %05 = Suppose w0"alls to w157 !he isocost curve rotates counterclock$iseP $hich represents the sa)e cost level prior to the $age change57 !o produce the sa)e level o" output8 @08 the "ir) $ill produce on a lo$er isocost line (C1 at a point B57 !he slope o" the ne$ isocost line represents the lo$er $age relative to the rental rate o" capital5Q((ALK%

+w" %

+w

%"+w"L

L"K

K"5%ost Analysis=!ypes o" %osts73i(ed costs (3%7:ariable costs (:%7!otal costs (!%7Sunk costs=A cost that is "orever lost a"ter it has been incurred5 Once paid they are irrelevant to decision )aking> L O 3% :% !%3i(ed 4nput :ariable 4nput Output 3i(ed %ost :ariable %ost !otal %ost2 0 0 L28000 L0 L20002 * 1/ L28000 ,00 L2,002 2 2,+ L28000 +00 L2+002 . ,22 L28000 *8200 L.2002 , 1+, L28000 *8/00 L./002 5 **00 L28000 28000 L,0002 / *8,*/ L28000 28,00 L,,002 1 *810+ L28000 28+00 L,+002 + *8252 L28000 .8200 L52002 2 28*2, L28000 .8/00 L5/002 *0 28200 L28000 ,8000 L/000Table 5! !he %ost 3unctionotal and !aria"le Costs2(Q)6Minimum total cost o! proucing alternati"e le"els o! output62(Q) = &2(Q) 7 F2&2(Q)62osts that "ar8 #ith output%F26 2osts that o not "ar8 #ith output%9#2(Q) = &2 7 F2&2(Q)F2($i%ed and Sun& CostsF262osts that o not change as output changes%'un* 2ost6A cost that is !ore"er lost a!ter it has $een pai%9#F22(Q) = &2 7 F2&2(Q)Some DefinitionsA"erage :otal 2ostA:2 = A&2 7 AF2A:2 = 2(Q)+QA"erage &aria$le 2ostA&2 = &2(Q)+QA"erage Fi;e 2ostAF2 = F2+QMarginal 2ostM2 = 2+Q9QA:2A&2AF2M2MR$i%ed Cost9QA:2A&2M2A:2A&2Q(AF2Fi;e 2ostQ((A:21A&2)= Q( AF2= Q((F2+ Q()= F2!aria"le Cost9QA:2A&2M2A&2&aria$le 2ostQ(Q(A&2= Q(-&2(Q()+ Q(,= &2(Q()9QA:2A&2M2A:2:otal 2ostQ(Q(A:2= Q(-2(Q()+ Q(,= 2(Q()otal CostO 3% :% !% A3% A:% A!%Output 3i(ed %ost :ariable %ost !otal %ost Average 3i(ed %ostAverage :ariable %ostAverage !otal %ost0 L28000 L0 L2000