Trying to maximize objective function with constraintsi.Firm Theorya.Overview1.How firm makes cost-min or profit-max production decisiona.Full info on production tech, ex: productivity, needed inputs1)Production Technologyi.What are limited resources?1)Cost constraintii.Resulting from 1 and 21)Input Choicesiii.Product decisionb.Big Picture of Firm Theory2.Given tech, how to evaluate performancea.Production Technology - 6.1A.Inputs into productiona.Labor, raw materials, capital (machines, land, etc)i.Examplesb.Factors of ProductionB.Show max output produced for combination of inputsa.Quantity of inputsi.f(K, L)b.Any quantity of output can be less than qi.q = f (K, L)c.Must have continuous inputs for production of outputs1)Inputs and outputs are flow variablesi.Describes given tech. 1)If no tech, no production2)q = f (K, L)ii.If a firm produces less than q, they will not survivea)All production will be at qb)Due to competition in the market1)Not efficient eg. Governmenta)No incentive to improve efficiency b)If no competition, output can be less than q2)Given f (K, L) actual output can be < q but we assume qiii.Features d.Production FunctionC.At least 1 input's Q cannot be changed within this time horizona.q (L) = K-bar (6L^2-L^3)i.Suppose K is fixedb.Short RunD.All inputs are variable (can be changed)a.Long RunE.Look at one variable input and get total amount of outputa.Total product of labor, given quantity of labori.TP (L) = q(L)b.Total ProductF.Ch 6 Production TheoryMonday, March 24, 20144:46 PM Int. Micro Lecture notes Page 1Total product of labor, given quantity of labori.TP (L) / Li.Total product of labor over laborii.Average Producta.MP (L) = ∆q/∆L i.= q (L + ∆L) - q (L)) / ∆Lii.d (TP (L)) / d L1)= derivative of TPiii.Marginal Product (of input)b.2 criteria used to evaluate techG.AP (L) = TP (L) / Li.Tangent angle at that pointii.Suppose TP is known, how to get APa.Tangent line to the curvei.Derive TP (L)ii.MP = ∆q/∆L 1)Or if asked with value of iii.How to get MPb.ApplicationsH.At max TP (L*) , MP (L*) = 0i.If TP(L) ↑, then MP (L) > 0a.Since TP (L) = L.AP(L)i.If AP (L) ↑ , then TP (L) ↑b.If average class height is 5.81)MP = 7.1a)AP will increaseb)Shaq walks in with height 7.12)Examplei.MP(L) = AP(L)a)d AP(L) / d L = 0b)ii.If MP(L) > AP(L) then AP(L) ↑c.Relationships between TP, AP, MPI.Since ∆ always leads to higher production functioni.If production tech is unchanged…a.At first as it goes up, MP upi....Then MP of a single factor will eventually decrease …b....When all amounts of all other factors stay constantc.Law of diminishing marginal returnsJ.There exists a best combination of inputsK.Output per unit of labor inputi.Average product of labora.Productivity growthb.Labor Productivity L. Int. Micro Lecture notes Page 2Ultimately leads to growth in overall consumption/standard of living due to factor paymentsi.Total amount of capital available for use in productiona)Stock of capital1)Development of new techa)Technological change2)Sources of growthii.Productivity growthb. Int. Micro Lecture notes Page 3What happens in LR when there are 2 variable inputs1.Raw materials GoodL.KFirmYInputProduction FunctionOutputY = f(L,K)Inputs (Food clothing) - > Consumer -> Utility a.Analogous to Consumer Theory 2.(Indifference Curves)a.Curve that shows all combination of inputs to produce same amount of outputb.Y-bar = f(L,K)c.d.Isoquant3.Marginal rate of technical substitution a.Ability of one input to be substituted for another to keep output sameb.= Slope of the Isoquantc.Ability of 1 labor to substitute for capitali.If L↑, how much less Kii.Marginal product of labor1)If one more labor, how much output up 2)MPᴸiii.|∆K/∆L| = 1MPᴸ/MPᴷd.MRTS = decreasing function of Li.Diminishing Marginal Returne.MRS of 1 for 2i.=MU1/MU2ii.Substitute A for Bf.Perfect Substitutesi.Two Special Casesg.MRTS4.6.3 Production with 2 variable inputsSunday, March 30, 201411:55 PM Int. Micro Lecture notes Page 4Straight Isoquants1)MRTS is equal to given constant2)Q = 2K + 3L3)Picture4)Perfect Substitutesi.Isoquants are "L"1)Fixed proportions between 2 inputs2)Fixed ratio not necessarily 1:13)Picture 4)If 2 labor required for 1 capitala)Y = f (L, K)b)f=min {.5L, K}c)Example5)Perfect Complements (Leontif Production Function)ii.Marginal Productivity a.∆K or ∆L on Qb.Returns to 1 Factor5.Y = f(L, K)i.What happens if we allow Y to change when L & K change proportionallyii.If production factors changed by α , then output scales upi.If f(αL, αK) = α.f(L, K)ii.Barbers, coffee shops1)Bigger shop, as much more production2)Ex: Service industries,iii.Equal space between them1)2)Isoquantsiv.Constant Returns to Scalea.Due to problems with coordinationi.More people, harder to coordinateii.Ex: film industryiii.Decreasing Returns to Scaleb.When large investments can be madei.Auto, Farms, electricity 1)Monopolistic firms under regulationii.Usually provided govs.iii.If entirely monopolistic, will not produce as much as the efficient leveliv.Become closer1)Isoquantsv.Increasing Returns to Scalec.Returns to Scale6. Int. Micro Lecture notes Page 5Become closer1)2)What is impact to Q when K and L increased by 20%, if it is decreasing returns to scalei.Exam Question Exampled.Impact of Q on costsi.Falls when MC < ACi.Unit cost falls as Q grows (LRAC falls as Q up)a.b.Economies of scale7. Int. Micro Lecture notes Page 6Y = f(L, K)i.What happens if we allow Y to change when L & K change proportionallyii.If production factors changed by α , then output scales upi.If f(αL, αK) = α.f(L, K)ii.Barbers, coffee shops1)Bigger shop, as much more production2)Ex: Service industries,iii.Equal space between them1)2)Isoquantsiv.Constant Returns to Scalea.Due to problems with coordinationi.More people, harder to coordinateii.Ex: film industryiii.Decreasing Returns to Scaleb.When large investments can be madei.Auto, Farms, electricity 1)Monopolistic firms under regulationii.Usually provided govs.iii.If entirely monopolistic, will not produce as much as the efficient leveliv.Become closer1)2)Isoquantsv.Increasing Returns to Scalec.What is impact to Q when K and L increased by 20%, if it is decreasing returns to scalei.Exam Question Exampled.Returns to Scale1.Returns/Econs to ScaleFriday, April 18, 20145:20 PM Int. Micro Lecture notes Page 7What is impact to Q when K and L increased by 20%, if it is decreasing returns to scalei.Impact of Q on costsi.Whether average cost is increasing or decreasing in