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1、Chapter FourProduction and Cost FunctionChapter Four includes:?4.1 Production Function?4.2 Cost FunctionOverview of Last ClassDefinition of Cost Functionopportunity costsExplicit and Implicit CostsTC, AC and MCFrom Cost Minimization to the Long Run Cost FunctionCost Functions In the Short RunSTC,VC,
2、FC;SAC,SAVC,AFC;SMCOutline of Todays ClassHow to get the Long Run Cost FunctionAn Graphic ApproachAn Algebraic ApproachLTC,LAC,LMCEconomies of Scale and Diseconomies of ScaleIntroduction: Long Run Cost ?In the long run there are no fixed factors of production?Firm can freely adjust inputs?Production
3、 costs are lower in the long run?In order to distinguish the Long-run and short-run cost, we rewrite the term of the costs:?In the Long-Run Cost: LTC,LAC,LMC.?In the Short-Run: STC,STVC,STFC;SAC,SAVC,SAFC;SMCSTC,STVC,STFC;SAC,SAVC,SAFC;SMCLong-Run Cost?Long-run cost is the cost of production when a
4、firm uses the economically efficient quantities of labor and capital.?Explain the relationship between a firms output and costs in the long run?Derive and explain a firms long-run total cost curve, long-run average cost curve and Long-run marginal cost curve.Introduction: LTC and LAC? ?The The longl
5、ong- -run total cost (LTC)run total cost (LTC) is the is the minimum total cost of production in the long minimum total cost of production in the long run when a firm is perfectly flexible in its run when a firm is perfectly flexible in its choice of inputs and can choose a production choice of inpu
6、ts and can choose a production facility of any size.facility of any size.? ?The The longlong- -run average cost of production run average cost of production (LAC)(LAC) is the longis the long- -run total cost divided by the run total cost divided by the quantity of output produced.quantity of output
7、produced.From Expansion Path to Long-Run Total Cost (LTC)How to get LTC for STC by graphic approachLTCLTC curve is the envelope of the STC curves?Suppose the firm wishes to produce q1, in the short run, some inputs are fixed, and this prevent the firm from producing q1at the lowest possible cost. ?T
8、here may be too much or too little of the fixed factors. Only in the very special case of just the right level of the fixed inputs would cost be at the lowest level possible. LTC curve is the envelope of the STC curves?The lowest level of cost possible for producing q1is precisely the long-run cost,
9、 as in the long run, the firm can vary all factors to minimize cost.?So the LTC must always be no larger than STC.?LTC is always below the STC curves at every level of output. Each STC curve just touches the LTC at at least one point. LTC curve is the envelope of the STC curves?At each level of q, t
10、here is a cheapest way of producing that output in the long run.?Thus each point on the LTC coincides with a point on some STCs. ?LTC curve is the envelope of the STC curvesSummary: LTC is the Summary: LTC is the envelopeenvelope of STCof STC? ?The The longlong- -run total cost (LTC)run total cost (
11、LTC) is the is the minimum total cost of production in the long minimum total cost of production in the long run when a firm is perfectly flexible in its run when a firm is perfectly flexible in its choice of inputs.choice of inputs.? ?LTC is a set of min. STC at any given outputs.LTC is a set of mi
12、n. STC at any given outputs.? ?So LTC is often referred to as being the So LTC is often referred to as being the envelopeenvelope of the shortof the short- -run cost curve.run cost curve.How to get LTC from STCs? An Algebraic Approach?In the long run, all inputs are variable, and the scale of produc
13、tion can change.?Assume production function is ?Short-run cost function is:?Holding w1,w2 constant, we can get:12(, )qf x x k=1 122( )STCw xw xk=+( , )( )STCC q kk=+How to get LTC from STC?Let:?The partial derivative of G(C,q,k) is?We can get:?Put k=k(q) into G(C,q,k),?LTC=LTC(q)( , )( )( , , )0CC q
14、 kkG C q k=( , , )( , , )0kG C q kG C q kk= ( )kk q=An example:?Suppose A group of STC is showed by the following form?k=1,2,3.?What is LTC?3220.040.9(11)5Cqqk qk=+320.10.040.9511kqLTCqqq=+How to get The Long-Run Average Cost CurveThe long-run average total cost curve is derived from the short-run a
15、verage total cost curves.The segment of the short-run average total cost curves along which average total cost is the lowest make up the long-run average total cost curve.Short-Run Costs of Four Different PlantsLong-Run Average Cost CurveHow to get LAC0SAC(q,K1)SAC(q,K2)SAC(q,K3)LAC is the envelope
16、of many SACsCLAC(q)q1q2q3qHow to get LMC?Why is LAC “U” shaped.?In the long-run:?Firms experience increasing and decreasing returns to scale and therefore long-run average cost is “U” shaped.Returns to scale and long run average cost?Economies of scale(规模经济)a cost function exhibits economies of scale if average cost falls as output expands?Diseconomies of scale（规模不经济）a cost function exhibits disecono
