Ch 7 Cost of Production
Ch 7 Cost of Production ECO 420K
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This 5 page Class Notes was uploaded by Natalie Strawn on Tuesday June 21, 2016. The Class Notes belongs to ECO 420K at 1 MDSS-SGSLM-Langley AFB Advanced Education in General Dentistry 12 Months taught by John Thompson in Summer 2016. Since its upload, it has received 24 views. For similar materials see MICROECONOMIC THEORY in Economcs at 1 MDSS-SGSLM-Langley AFB Advanced Education in General Dentistry 12 Months.
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Date Created: 06/21/16
6/13/16 Chapter 7 – Cost of Production Accounting cost = actual expenses + depreciation Accounting profit (pi symbol) Economic cost = accounting cost + opportunity cost The opportunity cost of production is the foregone return from resources being employed in their next best use. Sunk costs are past costs that cannot be recovered. Firms should only consider future costs – marginal costs – which are relevant because they can be avoided. -Short run costs (Figure 7.1) Fixed cost (FC or TFC) does not vary with output (q). Variable cost (VC or TVC) varies directly with output (q). Total cost (C or TC) is the sum of all fixed and variable costs.TC = TFC + TVC Average fixed cost (AFC) AFC = TFC/q Average variable cost (AVC) AVC = TVC/q Average total cost (ATC) ATC = TC/q = AFC + AVC Marginal cost (MC) is the incremental cost of producing one more unit. Long run costs In the long run, all costs are variable. The cost of labor is the wage (w). The cost of capital is depreciation plus opportunity cost (interest rate on rented capital). r = d + I d = depreciation, i = opportunity cost An isocost describes various combinations of K and L that have the same cost. (illustrate isocost w/ output maximizing bundle (also known as cost minimizing bundle), input price change) C =wL + rK K = C/r – (w/r)L Note: MRTS = -deltaK/deltaL = MPl/MPk. Since deltaK/deltaL = -w/r, then… MPl/w = MPk/r -This is a necessary condition for maximizing output subject to cost, or minimizing cost subject to output. * Long run costs An expansion path shows the cost minimizing combinations of K and L a firm will use as it increases output. (Figure 7.6) Long run total cost can be derived from the expansion. *long run average cost is constant, marginal cost is constant Long run versus short run costs -Short run costs will never be lower than long run costs. Sometimes they will be equal, but usually short run cost will be higher. (Figure 7.7 and 7.8) Economies of scale (EOS) exist if LAC is decreasing as a firm expands output. -EOS is consistent with IRTS Diseconomies of scale (DOS) exist if LAC is increasing as a firm expands output. -DOS is consistent with DRTS Economies of returns to scale For q = AK^(a)L^(B) … -if a + B = 1, then CRTS -if a + B > 1, then IRTS and economies of scale -if a + B < 1, then DRTS and diseconomies of scale Which exhibit CRTS, IRTS, and DRTS? Q = K^(2)L IRTS Q = 10K + 5L CRTS Q = (KL)^(.5) CRTS Q = K^(.44)L^(.36)M^(.13) DRTS Cost structure and returns to scale: (a)Market structure – minimum efficient scale (MES) i) Automobiles (MES is large) ii) Breweries (MES is small) (b) Barriers to entry Long run costs -LAC will be the “envelope” or lower limit of SACs at various levels of capital (or plant size). (Figure 7.9) Costs Economies of scope exist if it is cheaper for a single firm to produce two products jointly than it is for two or more firms to produce the same output separately. ….often come from avoiding the duplication of costs – production facilities, marketing teams, management, supply chain, etc. Diseconomies of scope (opposite of EOS) too much is combined and it would be more efficient for the products to be produced separately Learning or a “learning curve” exists if marginal cost declines with cumulative output. (Figure 7.11 and 7.12) The Lagrangian Method -We can use this method to: a) maximize ouput, given cost b) minimize cost, given output a) maximize q = f(K,L) s.t. Co = wL + rK Step 1: State the problem Ø = f(K,L) - ʎ (wL + rK -Co) Step 2: Differentiating the Lagrangian First order conditions (FOCs): 1) ∂ Ø/∂k = MPk - ʎr = 0 2) ∂ Ø /∂L = MPl ʎw = 0 3) ∂ Ø /∂ ʎ = Co – wL – rK = 0 Step 3: Solving the FOCs 1) MPk/r = ʎ 2) MPl /w = ʎ 3) Co = wL + rK Interpret the FOCs: (1) and (2) give us the equal marginal principal 3) output is fixed at Co b) minimize C = wL + rK s.t. Qo = f(K,L) Step 1: state the problem Ø = wL + rK - ʎ [f(K,L) – Qo] Step 2: Differentiate 1) ∂ Ø/∂k = r - ʎMPk = 0 2) ∂ Ø /∂L = w ʎMPl = 0 3) ∂ Ø /∂ ʎ = Qo – f(K,L) = 0 Step 3: Solve for FOCs 1) MPk/r = 1/ ʎ 2) MPl/w = 1/x 3) Qo = f(K,L) Interpret the FOCs: -(1) and (2) are equal marginal principle -(3) says output is fixed at Qo Duality Whether we’re minimizing cost or maximizing output, we have the same necessary condition: MPk/r = MPl/w -The firm’s optimal K and L has a dual nature: -maximizing Q subject to Co -minimizing C subject to Qo This is known as duality. Production Problems (USING THE SHORT CUT METHOD)*** Suppose q = 100KL, r =120 and w = 30. Find K and L to minimize cost subject to q =100 1) Ø = 120k + 30L - ʎ (100KL – 1000) 2) MPk/r = MPl/w >>> (100L/120) = (100K/30) >>> L = 4K 3) Plug into formula C = 120K + 30L Answers: K*=1.58 L*=6.32 C*=379.47 (SHORT CUT METHOD)*** Suppose q = 100K^(.6)L^(.4), r =100 and w=20. Find K and L to max Q s.t C =2000 1) Ø = 100K^(.6)L^(.4) - ʎ (100K + 20L - 2000) 2) MPk/r = MPL/w 60L^(.4)/100K^(0.4) = 40K^(.6)/20L^(.6) >>> 3L = 10K >>> L = 3.33K 3) Plug L in to this formula: 100K +20L = 2000 K = 12 L = 40 Q = 1,942
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