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Chapters 8: Costs of Production

Chapters 8: Costs of Production. Cost Definitions. Total cost (TC) = all costs of production If r is the cost of capital (rental cost), and w is the wage, then TC = rK + wL Average total cost (ATC) = total cost/quantity produced

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Chapters 8: Costs of Production

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  1. Chapters 8: Costs of Production

  2. Cost Definitions • Total cost (TC) = all costs of production • If r is the cost of capital (rental cost), and w is the wage, then TC = rK + wL • Average total cost (ATC) = total cost/quantity produced • Fixed cost (FC) = costs that do not vary with the level of output produced • Average fixed cost (AFC) = fixed cost/quantity produced • Variable cost (VC) = costs that vary with the level of output produced • Average variable cost (AVC) = variable cost/quantity produced • Marginal Cost (MC) = change in TC with a 1 unit change in output TC = FC + VC ATC = AFC + AVC MC = .

  3. Numerical Example of Costs (1)

  4. Numerical Example of Costs (2)

  5. Graphical Representation of Relationship Between Diminishing Marginal Returns and Increasing Marginal Cost APL L MPL MC AVC L

  6. Graphical Representation of All Costs r1 TC $/L VC r2 FC FC Q $/Q MC ATC AVC AFC Q

  7. Costs in the Long Run and the Optimal Input Combination • Isocost line - a set of input bundles each of which costs the same amount • The production equivalent of a budget line • The slope of the isocost line is the negative of the input price ratio (-w/r if labor is on the x-axis and capital is on the y-axis) • Maximum output for a given input cost is a point where isoquant is just tangent to the isocost line • Also the point of minimum cost for a given level of output

  8. Production Optimality • If isoquant is tangent to isocost line at optimum, we know that: • Slope of isoquant = slope of the isocost line and • Slope of isoquant = MRTS = (-K/ L) = (-MPL/MPK) and • Slope of isocost line = (-w/r) therefore • (-MPL/MPK) = (-w/r) and (MPL/w) = (MPK/r) • Economic interpretation is that firms should hire inputs to the point where the marginal output per dollar is the same for all inputs • Were this not the case, firm could increase output and reduce cost - would not be at an optimum

  9. Graphical Representation of Production Optimality K Isoquant K* Q = Q1 Isocost Line Slope = -w/r L L*

  10. Optimality: Cost Minimization K TC=$2000 TC=$1750 TC=$1500 K* Q=100 L L*

  11. Optimality: Profit (Output) Maximization K K* TC = $1500 Q=100 Q = 90 Q = 80 L L*

  12. Effects of a Change in Input Prices: Cost Minimization K Q=100 L

  13. Output Expansion Path TC1/r Expansion Path TC2/r Q3 TC1/r Q2 Q1 TC2/w TC1/w TC2/w

  14. Long Run ATC Curve SMC1 SMC1 ATC1 ATC3 SMC1 LATC ATC2 LMC

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