1. 1 Chapters 8: Costs of Production

2. 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. 3 Numerical Example of Costs (1) LaborTotal Product Marginal Product of Labor Total Fixed Cost Total Variable Cost Total Cost Average Total Cost Marginal Cost 00---1000 --- 110.00 1005015015.005.00 214.144.14100 20014.1412.07 317.323.1810015025014.4315.73 420.002.6810020030015.0018.66 522.362.3610025035015.6521.18 624.492.1310030040016.3323.43 726.461.9610035045017.0125.48 828.281.8310040050017.6827.37 930.001.7210045055018.3329.14 1031.621.6210050060018.9730.81 1133.171.5410055065019.6032.39 1234.641.4710060070020.2133.90

4. 4 Numerical Example of Costs (2) LaborTotal Product Marginal Product of Labor Total Fixed Cost Total Variable Cost Total Cost Average Total Cost Marginal Cost 00---2000 --- 14052.50 210022.00 319012.11 42708.89 53407.35 64006.50 74506.00 84905.71 95205.58 105405.56 115505.64 125555.77

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

6. 6 Graphical Representation of All Costs FC AFC MC ATC AVC TC VC r1r1 r2r2 FC Q Q $/Q $/L

7. 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. 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) = (-MP L /MP K ) and –Slope of isocost line = (-w/r) therefore –(-MP L /MP K ) = (-w/r) and (MP L /w) = (MP K /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. 9 Graphical Representation of Production Optimality L K Q = Q 1 Isocost Line Slope = -w/r Isoquant L*L* K*K*

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

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

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

13. 13 Output Expansion Path TC 1 /wTC 2 /w TC 1 /r TC 2 /r TC 1 /r Q1Q1 Q2Q2 Q3Q3 Expansion Path

14. 14 Long Run ATC Curve SMC 1 LMC LATC ATC 1 ATC 3 ATC 2