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# Ch 5 Unit5

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### Ch 5 Unit5

1. 1. Managerial Economics & Business Strategy Chapter 5 goes with unit 5 The Production Process and Costs (pp. 168-187 but place most emphasis on costs which start at the bottom of page 177)
2. 2. Overview <ul><li>Cost Analysis </li></ul><ul><ul><li>Total Cost, Variable Cost, Fixed Costs </li></ul></ul><ul><ul><li>Cubic Cost Function </li></ul></ul><ul><ul><li>Cost Relations </li></ul></ul>
3. 3. Production Analysis <ul><li>Production Function </li></ul><ul><ul><li>Q = F(K,L) </li></ul></ul><ul><ul><li>The maximum amount of output that can be produced with K units of capital and L units of labor. </li></ul></ul><ul><li>Short-Run vs. Long-Run Decisions </li></ul><ul><li>Fixed vs. Variable Inputs </li></ul>
4. 4. Marginal Productivity Measures <ul><li>Marginal Product of Labor: MP L =  Q/  L </li></ul><ul><ul><li>Measures the output produced by the last worker. </li></ul></ul><ul><li>Marginal Product of Capital: MP K =  Q/  K </li></ul><ul><ul><li>Measures the output produced by the last unit of capital. </li></ul></ul>
5. 5. Average Productivity Measures <ul><li>Average Product of Labor </li></ul><ul><ul><li>AP L = Q/L. </li></ul></ul><ul><ul><li>Measures the output of an “average” worker. </li></ul></ul><ul><li>Average Product of Capital </li></ul><ul><ul><li>AP K = Q/K. </li></ul></ul><ul><ul><li>Measures the output of an “average” unit of capital. </li></ul></ul>
6. 6. Isoquant <ul><li>The combinations of inputs (K, L) that yield the producer the same level of output. </li></ul><ul><li>The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output. </li></ul>
7. 7. Marginal Rate of Technical Substitution (MRTS) <ul><li>The rate at which two inputs are substituted while maintaining the same output level. </li></ul>
8. 8. Linear Isoquants <ul><li>Capital and labor are perfect substitutes </li></ul><ul><ul><li>Q = aK + bL </li></ul></ul><ul><ul><li>Linear isoquants imply that inputs are substituted at a constant rate, independent of the input levels employed. </li></ul></ul>Q 3 Q 2 Q 1 Increasing Output L K
9. 9. Leontief Isoquants <ul><li>Capital and labor are perfect complements. </li></ul><ul><li>Capital and labor are used in fixed-proportions. </li></ul><ul><li>Since capital and labor are consumed in fixed proportions there is no input substitution along isoquants </li></ul>L Q 3 Q 2 Q 1 K Increasing Output
10. 10. Cobb-Douglas Isoquants <ul><li>Inputs are not perfectly substitutable. </li></ul><ul><li>Diminishing marginal rate of technical substitution. </li></ul><ul><ul><li>As less of one input is used in the production process, increasingly more of the other input must be employed to produce the same output level. </li></ul></ul>Q 1 Q 2 Q 3 K L Increasing Output
11. 11. Isocost <ul><li>The combinations of inputs that produce a given level of output at the same cost: </li></ul><ul><li>wL + rK = C </li></ul><ul><li>Rearranging, </li></ul><ul><li>K= (1/r)C - (w/r)L </li></ul><ul><li>For given input prices, isocosts farther from the origin are associated with higher costs. </li></ul><ul><li>Changes in input prices change the slope of the isocost line. </li></ul>K L C 1 L K C 1 / r C 1 / w C / w 0 C / r New Isocost Line for a decrease in the wage (price of labor: w 0 > w 1 ). C 0 C 0 / w C 0 / r C / w 1 New Isocost Line associated with higher costs (C 0 < C 1 ).
12. 12. Cost Minimization Q L K Point of Cost Minimization Slope of Isocost = Slope of Isoquant
13. 13. Cost Analysis <ul><li>Types of Costs </li></ul><ul><ul><li>Fixed costs (FC) </li></ul></ul><ul><ul><li>Variable costs (VC) </li></ul></ul><ul><ul><li>Total costs (TC) </li></ul></ul><ul><ul><li>Sunk costs </li></ul></ul>
14. 14. Total and Variable Costs <ul><li>C(Q): Minimum total cost of producing alternative levels of output: </li></ul><ul><ul><li>C(Q) = VC(Q) + FC </li></ul></ul><ul><li>VC(Q): Costs that vary with output. </li></ul><ul><li>FC: Costs that do not vary with output. </li></ul>0 \$ Q C(Q) = VC + FC VC(Q) FC
15. 15. Fixed and Sunk Costs FC: Costs that do not change as output changes. Sunk Cost: A cost that is forever lost after it has been paid. \$ Q FC C(Q) = VC + FC VC(Q)
16. 16. Some Definitions <ul><li>Average Total Cost </li></ul><ul><ul><li>ATC = AVC + AFC </li></ul></ul><ul><ul><li>ATC = C(Q)/Q </li></ul></ul><ul><li>Average Variable Cost </li></ul><ul><ul><li>AVC = VC(Q)/Q </li></ul></ul><ul><li>Average Fixed Cost </li></ul><ul><ul><li>AFC = FC/Q </li></ul></ul><ul><li>Marginal Cost </li></ul><ul><ul><li>MC =  C/  Q </li></ul></ul>MR \$ Q ATC AVC AFC MC
17. 17. Fixed Cost ATC AVC Q 0 AFC Fixed Cost Q 0  (ATC-AVC) = Q 0  AFC = Q 0  (FC/ Q 0 ) = FC \$ Q ATC AVC MC
18. 18. Variable Cost AVC Variable Cost Q 0 Q 0  AVC = Q 0  [VC(Q 0 )/ Q 0 ] = VC(Q 0 ) \$ Q ATC AVC MC
19. 19. ATC Total Cost Q 0 Q 0  ATC = Q 0  [C(Q 0 )/ Q 0 ] = C(Q 0 ) Total Cost \$ Q ATC AVC MC
20. 20. Conclusion <ul><li>Cost functions are the foundation for helping to determine profit-maximizing behavior in future chapters. </li></ul>