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Cost and production

Cost and production. Firms maximize profits Types of costs and their relevance for decision making. Long run vs. short run Optimal choice between the inputs. Marginal product of labor. MP L = D Q/ D L Increase in total output associated with increase in labor

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Cost and production

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  1. Cost and production Firms maximize profits Types of costs and their relevance for decision making. Long run vs. short run Optimal choice between the inputs

  2. Marginal product of labor • MPL = DQ/DL • Increase in total output associated with increase in labor NOTE: not the output produced by the last worker

  3. Average Product of Labor • APL = Q/L • Measures the output of an “average” worker.

  4. AP MP Stages of Production Q Increasing Marginal Returns Diminishing Marginal Returns Negative Marginal Returns TP L

  5. Value of marginal product of labor • Market value of the marginal product of labor • Optimal input employment rule: marginal benefit equals marginal cost. Value of marginal product of labor equals wage

  6. What is the value of marginal product of a place-kicker?

  7. Short run vs. Long run • In the short run, some costs do not change. Some costs are fixed. • In the long run, all costs change. There are no fixed costs. • How long is the long run • For a hot dog stand? • For a nuclear power plant? • For a coffee shop on the corner?

  8. Average Cost • Total cost per unit • Sum of average variable cost and average fixed cost

  9. Marginal Cost • The cost of producing an additional unit of output • Increase in cost divided by the increase in output

  10. Relation between the cost curves $ MC ATC AVC A TFC D B C AFC Q 1

  11. Sunk cost • Sunk cost is irrelevant • My laptop was $1,400 when I bought it in 2000. I have never used it. I should be able to sell it for $1,200 • When you drive a car off the dealer’s lot, how much cost do you “sink”?

  12. Short-Run Costs of Four Different Plants

  13. Long-Run Average Cost Curve

  14. Legally imposed decreasing returns to scale • Tanker companies and unlimited liability • From 1967 to 1980 the number of firms in hazardous sectors has increased. • Single-engine airplane producers Cessna and Piper Aircraft stopped production in 90’s. At the same time, it is legal to fly a non-certified plane if you built at least half of it yourself.

  15. Learning by doing vs. increasing returns to scale: after producing 15 million cars the cost of one Model T fell from $3,000 to $300 Cost Economies of scale ATC Learning by doing Output

  16. Capital and labor:optimal choice between two inputs Are we in long or short run? • Isoquants • Isocosts

  17. Isoquant(production indifference curves) • The combinations of inputs (K, L) that yield the producer the same level of output. • The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output. L

  18. Linear Isoquants • Capital and labor are perfect substitutes K Increasing Output Q2 Q3 Q1 L

  19. Leontief Isoquants • Capital and labor are perfect complements • Capital and labor are used in fixed-proportions Q3 K Q2 Q1 Increasing Output

  20. Isoquants in a “normal” case • Inputs are not perfectly substitutable • Diminishing marginal rate of technical substitution • Most production processes have isoquants of this shape K Q3 Increasing Output Q2 Q1 L

  21. K 6 3 L 2 4 Concave indifference curves can be thought of as an approximation to a set of fixed-proportions technologies: there are three isoquants for 10 units of output.

  22. How do you get to the point A. K 6 A 3 B L 4 2 At what relative price of capital production will use combination of inputs given by B.

  23. Isocost(production budget line) K • The combinations of inputs that cost the producer the same amount of money • For given input prices, isocosts farther from the origin are associated with higher costs. • Changes in input prices change the slope of the isocost line C0 C1 L K New Isocost Line for a decrease in the wage (price of labor). L

  24. Cost Minimization K Point of Cost Minimization Slope of Isocost = Slope of Isoquant Q L

  25. Cost Minimization • Marginal product per dollar spent should be equal for all inputs: • Expressed differently

  26. The firm is using inputs at point C and uses the inputs efficiently. The price of capital is 5. What is the price of labor?

  27. Inputs substitution in production of parking • There are two inputs: Land and Concrete. • How is the choice of inputs affected by the price (relative scarcity) of land?

  28. Downtown Chicago C Q = 200 parking spots L Oxford, Ohio.

  29. Multi-Product Cost Function C(Q1, Q2): Cost of producing two outputs jointly

  30. Economies of Scope • C(Q1, Q2) < C(Q1, 0) + C(0, Q2) • It is cheaper to produce the two outputs jointly instead of separately. • Examples? • How is it different from economies of scale?

  31. Mergers. Economies of scope or economies of scale? • Daimler-Chrysler • AOL-Time Warner • Cingular – AT&T

  32. Cost Complementarity • The marginal cost of producing good 1 declines as more of good two is produced: DMC1/DQ2 < 0. • Examples?

  33. Functional forms of cost functions an Example • Total Cost: C(Q) = 10 + Q + Q2 • Variable cost function: VC(Q) = Q + Q2 • Variable cost of producing 2 units: VC(2) = 2 + (2)2 = 6 • Fixed costs: FC = 10 • Marginal cost function: MC(Q) = 1 + 2Q • Marginal cost of producing 2 units: MC(2) = 1 + 2(2) = 5

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