Lecture 3 Production and Costs

1. Lecture 3 Production and Costs

2. Outline • Production Theory: Basics • Cost Theory: Basics • Economies and Diseconomies of Scale • Production With Multiple Inputs • Time and Costs: Observations on Fixed Costs • Ideas That Matter • Complications

3. Production Theory: Basics • Production Function: The relationship describing the most output possible with a given quantity of an input. • (Or the least amount inputs necessary to produce some given level of output.) • Marginal Product: The change in total product when one of the inputs is changed. • Approximation: MPx =Change in output/change in input • Exact (calculus): MPx =dq/dx • Average Product: Output per unit of input APx =Q/X

4. Example EXTRA Q PER EXTRA L

5. The Graph Max AC occurs when MC=AC MP increase and then decreases

6. Useful Stuff • MP increases and then decreases • Think about what an odd world it would be if MP did not decrease. • (This is commonly defined as diminishing marginal returns). • AP begins to decrease only when MP<AP • Techies can prove this using about two lines of calculus, but it has a common sense explanation as well

7. Application: Optimal Choice of Input

8. Suppose that the output is worth $10 per unit and labor costs $15 per hour. Total value (value of output – cost of inputs) is as follows.

9. More Marginals • Marginal revenue product: the revenue obtained from the extra output produced when another unit of the input is employed. Formally, • MRP = Marginal Product x Price of output

10. Output price=$10Input price =$15 MRP=10*MP If MRP > Input price, buy more input

11. Cost Function: Basics • Cost Function: The relationship describing the least expensive way producing a given quantity of output. (Or, equivalently, the most output that can be produced for a given level of expenditure.) • “Costs” are simply of way of expressing economically important information about what the firm does. As such, when we describe costs, we are really summarizing two kinds of things • The production technology (e.g., what sorts of inputs are able to produce what sorts of outputs) • The cost of the inputs • Thus, if we have described the technology by writing out the production function, we need only to know the price of the inputs before we can describe costs.

12. Example: Given the production function suppose that cost of the fixed input=$10 and wage rate=$5)

13. Economies and diseconomies of scale • Economies of scale the tendency for AC to decrease when output increases • MC<AC • Diseconomies of Scale: The tendency for AC to increase when output increases • MC>AC

14. Why Economies of Scale? • Learning by doing/gains from specialization • The presence of fixed costs • Pure technological factors • Pecuniary Economies: Reduction in input prices by purchasing in volume.

15. Why Diseconomies of Scale? • Managerial complexities • Pecuniary diseconomies

16. Production with multiple inputs • There is more than one way to do most things. (Think of examples where this is and isn’t the case.) Thus, the essential problem is how to find the optimal mix of inputs. This can be stated formally in either of two ways. • Minimize the cost of producing a given quantity of output • Maximize the output from a given level of expenditures.

17. Isoquant: various combinations of inputs that will produce a given level of output. (equivalent to an indifference curve)

18. Marginal Rate of Technical Substitution: The rate at which one input can be substituted for another without any change in output

19. Optimal Input Mix (Price of labor = $10, Price of Labor =$25) What is the Marginal Condition That Makes This Optimal

20. MRTS measures the relative productivity of the two inputs • The ratio of their prices measures their relative costs • If an input’s relative productivity is greater than its relative cost, buy more of that input and less of the other

21. Time and Costs: Observations on Fixed Costs • “Long run”, “short run” and fixed costs • Long Run: Period of time sufficiently long to vary all costs. • Short Run: Any period less than the long run. • Fixed Costs: Those costs that cannot be varied in the short run.

22. Distinguishing fixed and sunk costs • Fixed costs: Costs that don’t vary with output • an airplane • Sunk costs: Costs that can’t be recovered • a railroad track

23. Opportunity Cost: The total value of what must be given up to get something (which is often more than the measured monetary cost) • Economic profit: Revenues-Opportunity Cost • As distinguished from accounting cost: The dollars that must be given up to get something else. and accounting profit: Revenues-accounting cost • Examples of Opportunity Cost • Retained earnings (was Coca Cola’s great cash flow free?) • Make vs buy (Was Valuejet really wrong to outsource maintenance?) • Time (Who gets the keys to the company jet?)

24. Ideas That Matter: Relevant Costs • When do fixed costs matter? As we’ve already seen, certainly not in any decision involving production levels, or pricing. Consider these examples • R&D: “We’ve come too far to stop now. • Buildings: “We built in the wrong location, but we’re there now • Eternal problem: Managers who are given the power to make fixed investments need to be held accountable for those decisions. But how do you get them to ignore the investment once it’s made?

25. Ideas That Matter: Defining and measuring efficiency • Pure Waste: not obtaining maximum output from a given amount of inputs • Allocative Efficiency: Employing the wrong mix of inputs • Caution: Is waste really waste if it would cost more to eliminate than would be saved by eliminating

26. Ideas That Matter: Comparative Advantage • Suppose: • Attilla can produce 4 units of clean room or 2 units of clean dog per hour • Godzilla can produce 1 unit of clean room or 1 unit of clean dog per hour. • Note: Godzilla is, by one measure, less productive. • Can It Ever Be Efficient to Use a Less Productive Asset? Sure : • Suppose both kids spent 1 hour on each chore (4 hours of total work), producing 5 units of clean room and 3 units of clean dog. • They could produce the same output with less effort. Godzilla could spend 2 hours on dog (producing 2 units of clean dog). Attilla could spend 1.25 hours on room (producing 5 units of clean room) and 0.5 hours on dog (producing 1 unit of clean dog). They get the same output with only 3.75 hours of labor

27. Conclusion: The Value of Comparative Advantage • An input is said to have a comparative advantage over another input if the relative cost of producing one good is lower (Godzilla has a comparative advantage in the production of clean dog since she only has to give up one unit of clean room to get an extra unit of clean dog.) • As long as there is a comparative advantage, specialization increases output • Implications of Comparative Advantage • What do “menial” workers really produce? • Trade is good: the U.S. might benefit from trade with developing countries that are not as absolutely productive but that have a comparative advantage in the production of some goods

28. Complications:Multiple Outputs • Most production processes produce more than one output • Cars and SUV’s. Consulting services and audits. Finance majors and marketing majors • Economies of Scope are said to exist when it is less expensive to produce more than one output jointly than separately. • Why economies of scope? • The most likely source of economies of scope is common overhead

29. Complications: Multiple Plants • : Some firms have several plants that produce the same output. This raises two kinds of issues. • Why? • If it is efficient to have more than one plant, how much output should be assigned to each plant

30. Transfer Pricing • Many firms use a separate division to produce some intermediate input. What “price’ should the division charge for its input.? • The “customer” would like to have a low price (zero is nice) but this creates incentives to produce too much . • The “seller” would like to have a high price (it is in the position of being a monopolist with a captive customer) but this creates incentives to produce too little • Principle: transferring at marginal cost requires the end user to recognize the true cost of the good.ComplicationsHow do you measure marginal cost (especially when the manager of the intermediate division has incentives to inflate costs).What if marginal costs are below average costs meaning that the intermediate division operates at a loss (Certainly a possibility and if so, how do you assure the manager of the intermediate division that its good to run a losing operation.)What if the intermediate good can also be sold on an open marketActually a blessing since the cost of transfering the intermediate good to the final producer is really just the price at which it could be sold on the marketBut this may create real hard feelings if the outside customers of the intermediate good compete with the final manufacturer.

31. Complications • How do you measure marginal cost (especially when the manager of the intermediate division has incentives to inflate costs). • What if marginal costs are below average costs meaning that the intermediate division operates at a loss (Certainly a possibility and if so, how do you assure the manager of the intermediate division that its good to run a losing operation.) • What if the intermediate good can also be sold on an open market • Actually a blessing since the cost of transfering the intermediate good to the final producer is really just the price at which it could be sold on the market • But this may create real hard feelings if the outside customers of the intermediate good compete with the final manufacturer.