Chapter 8 Production and Cost in the Short Run

1. Chapter 8Production and Cost in the Short Run

2. Learning Objectives • Explain general concepts of production and cost analysis • Examine the structure of short-run production based on the relation among total, average, and marginal products • Examine the structure of short-run costs using graphs of the total cost curves, average cost curves, and the short-run marginal cost curve • Relate short-run costs to the production function using the relations between (i) average variable cost and average product, and (ii) short-run marginal cost and marginal product

3. Basic Concepts of Production Theory • Production function • A schedule showing the maximum amount of output that can be produced from any specified set of inputs, given existing technology • Variable proportions production • Production in which a given level of output can be produced with more than one combination of inputs • Fixed proportions production • Production in which one, and only one, ratio of inputs can be used to produce a good

4. Basic Concepts of Production Theory • Technical efficiency • Achieved when maximum amount of output is produced with a given combination of inputs and technology • Economic efficiency • Achieved when firm is producing a given output at the lowest possible total cost

5. Basic Concepts of Production Theory • Inputs are considered variable or fixed depending on how readily their usage can be changed • Variable input • An input for which the level of usage may be varied to increase or decrease output • Fixed input • An input for which the level of usage cannot be changed and which must be paid even if no output is produced • Quasi-fixed input • A “lumpy” or indivisible input for which a fixed amount must be used for any positive level of output • None is purchased when output is zero

6. Basic Concepts of Production Theory • Short run • Current time span during which at least one input is a fixed input • Long run • Time period far enough in the future to allow all fixed inputs to become variable inputs • Planning horizon • Set of all possible short-run situations the firm can face in the future

7. Sunk Costs • Sunk cost • Payment for an input that, once made, cannot be recovered should the firm no longer wish to employ that input • Irrelevant for all future time periods; not part of the economic cost of production in future time periods • Should be ignored for decision making purposes • Fixed costs are sunk costs

8. Avoidable Costs • Avoidable costs • Input costs the firm can recover or avoid paying should it no longer wish to employ that input • Matter in decision making and should not be ignored • Variable costs and quasi-fixed costs are avoidable costs

9. Inputs in Production (Table 8.1) Avoidable SR & LR Direct Constant Sunk SR only Avoidable Constant If required: SR & LR

10. Short Run Production • In the short run, capital is fixed • Only changes in the variable labor input can change the level of output • Short run production function Q = f (L, K) = f (L)

11. Average & Marginal Products • Average product of labor • AP = Q/L • Marginal product of labor • MP = Q/L • When AP is rising, MP is greater than AP • When AP is falling, MPis less than AP • When AP reaches it maximum, AP = MP • Law of diminishing marginal product • As usage of a variable input increases, a point is reached beyond which its marginal product decreases

12. Total, Average, & Marginal Products of Labor, K = 2 (Table 8.3) -- -- 52 52 60 56 58 56.7 50 55 38 51.6 28 47.7 18 43.4 10 39.3 4 35.3 -4 31.4

13. Total, Average, & Marginal Products K = 2 (Figure 8.1)

14. Short Run Production Costs • Total fixed cost (TFC) • Total amount paid for fixed inputs • Does not vary with output • Total variable cost (TVC) • Total amount paid for variable inputs • Increases as output increases • Total cost (TC) TC = TFC + TVC

15. Short-Run Total Cost Schedules (Table 8.5) $ 6,000 $ 0 10,000 4,000 12,000 6,000 15,000 9,000 20,000 14,000 28,000 22,000 40,000 34,000

16. Total Cost Curves(Figure 8.3)

17. Average Costs • Average fixed cost (AFC) • Average variable cost (AVC) • Average total cost (ATC)

18. Short Run Marginal Cost • Short run marginal cost (SMC) measures rate of change in total cost (TC) as output varies

19. Average & Marginal Cost Schedules (Table 8.6) -- -- -- -- $100 $40 $60 $40 60 30 30 20 50 30 20 30 50 35 15 50 56 44 12 80 66.7 56.7 120 10

20. Average & Marginal Cost Curves (Figure 8.4)

21. Short Run Average & Marginal Cost Curves (Figure 8.5)

22. Short Run Cost Curve Relations • AFC decreases continuously as output increases • Equal to vertical distance between ATC & AVC • AVC is U-shaped • Equals SMC at AVC’s minimum • ATC is U-shaped • Equals SMC at ATC’s minimum

23. Short Run Cost Curve Relations • SMC is U-shaped • Intersects AVC & ATC at their minimum points • Lies below AVC & ATC when AVC & ATC are falling • Lies above AVC & ATC when AVC & ATC are rising

24. Relations Between Short-Run Costs & Production • In the case of a single variable input, short-run costs are related to the production function by two relations Wherewis the price of the variable input TC = wL + rK

25. Short-Run Production & Cost Relations (Figure 8.6)

26. Relations Between Short-Run Costs & Production • When marginal product (average product) is increasing, marginal cost (average cost) is decreasing • When marginal product (average product) is decreasing, marginal cost (average variable cost) is increasing • When marginal product = average product at maximum AP, marginal cost = average variable cost at minimum AVC

27. Summary • Technical efficiency occurs when a firm produces maximum output for a given input combination and technology; economic efficiency is achieved when the firm produces a given output at the lowest total cost • Production inputs can be variable, fixed, or quasi-fixed inputs • Short run refers to the current time span during which one or more inputs are fixed; Long run refers to the period far enough in the future that all fixed inputs become variable inputs • Sunk costs are irrelevant for future decisions and are not part of economic cost of production in future time periods; avoidable costs are payments a firm can recover or avoid, thus they do matter in decisions

28. Summary • The total product curve gives the economically efficient amount of labor for any output level when capital is fixed in the short run • Average product of labor is the total product divided by the number of workers: AP = Q/L • Marginal product of labor is the additional output attributable to using one additional worker with the use of capital fixed: MP = ∆Q/∆L • The law of diminishing marginal product states that as the number of units of the variable input increases, other inputs held constant, a point will be reached beyond which the marginal product of the variable input declines

29. Summary • Short-run total cost, TC, is the sum of total variable cost, TVC, and total fixed cost, TFC: TC = TVC + TFC • Average fixed cost, AFC, is TFCdivided by output: AFC = TFC/Q; average variable cost, AVC, is TVCdivided by output: AVC = TVC/Q; average total cost (ATC) is TCdivided by output: ATC = TC/Q • Short-run marginal cost, SMC, is the change in either TVCor TCper unit change in output Q • The link between product curves and cost curves in the short run when one input is variable is reflected in the relations, AVC = w/AP and SMC = w/MP, where wis the price of the variable input