Measuring Cost: Which Costs Matter? (pp )

Transcription

1 Measuring Cost: Which Costs Matter? (pp ) Some costs vary with output, while some remain the same no matter the amount of output Total cost can be divided into: 1. Fixed Cost (FC) Does not vary with the level of output 2. Variable Cost (VC) Cost that varies as output varies Chapter 7 1

2 Fixed and Variable Costs (pp ) Total output is a function of variable inputs and fixed inputs Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or TC = FC + VC Chapter 7 2

3 Fixed and Variable Costs (pp ) Which costs are variable and which are fixed depends on the time horizon Short time horizon (Short-run) most costs are fixed Long time horizon(long-run) many costs become variable In determining how changes in production will affect costs, must consider if fixed or variable costs are affected. Chapter 7 3

4 Marginal and Average Cost (pp ) In completing a discussion of costs, must also distinguish between Average Cost Marginal Cost After definition of costs is complete, one can consider the analysis between shortrun and long-run costs Chapter 7 4

5 Measuring Costs (pp ) Marginal Cost (MC): The cost of expanding output by one unit Fixed costs have no impact on marginal cost, so it can be written as: Preview: p=mc is the profit maximizing condition to determine the quantity supplied, q, by a firm. MC = ΔVC Δq = ΔTC Δq Chapter 7 5

6 Measuring Costs (pp ) Average Total Cost (ATC) Cost per unit of output Also equals average fixed cost (AFC) plus average variable cost (AVC) by definition. ATC = TC q = TFC q + TVC q AFC + AVC Chapter 7 6

7 Measuring Costs (pp ) All the types of costs relevant to production have now been discussed Can now discuss how they differ in the long and short run Costs that are fixed in the short run may not be fixed in the long run Typically in the long run, most if not all costs are variable Chapter 7 7

8 A Firm s Short Run Costs (pp ) Chapter 7 8

9 Determinants of Short Run Costs (pp ) The rate at which these costs increase depends on the nature of the production process The extent to which production involves diminishing returns to variable factors Diminishing returns to labor When marginal product of labor is decreasing Chapter 7 9

10 Determinants of Short Run Costs (pp ) If marginal product of labor decreases significantly as more labor is hired Costs of production increase rapidly Greater and greater expenditures must be made to produce more output If marginal product of labor decreases only slightly as increase labor Costs will not rise very fast when output is increased Chapter 7 10

11 Determinants of Short Run Costs An Example (pp ) Assume the wage rate (w) is fixed relative to the number of workers hired Variable costs is the per unit cost of extra labor times the amount of extra labor: wl MC = ΔVC Δq = wδl Δq Chapter 7 11

12 Determinants of Short Run Costs An Example (pp ) Remembering that And rearranging MP L = Δq ΔL ΔL for a 1 unit Δq = ΔL Δq = 1 MP L Chapter 7 12

13 Determinants of Short Run Costs An Example (pp ) We can conclude: MC = w MP L and a low marginal product (MP L ) leads to a high marginal cost (MC) and vice versa Chapter 7 13

14 Determinants of Short Run Costs (pp ) Consequently (from the table): MC decreases initially with increasing returns 0 through 4 units of output MC increases with decreasing returns 5 through 11 units of output Chapter 7 14

15 Cost Curves (pp ) The following figures illustrate how various cost measures change as outputs change Curves based on the information in table 7.1 discussed earlier Chapter 7 15

16 Cost ($ per year) Short-run Cost Curves for a Firm (pp ) Total cost is the vertical sum of FC and VC. TC VC Variable cost increases with production and the rate varies with increasing and decreasing returns Fixed cost does not vary with output FC Output Chapter 7 16

17 Cost Curves (pp ) Cost ($/unit) MC ATC AVC AFC Output (units/yr) Chapter 7 17

18 Cost Curves (pp ) When MC is below AVC, AVC is falling When MC is above AVC, AVC is rising When MC is below ATC, ATC is falling When MC is above ATC, ATC is rising Therefore, MC crosses AVC and ATC at the minimums The Average Marginal relationship (Remember the examples of exam scores; batting scores) Chapter 7 18

19 Cost Curves for a Firm (pp ) The line drawn from the origin to the variable cost curve: Its slope equals AVC The slope of a point on VC or TC equals MC Therefore, MC = AVC at 7 units of output (point A) P A TC VC FC Output Chapter 7 19

20 Cost in the Long Run (pp ) In the long run a firm can change all of its inputs In making cost minimizing choices, must look at the cost of using capital and labor in production decisions Chapter 7 20

21 Cost in the Long Run (pp ) Capital is either rented/leased or purchased We will consider capital rented as if it were purchased User Cost of Capital = Economic Depreciation + (Interest Rate) (Value of Capital) See the example of aircraft on pp Why do we need this argument? (Profits, revenue, and costs are all in terms of flow, i.e., per period concepts.) Chapter 7 21

22 Cost in the Long Run (pp ) The Isocost Line A line showing all combinations of L & K that can be purchased for the same cost Total cost of production is sum of firm s labor cost, wl, and its capital cost, rk: C = wl + rk For each different level of cost, the equation shows another isocost line Chapter 7 22

23 Cost in the Long Run (pp ) Rewriting C as an equation for a straight line: K = C/r - (w/r)l Slope of the isocost: ΔK ( w ) ΔL r -(w/r) is the ratio of the wage rate to rental cost of capital. This shows the rate at which capital can be substituted for labor with no change in cost = Chapter 7 23

24 Choosing Inputs (pp ) We will address how to minimize cost for a given level of output by combining isocost lines with isoquants We choose the output we wish to produce and then determine how to do that at minimum cost Isoquant is the quantity we wish to produce Isocost is a set of combinations of K and L that costs equal each other. Chapter 7 24

25 Producing a Given Output at Minimum Cost (pp ) Capital per year K 2 Q 1 is an isoquant for output Q 1. There are three isocost lines, of which 2 (C 1 & C 2 ) are possible choices in which to produce Q 1. K 1 A Isocost C 2 shows quantity Q 1 can be produced with combination K2,L2 or K3,L3. However, both of these are higher cost combinations than K1,L1. K 3 Q 1 L 2 L 1 C 0 C 1 C 2 Labor per year L 3 Chapter 7 25

26 Cost in the Long Run (pp ) How does the isocost line relate to the firm s production process? MRTS = - ΔK ΔL = MP L MP K Slope of isocost line = w r MP L = MPK w r when firmminimizes cost Chapter 7 26

27 Cost in the Long Run (pp ) A firm s choice of inputs is determined by the cost minimization condition: An isocost line is tangent to a given isoquant. MRTS = w r Chapter 7 27

28 Input Substitution When an Input Price Change (pp ) If the price of labor changes, then the slope of the isocost line changes, -(w/r) It now takes a new quantity of labor and capital to produce the output If price of labor increases relative to price of capital, and capital is substituted for labor Chapter 7 28

29 Input Substitution When an Input Price Change Capital per year If the price of labor rises, the isocost curve becomes steeper due to the change in the slope -(w/l). K 2 B The new combination of K and L is used to produce Q 1. Combination B is used in place of combination A. K 1 A Q 1 C 2 C 1 L 2 L 1 Labor per year Chapter 7 29

30 Cost in the Long Run The minimum cost combination can then be written as: MP L MP = K w Minimum cost for a given output will occur when each dollar of input added to the production process will add an equivalent amount of output. r Chapter 7 30

31 Cost in the Long Run If w = $10, r = $2, and MP L = MP K, which input would the producer use more of? Labor because it is cheaper Increasing labor lowers MP L Decreasing capital raises MP K Substitute labor for capital until MP w L = MP r K Chapter 7 31

32 Cost in the Long Run Cost minimization with Varying Output Levels For each level of output, there is an isocost curve showing minimum cost for that output level A firm s expansion path shows the minimum cost combinations of labor and capital at each level of output Slope equals ΔK/ΔL Chapter 7 32

33 A Firm s Expansion Path Capital per year 150 $3000 The expansion path illustrates the least-cost combinations of labor and capital that can be used to produce each level of output in the long-run $2000 A 50 B C 200 Units Expansion Path 300 Units Labor per year Chapter 7 33

34 Expansion Path and Long Run Costs Firm s expansion path has same information as long-run total cost curve To move from expansion path to LR cost curve Find tangency with isoquant and isocost Determine min cost of producing the output level selected Graph output-cost combination Chapter 7 34

35 A Firm s Long Run Total Cost Curve Cost/ Year 3000 F Long Run Total Cost 2000 E 1000 D Output, Units/yr Chapter 7 35

36 Review (Chs. 1-7)

37 Ch. 1 (1):Themes of Microeconomics Microeconomics deals with limits Limited budgets Limited time Limited ability to produce How do we make the most of limits? How do we allocate scarce resources? Chapter 7 37

38 Ch. 1(2): Themes of Microeconomics Workers, firms and consumers must make trade-offs (i.e.,choices) Do I work or go on vacation? Do I purchase a new car or save my money? Do we hire more workers or buy new machinery? How are these trade-offs best made? (Rational choices for consumers & firms interests) Chapter 7 38

39 Ch. 2 (1): Topics to Be Discussed How do short-run and long-run elasticities differ? How do we understand and predict the effects of changing market conditions? --- Demand and Supply Analysis Chapter 7 39

40 Ch. 2 (2): Supply and Demand Supply and demand analysis can: 1. Help us understand and predict how real world economic conditions affect market price and production 2. Analyze the impact of government price controls, minimum wages, price supports, and production incentives on the economy 3. Determine how taxes, subsidies, tariffs and import quotas affect consumers and producers Chapter 7 40

41 Ch. 3 (1) There are three steps involved in the study of consumer behavior 1. Consumer Preferences To describe how and why people prefer one good to another 2. Budget Constraints People have limited incomes Chapter 7 41

42 Ch. 3 (2) 3. Given preferences and limited incomes, what amount and type of goods will be purchased? What combination of goods will consumers buy to maximize their satisfaction? Chapter 7 42

43 Ch. 4 Individual Demand Income and Substitution Effects Market Demand Consumer Surplus Chapter 7 43

44 Ch. 5 Describing Risk Preferences Toward Risk Reducing Risk Chapter 7 44

45 Ch. 6 (1) The Technology of Production Production with One Variable Input (Labor) Isoquants Production with Two Variable Inputs Returns to Scale Chapter 7 45

46 Ch. 6(2) Production decisions of a firm are similar to consumer decisions Can also be broken down into three steps 1. Production Technology Describe how inputs can be transformed into outputs Inputs: land, labor, capital and raw materials Outputs: cars, desks, books, etc. Firms can produce different amounts of outputs using different combinations of inputs Chapter 7 46

47 Ch. 6 (3) 2. Cost Constraints Firms must consider prices of labor, capital and other inputs Firms want to minimize total production costs partly determined by input prices As consumers must consider budget constraints, firms must be concerned about costs of production Chapter 7 47

48 Ch. 6(4) 3. Input Choices Given input prices and production technology, the firm must choose how much of each input to use in producing output Given prices of different inputs, the firm may choose different combinations of inputs to minimize costs If labor is cheap, firm may choose to produce with more labor and less capital Chapter 7 48