Overview BA 210 Lesson III 1 Inputs and

Overview BA 210 Lesson III. 1 Inputs and Costs 1

Overview Chapter 12 Inputs and Costs Lesson III. 1 Inputs and Costs Total Product Marginal Product Total Cost and Marginal Cost Diminishing Returns Cost Relations Short Run verses Long Run Costs Summary Review Questions BA 210 Lesson III. 1 Inputs and Costs 2

Total Product BA 210 Lesson III. 1 Inputs and Costs 3

Total Product Study Inputs and Costs to Minimize Costs. Everyone should: • All firms in all market environments n Monopoly (1 firm with restricted entry) n Duopoly (2 firms with restricted entry) n Perfect Competition (many firms with free entry) • Charities n Toys for Tots should minimize the cost of getting toys to tots • They should often solicit cash over donated toys or labor. (Instead of having 1000 people each buying 1 toy for $20, people could each donate $20 and Toys for Tots could buy more than 1000 toys for $20, 000 by getting a quantity discount. ) • Donors n Perfectly altruistic people helping kids (not feeling warm and fuzzy) should donate money rather than toys or labor, and so minimize their own cost of giving. (see http: //faculty. pepperdine. edu/jburke 2/giving. pdf) BA 210 Lesson III. 1 Inputs and Costs 4

Total Product • A production function is the relationship between the quantity of inputs a firm uses and the quantity of output it produces. • A fixed input is an input whose quantity is fixed for a period of time and cannot be varied. • A variable input is an input whose quantity the firm can vary at any time. • The short run is the time period in which at least one input is fixed. • The long run is the time period in which all inputs can be varied. • For example, a Subway shop cannot change its ovens within 24 hours, but it could with a year. BA 210 Lesson III. 1 Inputs and Costs 5

Total Product Short-Run vs. Long-Run Decisions • Examples where some capital or labor is fixed in the short-run. n Office space may not be adjustable in the short-run. n Labor with contracts is not completely adjustable in the short-run. • It takes time to terminate labor. • Unless stated otherwise in a homework or exam problem, just consider the case where labor is variable in both the short-run and long-run, and capital is fixed in the short-run but flexible in the long-run. BA 210 Lesson III. 1 Inputs and Costs 6

Total Product • The total product curve shows how the quantity of output depends on the quantity of the variable input, for a given quantity of the fixed input. BA 210 Lesson III. 1 Inputs and Costs 7

Marginal Product BA 210 Lesson III. 1 Inputs and Costs 8

Total Product, Marginal Product, Average Product • Average Product of an Input: measures output produced per unit of input. (It is a common measure of productivity, but it is less useful than marginal product, explained later. ) • Marginal Product on an Input: change in total output attributable to the last unit of an input. • As we will see, Marginal Product is the essential measure of input productivity for cost minimization. BA 210 Lesson III. 1 Inputs and Costs 9

Marginal Production Function and Total Product Curve for George and Martha’s Farm Quantity of wheat (bushels) Adding a 7 th worker leads to an increase in output of only 7 bushels Quantity MP of labor L of wheat Q MPL= DQ/DL (worker) (bushels per worker) 2 0 2 3 4 5 6 7 75 84 91 8 1 64 7 20 51 6 40 36 4 60 19 5 80 0 1 Total product, TP Adding a 2 nd worker leads to an increase in output of 17 bushels 0 3 100 96 19 17 15 13 11 9 7 5 8 Quantity of labor (workers) BA 210 Lesson III. 1 Inputs and Costs 10

Marginal Product of Labor Curve Marginal product of labor (bushels per worker) There are diminishing returns to labor. 19 17 15 13 11 9 7 5 0 Marginal product of labor, MPL 1 2 3 4 5 6 7 8 Quantity of labor (workers) BA 210 Lesson III. 1 Inputs and Costs 11

Marginal Product • There are diminishing returns to an input when an increase in the quantity of that input, holding the levels of all other inputs fixed, leads to a decline in the marginal product of that input. BA 210 Lesson III. 1 Inputs and Costs 12

Marginal Product Increasing, Diminishing and Negative Marginal Productivity Q Increasing Marginal Productivity Diminishing Marginal Productivity Negative (and diminishing) Marginal Productivity Total Product MP BA 210 Lesson III. 1 Inputs and Costs L 13

Total Cost and Marginal Cost BA 210 Lesson III. 1 Inputs and Costs 14

Total Cost and Marginal Cost • Types of Costs n Short-Run • Fixed costs (FC) is a fixed amount owed for any positive output. – If capital is fixed in the short-run, then FC equals the cost of capital. – For example, you lease a railroad car for $10, 000 for a month, FC = $10, 000. • Short-run total costs (TC) • Short-run variable costs (VC). Defined by VC = TC – FC. n Long-Run • All costs are variable. • Zero fixed costs. BA 210 Lesson III. 1 Inputs and Costs 15

Total Cost and Marginal Cost C(Q): Minimum total cost of producing alternative levels of $ output: C(Q) = VC(Q) + FC C(Q) = VC + FC VC(Q): Costs that vary with output. VC(Q) FC: Costs if output is zero. FC 0 BA 210 Lesson III. 1 Inputs and Costs Q 16

Total Cost and Marginal Cost FC: Costs that do not change as output changes. Since fixed cost is forever lost $ after it has been paid, decision makers should ignore fixed costs to minimize costs. • Being rational in your personal life is a challenge. The extra $120, 000 I paid for my house in 2007 (compared with prices 1 year later) is like a sunk cost. C(Q) = VC + FC VC(Q) FC Q BA 210 Lesson III. 1 Inputs and Costs 17

Total Cost and Marginal Cost MC = DC/DQ • Marginal cost curves often initially decrease with output Q because of specialization of labor. • Example: Workers at the Malibu $ MC subway work best when there are several customers (Q midsize) because the workers specialize. • Marginal cost curves eventually increase with output when inputs crowd. • Example: Workers at the Malibu subway work become less productive and costs increase if Q is so large that workers are crowded. • Unless a homework or exam problem explicitly states otherwise, draw the marginal cost curves Ushaped, as on the right. Specialization of Labor BA 210 Lesson III. 1 Inputs and Costs Decreasing productivity of inputs because of diminishing returns Q 18

Total Cost and Marginal Cost • The total cost curve becomes steeper as more output is produced due to diminishing returns. BA 210 Lesson III. 1 Inputs and Costs 19

Total Cost and Marginal Cost Total Cost Curve for George and Martha’s Farm if labor cost $200 each unit, and capital is fixed and costs $400 total. $2, 000 Total cost, TC I 1, 800 H 1, 600 G 1, 400 F 1, 200 E 1, 000 Total cost, TC D 800 C 600 B 400 A 200 0 19 36 51 64 75 84 91 96 Quantity of wheat (bushels) Point on graph A B C D E F G H I Quantity of labor L (worker) 0 1 2 3 4 5 6 7 8 Quantity of wheat Q (bushels) 0 19 36 51 64 75 84 91 96 Variable cost (VC) $O 200 400 600 800 1, 000 1, 200 1, 400 1, 600 Fixed Cost (FC) Total cost (TC = FC+VC) $400 400 400 $ 400 600 800 1, 000 1, 200 1, 400 1, 600 1, 800 2, 000 BA 210 Lesson III. 1 Inputs and Costs 20

Diminishing Returns BA 210 Lesson III. 1 Inputs and Costs 21

Diminishing Returns Costs at Selena’s Gourmet Salsas BA 210 Lesson III. 1 Inputs and Costs 22

Diminishing Returns Total Cost and Marginal Cost Curves for Selena’s Gourmet Salsas (a) Total Cost 8 th case of salsa increases total cost by $180. $1, 400 (b) Marginal Cost of case TC $250 MC 1, 200 1, 000 800 2 nd case of salsa increases total cost by $36. 150 600 100 400 50 200 0 1 2 3 4 5 6 7 8 9 10 0 1 2 Quantity of salsa (cases) BA 210 Lesson III. 1 Inputs and Costs 3 4 5 6 7 8 9 10 Quantity of salsa (cases) 23

Diminishing Returns Why is the Marginal Cost Curve Upward Sloping? • Because there are diminishing returns to inputs in this example. As output increases, the marginal product of the variable input declines. • This implies that more and more of the variable input must be used to produce each additional unit of output as the amount of output already produced rises. • And since each unit of the variable input must be paid for, the cost per additional unit of output also rises. BA 210 Lesson III. 1 Inputs and Costs 24

Cost Relations BA 210 Lesson III. 1 Inputs and Costs 25

Cost Relations Average Total Cost Curve • Increasing output has two opposing effects on average total cost: n n The spreading effect: the larger the output, the greater the quantity of output over which fixed cost is spread, leading to lower the average fixed cost. The diminishing returns effect: the larger the output, the greater the amount of variable input required to produce additional units leading to higher average variable cost. BA 210 Lesson III. 1 Inputs and Costs 26

Cost Relations Average Costs for Selena’s Gourmet Salsas BA 210 Lesson III. 1 Inputs and Costs 27

Cost Relations Average Total Cost Curve for Selena’s Gourmet Salsas Cost of case $140 Average total cost, ATC Minimum average total cost 120 100 M 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 Quantity of salsa (cases) Minimum-cost output BA 210 Lesson III. 1 Inputs and Costs 28

Cost Relations Average Total Cost ATC = AVC + AFC ATC(Q) = C(Q)/Q $ Relation of MC and ATC: • MC > ATC implies ATC is increasing MC ATC • MC < ATC implies ATC is decreasing (There is an analogy to your GPA: If your next grade > GPA, your GPA is increasing. ) Thus, ATC is decreasing until it intersects MC, then it is increasing. Q BA 210 Lesson III. 1 Inputs and Costs 29

Cost Relations Average Variable Cost AVC = VC(Q)/Q $ Relation of ATC and AVC: ATC > AVC in the short-run, since FC > 0. MC ATC AVC Relation of MC and AVC: • MC > AVC implies AVC is increasing • MC < AVC implies AVC is decreasing Q BA 210 Lesson III. 1 Inputs and Costs 30

Cost Relations Summary Average Total Cost ATC = AVC + AFC ATC = C(Q)/Q $ MC ATC AVC Average Variable Cost AVC = VC(Q)/Q Average Fixed Cost AFC = FC/Q = ATC-AVC Marginal Cost MC = DC/DQ AFC Q BA 210 Lesson III. 1 Inputs and Costs 31

Cost Relations Recovering Fixed Cost Q 0 (ATC-AVC) $ = Q 0 AFC = Q 0 (FC/ Q 0) MC ATC AVC = FC ATC AFC Fixed Cost AVC Q 0 BA 210 Lesson III. 1 Inputs and Costs Q 32

Cost Relations Recovering Variable Cost $ Q 0 AVC MC ATC = Q 0 [VC(Q 0)/ Q 0] AVC = VC(Q 0) AVC Variable Cost Minimum of AVC Q 0 BA 210 Lesson III. 1 Inputs and Costs Q 33

Cost Relations Recovering Total Cost Q 0 ATC $ MC ATC = Q 0 [C(Q 0)/ Q 0] AVC = C(Q 0) ATC Minimum of ATC Total Cost Q 0 BA 210 Lesson III. 1 Inputs and Costs Q 34

Short Run verses Long Run Costs BA 210 Lesson III. 1 Inputs and Costs 35

Short Run verses Long Run Costs Short-Run versus Long-Run Costs • In the short run, fixed cost is completely outside the control of a firm. But all inputs are variable in the long run. • The firm will choose its fixed input (fixed cost) in the long run based on the level of output it expects to produce. BA 210 Lesson III. 1 Inputs and Costs 36

Short Run verses Long Run Costs Cost of case Choosing the Level of Fixed Cost of Selena’s Gourmet Salsas: $250 At low output levels, low fixed cost yields lower average total cost At high output levels, high fixed cost yields lower average total cost 200 Low fixed cost ATC 1 150 100 A 2 TC High fixed cost 50 0 1 2 3 4 5 Low fixed cost (FC = $108) Quantity of salsa (salsa) 1 2 3 4 5 6 7 8 9 10 High variable cost Total cost $12 48 108 192 300 432 588 768 972 1, 200 $120 156 216 300 408 540 696 876 1, 080 1, 308 ATC of case ATC 1 $120. 00 78. 00 72. 00 75. 00 81. 60 90. 00 99. 43 109. 50 120. 00 130. 80 6 7 8 9 10 Quantity of salsa (cases) High fixed cost (FC = $216) Low variable cost $6 24 54 96 150 216 294 384 486 600 Total cost $222 240 270 312 366 432 510 600 702 816 ATC of case A 2 TC $222. 00 120. 00 90. 00 78. 00 73. 20 72. 00 72. 86 75. 00 78. 00 81. 60 BA 210 Lesson III. 1 Inputs and Costs 37

Short Run verses Long Run Costs The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost for each level of output. BA 210 Lesson III. 1 Inputs and Costs 38

Short Run verses Long Run Costs Short-Run and Long-Run Average Total Cost Curves If you anticipated producing quantity 3, you would have selected the fixed costs (fixed inputs) in curve ATC 3 so to minimize ATC Cost of case Constant returns to scale Increasing returns to scale ATC Decreasing returns to scale ATC LRATC 6 9 3 B Y A 0 X C 3 4 5 6 7 8 9 BA 210 Lesson III. 1 Inputs and Costs Quantity of salsa (cases) 39

Short Run verses Long Run Costs Returns to Scale • There are increasing returns to scale (economies of scale) when long-run average total cost declines as output increases. • There are decreasing returns to scale (diseconomies of scale) when long-run average total cost increases as output increases. • There are constant returns to scale when long-run average total cost is constant as output increases. BA 210 Lesson III. 1 Inputs and Costs 40

Summary BA 210 Lesson III. 1 Inputs and Costs 41

Summary 1. The relationship between inputs and output is a producer’s production function. In the short run, the quantity of a fixed input cannot be varied but the quantity of a variable input can. In the long run, the quantities of all inputs can be varied. For a given amount of the fixed input, the total product curve shows how the quantity of output changes as the quantity of the variable input changes. 2. There are diminishing returns to an input when its marginal product declines as more of the input is used, holding the quantity of all other inputs fixed. 3. Total cost is equal to the sum of fixed cost, which does not depend on output, and variable cost, which does depend on output. BA 210 Lesson III. 1 Inputs and Costs 42

Summary 4. Average total cost, total cost divided by quantity of output, is the cost of the average unit of output, and marginal cost is the cost of one more unit produced. U-shaped average total cost curves are typical, because average total cost consists of two parts: average fixed cost, which falls when output increases (the spreading effect), and average variable cost, which rises with output (the diminishing returns effect). 5. When average total cost is U-shaped, the bottom of the U is the level of output at which average total cost is minimized, the point of minimum-cost output. This is also the point at which the marginal cost curve crosses the average total cost curve from below. BA 210 Lesson III. 1 Inputs and Costs 43

Summary 6. In the long run, a producer can change its fixed input and its level of fixed cost. The long-run average total cost curve shows the relationship between output and average total cost when fixed cost has been chosen to minimize average total cost at each level of output. 7. As output increases, there are increasing returns to scale if long-run average total cost declines; decreasing returns to scale if it increases; and constant returns to scale if it remains constant. Scale effects depend on the technology of production. BA 210 Lesson III. 1 Inputs and Costs 44

Review Questions § You should try to answer some of the following questions before the next class. § You will not turn in your answers, but students may request to discuss their answers to begin the next class. § Your upcoming cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exam. BA 210 Lesson III. 1 Inputs and Costs 45

Review Questions Follow the link http: //faculty. pepperdine. edu/jburke 2/ba 210/Power. P 3/Set 8 Answers. pdf for review questions for Lesson III. 1 BA 210 Lesson III. 1 Inputs and Costs 46

BA 210 Introduction to Microeconomics End of Lesson III. 1 BA 210 Lesson III. 1 Inputs and Costs 47