Michael Parkin ECONOMICS 5e Output and Costs 1

Learning Objectives Distinguish between the short-run and the long-run Explain the relationship between a firm’s output and labor employed in the short-run Explain the relationship between a firm’s output and costs in the short-run Derive and explain a firm’s short-run cost curves 2

Learning Objectives (cont.) Explain the relationship between a firm’s output and costs in the long-run Derive and explain a firm’s long-run average cost curve 3

Learning Objectives Distinguish between the short-run and the long-run Explain the relationship between a firm’s output and labor employed in the short-run Explain the relationship between a firm’s output and costs in the short-run Derive and explain a firm’s short-run cost curves 4

Sidney’s Sweaters Inc. Throughout the chapter we are going to refer to Sidney’s Sweaters Inc., a producer of knitted sweaters. The firm is owned and operated by Sidney. 5

Decision Time Frames The Objective: Profit Maximization All of the firm’s decisions are aimed at one overriding objective: maximum attainable profit. To study the relationship between a firm’s output decision and its costs, we distinguish two decision time frames: The short-run The long-run 6

Decision Time Frames The Short-Run and the Long-Run The short-run is a time frame in which the quantity of at least one input is fixed and the quantities of the other inputs can be varied. The long-run is a time frame in which the quantities of all inputs can be varied. A sunk cost is irrelevant to the firm’s decisions. 8

Decision Time Frames Total product is the total output produced. To increase output in the short-run, a firm must increase the quantity of labor employed. Total product is the total output produced. Marginal product is the increase in total product that result from a one-unit increase in an input. Average product is the total product divided by the quantity of inputs. 9

Learning Objectives Distinguish between the short-run and the long-run Explain the relationship between a firm’s output and labor employed in the short-run Explain the relationship between a firm’s output and costs in the short-run Derive and explain a firm’s short-run cost curves 10

Total Product, Marginal Product, and Average Product Total Marginal Average Labor product product product (workers (sweaters (sweaters per (sweaters per day) per day) additional worker) per worker) a 0 0 b 1 4 c 2 10 d 3 13 e 4 15 f 5 16 Instructor Notes: Total product is the total amount produced. 11

Total Product, Marginal Product, and Average Product Total Marginal Average Labor product product product (workers (sweaters (sweaters per (sweaters per day) per day) additional worker) per worker) a 0 0 b 1 4 c 2 10 d 3 13 e 4 15 f 5 16 4 6 3 2 1 Instructor Notes: 1) Marginal product is the change in total product that results from a one-unit increase in labor. 2) For example, when labor increases from 2 to 3 workers a day (row c to row d), total product increases from 10 to 13 sweaters. 3) The marginal product of the third worker is 3 sweaters. 12

Total Product, Marginal Product, and Average Product Total Marginal Average Labor product product product (workers (sweaters (sweaters per (sweaters per day) per day) additional worker) per worker) a 0 0 b 1 4 4.00 c 2 10 5.00 d 3 13 4.33 e 4 15 3.75 f 5 16 3.20 4 6 3 2 1 Instructor Notes: 1) Average product is total product divided by the quantity of labor employed. 2) For example, the average product of 3 workers is 4.33 sweaters per worker (13 sweaters a day divided by 3 workers). 13

Total Product Curve TP 15 f e Unattainable d 10 c Attainable 5 b a Output (sweaters per day) 10 Attainable 5 Instructor Notes: 1) The total product curve, TP, is based on these data. 2) Points a through f on the curve correspond to the rows of the table. 30 The total product curve separates the attainable output from the unattainable. 0 1 2 3 4 5 Labor (workers per day) 17

Marginal Product Curve Marginal product is also measured by the slope of the total product curve. Increasing marginal returns occur when the marginal product of an additional worker exceeds the marginal product of the previous worker. 18

Marginal Product Curve Diminishing marginal returns Occur when the marginal product of an additional worker is less than the marginal product of the previous worker Law of diminishing returns As a firm uses more of a variable input, with a given quantity of fixed inputs, the marginal product of the variable input eventually diminishes 19

Marginal Product TP d c MP 6 Output (sweaters per day) 15 TP 6 d 13 Output (sweaters per day) Marginal product (sweaters per day per worker) 10 4 c 3 Instructor Notes: 1) Marginal product is illustrated by the orange bars. For example, when labor increases from 2 to 3, marginal product is the orange bar whose height is 3 sweaters. 2) Marginal product is shown midway between the labor input to emphasize that it is the result of changing inputs. 3) The steeper the slope of the total product curve (TP) in the first graph, the larger is marginal product (MP) in the second graph. 4) Marginal product increases to a maximum (when 1 worker is employed in this example) and then declines--diminishing marginal product. 5 2 4 MP 0 1 2 3 4 5 0 1 2 3 4 5 Labor (workers per day) Labor (workers per day) 26

Average Product Curve What does the average product curve look like? 27

Average Product AP MP Maximum average product 6 e f b d c c Average product & Marginal product (sweaters per day per worker) AP 4.33 4 3 Instructor Notes: 1) With 1 worker per day, marginal product exceeds average product, so average product is increasing. 2) With 2 workers per day, marginal product equals average product, so average product is at its maximum 3) With more that 2 workers per day, marginal product is less than average product, so average product is decreasing. 2 0 1 2 3 4 5 Labor (workers per day) 31

Learning Objectives Distinguish between the short-run and the long-run Explain the relationship between a firm’s output and labor employed in the short-run Explain the relationship between a firm’s output and costs in the short-run Derive and explain a firm’s short-run cost curves 32

Short-Run Cost Total cost (TC) is the cost of all productive resources used by a firm. Total fixed cost (TFC) is the cost of all the firm’s fixed inputs. Total variable cost (TVC) is the cost of all the firm’s variable inputs. 33

Short-Run Cost TC = TFC + TVC Total cost (TC) is the cost of all productive resources used by a firm. TC = TFC + TVC 34

Total Cost Curves Total Total fixed variable Total cost cost cost Labor Output (TFC) (TVC) (TC) (workers (sweaters per day) per day) (dollars per day) a 0 0 b 1 4 c 2 10 d 3 13 e 4 15 f 5 16 Instructor Notes: 1) Swanky rents its knitting machine for $25 a day. 2) This amount is its total fixed cost. 3) It hires workers at a wage rate of $25 a day, and this cost is Swanky’s total variable cost. 4) For example, if Swanky employs 3 workers, its total variable cost is (3 x $25), which equals $75. 5) Total cost is the sum of total fixed cost and total variable cost. 6) For example, when Swanky employs 3 workers, its total cost is $100---total fixed cost of $25 plus total variable cost of $75. 35

Total Cost Curves Total Total fixed variable Total cost cost cost Labor Output (TFC) (TVC) (TC) (workers (sweaters per day) per day) (dollars per day) a 0 0 25 b 1 4 25 c 2 10 25 d 3 13 25 e 4 15 25 f 5 16 25 Instructor Notes: 1) Swanky rents its knitting machine for $25 a day. 2) This amount is its total fixed cost. 3) It hires workers at a wage rate of $25 a day, and this cost is Swanky’s total variable cost. 4) For example, if Swanky employs 3 workers, its total variable cost is (3 x $25), which equals $75. 5) Total cost is the sum of total fixed cost and total variable cost. 6) For example, when Swanky employs 3 workers, its total cost is $100---total fixed cost of $25 plus total variable cost of $75. 36

Total Cost Curves Total Total fixed variable Total cost cost cost Labor Output (TFC) (TVC) (TC) (workers (sweaters per day) per day) (dollars per day) a 0 0 25 0 b 1 4 25 25 c 2 10 25 50 d 3 13 25 75 e 4 15 25 100 f 5 16 25 125 Instructor Notes: 1) Swanky rents its knitting machine for $25 a day. 2) This amount is its total fixed cost. 3) It hires workers at a wage rate of $25 a day, and this cost is Swanky’s total variable cost. 4) For example, if Swanky employs 3 workers, its total variable cost is (3 x $25), which equals $75. 5) Total cost is the sum of total fixed cost and total variable cost. 6) For example, when Swanky employs 3 workers, its total cost is $100---total fixed cost of $25 plus total variable cost of $75. 37

Total Cost Curves Total Total fixed variable Total cost cost cost Labor Output (TFC) (TVC) (TC) (workers (sweaters per day) per day) (dollars per day) a 0 0 25 0 25 b 1 4 25 25 50 c 2 10 25 50 75 d 3 13 25 75 100 e 4 15 25 100 125 f 5 16 25 125 150 Instructor Notes: 1) Swanky rents its knitting machine for $25 a day. 2) This amount is its total fixed cost. 3) It hires workers at a wage rate of $25 a day, and this cost is Swanky’s total variable cost. 4) For example, if Swanky employs 3 workers, its total variable cost is (3 x $25), which equals $75. 5) Total cost is the sum of total fixed cost and total variable cost. 6) For example, when Swanky employs 3 workers, its total cost is $100---total fixed cost of $25 plus total variable cost of $75. 38

Total Cost Curves TC TVC TFC 0 5 10 15 TC = TFC + TVC 150 Cost (dollars per day) 100 Instructor Notes: 1) The graph shows Swanky’s total cost curves. 2) Total fixed cost (TFC) is constant--it graphs as a horizontal line--and total variable cost (TVC) increases as output increases. 3) Total cost (TC) also increases as output increases. 4) The vertical distance between the total cost curve and the total variable cost curve is total fixed cost, as illustrated by the two green arrows. 50 TFC 0 5 10 15 Output (sweaters per day) 42

Marginal Cost Marginal cost is the increase in total cost that results from a one-unit increase in output. It equals the increase in total cost divided by the increase in output. Marginal costs decrease at low outputs because of the gains from specialization, but it eventually increases due to the law of diminishing returns. 43

Average Cost Average fixed cost (AFC) is total fixed cost per unit of output. Average variable cost (AVC) is total variable cost per unit of output. Average total cost (ATC) is total cost per unit of output. 44

Average Cost TC = TFC + TVC TC TFC TVC Q Q Q = + OR ATC = AFC + AVC

Marginal Cost and Average Costs Total Total Average Average fixed fixed Total Marginal fixed variable Total cost cost cost cost cost cost cost Labor Output (TFC) (TVC) (TC) (MC) (AFC) (AVC) (ATC) (workers (sweaters (dollars per per day) per day) (dollars per day) additional sweater) (dollars per sweater) a 0 0 25 0 25 b 1 4 25 25 50 c 2 10 25 50 75 d 3 13 25 75 100 e 4 15 25 100 125 f 5 16 25 125 150 46

Marginal Cost and Average Costs Total Total Average Average fixed fixed Total Marginal fixed variable Total cost cost cost cost cost cost cost Labor Output (TFC) (TVC) (TC) (MC) (AFC) (AVC) (ATC) (workers (sweaters (dollars per per day) per day) (dollars per day) additional sweater) (dollars per sweater) a b c d e f 1 2 3 4 5 4 10 13 15 16 25 25 50 75 100 125 25 50 75 100 125 150 6.25 4.17 8.33 12.50 25.00 Instructor Notes: 1) Marginal cost is calculated as the change in total cost divided by the change in output. 2) When output increases from 4 to 10, an increase of 6, total cost increases by $25 and marginal cost is $25/6, which equals $4.17. 47

Marginal Cost and Average Costs Total Total Average Average fixed fixed Total Marginal fixed variable Total cost cost cost cost cost cost cost Labor Output (TFC) (TVC) (TC) (MC) (AFC) (AVC) (ATC) (workers (sweaters (dollars per per day) per day) (dollars per day) additional sweater) (dollars per sweater) a b c d e f 1 2 3 4 5 10 13 15 16 25 50 75 100 125 150 6.25 4.17 8.33 12.50 25.00 — 2.50 1.92 1.67 1.56 Instructor Notes: 1) Each average cost concept is calculated by dividing the related total cost by output. 2) When 10 sweaters are produced, AFC is $2.50 ($25/10), AVC is $5.00 ($50/10), and ATC is $7.50 ($75/10). 48

Marginal Cost and Average Costs Total Total Average Average fixed fixed Total Marginal fixed variable Total cost cost cost cost cost cost cost Labor Output (TFC) (TVC) (TC) (MC) (AFC) (AVC) (ATC) (workers (sweaters (dollars per per day) per day) (dollars per day) additional sweater) (dollars per sweater) a b c d e f 1 2 3 4 5 4 10 13 15 16 25 25 50 75 100 125 25 50 75 100 125 150 — 6.25 2.50 1.92 1.67 1.56 — 6.25 5.00 5.77 6.77 7.81 6.25 4.17 8.33 12.50 25.00 Instructor Notes: 1) Each average cost concept is calculated by dividing the related total cost by output. 2) When 10 sweaters are produced, AFC is $2.50 ($25/10), AVC is $5.00 ($50/10), and ATC is $7.50 ($75/10). 49

Marginal Cost and Average Costs Total Total Average Average fixed fixed Total Marginal fixed variable Total cost cost cost cost cost cost cost Labor Output (TFC) (TVC) (TC) (MC) (AFC) (AVC) (ATC) (workers (sweaters (dollars per per day) per day) (dollars per day) additional sweater) (dollars per sweater) a b c d e f 1 2 3 4 5 4 10 13 15 16 25 25 50 75 100 125 25 50 75 100 125 150 — 6.25 2.50 1.92 1.67 1.56 — 6.25 5.00 5.77 6.77 7.81 — 12.50 7.50 7.69 8.33 9.38 6.25 4.17 8.33 12.50 25.00 Instructor Notes: 1) Each average cost concept is calculated by dividing the related total cost by output. 2) When 10 sweaters are produced, AFC is $2.50 ($25/10), AVC is $5.00 ($50/10), and ATC is $7.50 ($75/10). 50

Marginal Cost and Average Costs ATC = AFC + AVC 15 AVC ATC MC Cost (dollars per sweater) 10 AFC 5 Instructor Notes: 1) Average fixed cost (AFC) decreases as output increases. 2) The average total cost curve (ATC) and average variable cost curve (AVC) are U-shaped. 3) The vertical distance between these two curves is equal to average fixed cost, as illustrated by the two arrows. 4) The marginal cost curve (MC) is also U-shaped. 5) MC intersects the average variable cost curve and average total cost curve at their minimum points. 0 5 10 15 Output (sweaters per day) 55

Cost Curves and Product Curve How are the product curves related to the cost curves? 56

Product Curves and Cost Curves MP 6 AP 4 Average product and marginal product Instructor Notes: 1) A firm’s cost curves are linked to its product curves. 2) Over the range of rising marginal product, marginal cost is falling. 3) When marginal product is a maximum, marginal cost is a minimum. 4) Over the range of rising average product, average variable cost is falling. 5) When average product is a maximum, average variable cost is a minimum. 6) Over the range of diminishing marginal product, marginal cost is rising. 7) Over the range of falling average product, average variable cost is rising. 2 2 Rising MP and falling MC: rising AP and falling AVC Falling MP and rising MC: rising AP and falling AVC Falling MP and rising MC: falling AP and rising AVC 0 1.5 2.0 Labor 59

Product Curves and Cost Curves 12 AVC 9 MC Average product and marginal product Maximum MP and minimum MC Maximum AP and minimum AVC 6 Instructor Notes: 1) A firm’s cost curves are linked to its product curves. 2) Over the range of rising marginal product, marginal cost is falling. 3) When marginal product is a maximum, marginal cost is a minimum. 4) Over the range of rising average product, average variable cost is falling. 5) When average product is a maximum, average variable cost is a minimum. 6) Over the range of diminishing marginal product, marginal cost is rising. 7) Over the range of falling average product, average variable cost is rising. 3 0 6.5 10 Labor 62

Learning Objectives (cont.) Explain the relationship between a firm’s output and costs in the long run Derive and explain a firm’s long-run average cost curve 63

Long-Run Cost Long-run cost The cost of production when a firm uses the economically efficient quantities of labor and capital. Long-run costs are affected by the production function. Production function The relationship between the maximum output attainable and the quantities of both labor an capital. 64

Learning Objectives (cont.) Explain the relationship between a firm’s output and costs in the long run Derive and explain a firm’s long-run average cost curve 65

The Production Function Output (sweaters per day) Labor Plant 1 Plant 2 Plant 3 Plant 4 1 4 10 13 15 2 10 15 18 21 3 13 18 22 24 4 15 20 24 26 5 16 21 25 27 Instructor Notes: 1) The table shows the total product data for four quantities of capital 2) The greater the plant size, the larger is the total product for any given quantity of labor. 3) But for a given plant size, the marginal product of labor diminishes. 4) And for a given quantity of labor, the marginal product of capital diminishes. Knitting machines (number) 1 2 3 4 66

The Long-Run Average Cost Curve The long-run average total cost curve is derived from the short-run average total cost curves. The segment of the short-run average total cost curves along which average total cost is the lowest make up the long-run average total cost curve. 67

Short-Run Costs of Four Different Plants Instructor Notes: 1) The graph shows short-run average total cost curves for four different quantities of capital. 2) Swanky can produce 13 sweaters a day with 1 knitting machine on ATC1 or with 3 knitting machines on ATC3 for and average cost of $7.69 per sweater. 30 Swanky can produce the same number of sweaters by using 2 knitting machines on ATC2 for $6.80 per sweater or with 4 machines on ATC4 for $9.50 per sweater. 4) If Swanky produces 13 sweaters a day, the least-cost method of production--the long-run method--is with 2 machines on ATC2 .. 68

Long-Run Average Cost Curve Instructor Notes: 1) In the long run, Swanky can vary both capital and labor inputs. 2) The long-run average cost curve, LRAC, traces the lowest attainable average total cost of production. 3) Swanky produces on its long-run average cost curve if it uses 1 machine to produce up to 10 sweaters a day, 2 machines to produce between 10 and 18 sweaters a day, 3 machines to produce between 18 and 24 sweaters a day, and 4 machines to produce more than 24 sweaters a day. 5) Within these ranges, Swanky varies its output by varying its labor input. 69

Returns to Scale Returns to scale are the increases in output that result from increasing all inputs by the same percentage. Three possibilities: Constant returns to scale Increasing returns to scale Decreasing returns to scale 70

Returns to Scale Constant returns to scale Technological conditions under which a given percentage increase in all the firm’s inputs results in the firm’s output increasing by the same percentage 71

Returns to Scale Increasing returns to scale Technological conditions under which a given percentage increase in all the firm’s inputs results in the firm’s output increasing by a larger percentage 72

Returns to Scale Decreasing returns to scale Technological conditions under which a given percentage increase in all the firm’s inputs results in the firm’s output increasing by a smaller percentage 73

Minimum Efficient Scale A firm’s minimum efficient scale is the smallest quantity of output at which long-run average cost reaches its lowest level.