Production and Cost CHAPTER

Production and Cost CHAPTER
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Production Profit Business firm Production
Total revenue minus total cost Business firm Organization, owned and operated by private individuals Specializes in production Production Process of combining inputs to make goods and services © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Production Technology Assumption Long run
Methods available for combining inputs to produce a good or service Assumption Production technology Firm uses only two inputs: capital and labor Long run A time horizon long enough for a firm to vary all of its inputs © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Production Variable input Fixed input Short run
An input whose usage can change over some time period Fixed input An input whose quantity must remain constant over some time period Short run A time horizon during which at least one of the firm’s inputs cannot be varied © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Production in the Short Run
Total product The maximum quantity of output that can be produced from a given combination of inputs E.g.: maximum output for each number of workers Total product curve Horizontal axis: number of workers Vertical axis: total product © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Short-Run Production at Spotless Car Wash

Marginal product of labor (MPL= ΔQ/ΔL) The additional output produced when one more worker is hired Change in total product (ΔQ) divided by the change in the number of workers employed (ΔL) Tells us the rise in output produced when one more worker is hired © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Increasing marginal returns to labor The marginal product of labor increases as more labor is hired Diminishing marginal returns to labor The marginal product of labor decreases as more labor is hired Law of diminishing (marginal) returns As we continue to add more of any one input, holding the other inputs constant Its marginal product will eventually decline © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Total and Marginal Product Number of workers Units of output 1 2 3 4
5 6 130 160 184 196 30 90 Total product ΔQ from hiring fourth worker = 30 ΔQ from hiring third worker = 40 ΔQ from hiring second worker = 60 ΔQ from hiring first worker = 30 Increasing marginal returns Diminishing marginal returns © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Thinking About Costs A firm’s total cost
Of producing a given level of output Is the opportunity cost of the owners Everything they must give up in order to produce that amount of output Implicit and explicit costs © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Thinking About Costs Sunk cost Cost that has been paid or must be paid
Regardless of any future action being considered Should not be considered when making decisions © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Thinking About Costs Explicit costs Implicit costs
Involve actual payments Implicit costs No money changes hands Forgone rent Forgone interest Forgone labor income © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

2 A Firm’s Costs © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Thinking About Costs Least-Cost Rule
A firm produces any given output level using the lowest cost combination of inputs available Least-cost input combination depends on Nature of the firm’s technology Prices the firm must pay for its inputs Time horizon for the firm’s planning © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Cost in the Short Run Fixed costs Variable costs Costs of fixed inputs
Remain constant as output changes Variable costs Costs of variable inputs Change with output © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Short-Run Costs for Spotless Car Wash

Cost in the Short Run Total fixed cost (TFC) Total variable cost (TVC)
The cost of all inputs that are fixed in the short run Total variable cost (TVC) The cost of all variable inputs used in producing a particular level of output Total cost (TC = TFC + TVC) The costs of all inputs, fixed and variable, used to produce a given output level in the short run © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

2 The Firm’s Total Cost Curves Units of Output Dollars 30 184 90 130
160 510 630 750 $870 270 390 TC TVC TFC = $150 TFC At any level of output, total cost (TC) is the sum of total fixed cost (TFC) and total variable cost (TVC) © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Cost in the Short Run Average fixed cost (AFC = TFC / Q)
Total fixed cost divided by the quantity of output produced Average variable cost (AVC = TVC / Q) Total variable cost divided by the quantity of output produced Average total cost (ATC = TC / Q) Total cost divided by the quantity of output produced © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Cost in the Short Run Marginal cost (MC = ΔTC / ΔQ)
The increase in total cost from producing one more unit of output It tells us how much cost rises per unit increase in output © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Average and Marginal Costs Units of Output Dollars 30 184 90 130 160
Average variable cost (AVC) and average total cost (ATC) are U-shaped, first decreasing and then increasing. Average fixed cost (AFC), the vertical distance between ATC and AVC, becomes smaller as output increases. The marginal cost (MC) curve is also U-shaped, reflecting first increasing and then diminishing marginal returns to labor. MC passes through the minimum points of both the AVC and ATC curves. Units of Output Dollars 30 184 90 130 160 2 196 4 6 8 $10 MC ATC AFC AVC © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Cost in the Short Run Explaining the shape of the MC curve
When the marginal product of labor (MPL) rises, marginal cost (MC) falls When MPL falls, MC rises Since MPL ordinarily rises and then falls, MC will do the opposite MC curve is U-shaped Increasing then diminishing marginal returns to labor © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

4 Average and Marginal Test Scores

Cost in the Short Run ATC curve is U-shaped
Because AFC decreases and AVC first decreases, then increases At low levels of output, AVC and AFC are both falling, so the ATC curve slopes downward At higher levels of output, rising AVC overcomes falling AFC, and the ATC curve slopes upward © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Cost in the Short Run AVC curve is U-shaped MC curve
Because MC curve is U-shaped (increasing and then diminishing returns to labor) MC curve Crosses both the AVC curve and the ATC curve at their respective minimum points © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Production and Cost in the Long Run
No fixed inputs; no fixed costs All inputs and all costs are variable Output production Least-cost rule Long-run total cost (LRTC) Cost of producing each quantity of output when all inputs are variable and the least-cost input mix is chosen © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Long-run average total cost (LRATC = LRTC / Q) Cost per unit of producing each quantity of output, in the long run, when all inputs are variable Long-run total cost divided by quantity Relationship between long-run and short-run costs LRTC ≤ TC LRATC ≤ ATC © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

5 Four Ways to Wash 196 Cars per Day

6 Long-Run Costs for Spotless Car Wash

Plant The collection of fixed inputs at a firm’s disposal Size of the firm’s plant Can be changed in the long run Cannot be changed in the short run © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

A firm’s LRATC curve Combines portions of each ATC curve available to the firm in the long run For each output level, the firm will always choose to operate on the ATC curve with the lowest possible cost © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

In the short run A firm can only move along its current ATC curve In the long run A firm can move from one ATC curve to another By varying the size of its plant Moving along its LRATC curve © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

4 Long-Run Average Total Cost 90 130 Units of Output Dollars $8.00
Units of Output Dollars $8.00 $6.00 $4.00 $2.00 30 175 184 250 300 Average-total cost curves ATC0, ATC1, ATC2, and ATC3 show average costs when the firm has zero, one, two, and three automated lines, respectively. The LRATC curve combines portions of all the firm’s ATC curves. In the long run, the firm will choose the lowest-cost ATC curve for each level of output. ATC1 ATC2 ATC0 ATC3 LRATC C B D A E Use 0 automated lines Use 1 automated lines Use 2 automated lines Use 3 automated lines © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

The U-shape of the LRATC curve: As output increases, long-run average costs: First decline (economies of scale) Then remain constant (constant returns to scale) And finally rise (diseconomies of scale) © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Economies of scale Long-run average total cost decreases as output increases LRATC curve slopes downward Long-run total cost rises proportionately less than output Causes for economies of scale Gains from specialization Spreading costs of lumpy inputs © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Lumpy input An input whose quantity cannot be increased gradually as output increases But must instead be adjusted in large jumps © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Diseconomies of scale Long-run average total cost increases as output increases LRATC curve slopes upward Long-run total cost rises more than in proportion to output © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Constant returns to scale Long-run average total cost is unchanged as output increases LRATC curve is flat Both output and long-run total cost rise by the same proportion © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

5 The Shape of LRATC Pizzas Served per Day Dollars 200 250 $8.00 $6.00
$6.00 $4.00 $2.00 LRATC If long-run total cost rises proportionately less than output, production reflects economies of scale, and LRATC slopes downward. If cost rises proportionately more than output, there are diseconomies of scale, and LRATC slopes upward. Between those regions, cost and output rise proportionately, yielding constant returns to scale. The lowest output level at which the LRATC hits bottom is the firm’s minimum efficient scale. Minimum efficient scale (MES) Constant Returns to Scale Economies of Scale Diseconomies of Scale © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Minimum efficient scale (MES) The lowest output level at which the firm’s LRATC curve hits bottom Tells us how large a firm must grow in order to fully exploit economies of scale Firms that grow to their MES Have a cost advantage over other firms that operate at smaller output levels © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

7 Types of Costs Term Symbol/Formula Definition Costs in general
Explicit cost Implicit cost Sunk cost Lumpy input cost Short-run costs Total fixed cost Total variable cost Total cost Average fixed cost Average variable cost Average total cost Marginal cost Long-run costs Long-run total cost Long-run average total cost TFC TVC TC=TFC+TVC AFC = TFC/Q AVC = TVC/Q ATC = TC/Q MC=ΔTC/ΔQ LRTC LRATC=LRTC/Q An opportunity cost where an actual payment is made An opportunity cost, but no actual payment is made An irrelevant cost because it cannot be affected by any current or future decision The cost of an input that can only be adjusted in large, indivisible amounts The cost of all inputs that are fixed (cannot be adjusted) in the short run The cost of all inputs that are variable (can be adjusted) in the short run The cost of all inputs in the short run The cost of all fixed inputs per unit of output The cost of all variable inputs per unit of output The cost of all inputs per unit of output The change in total cost for each one-unit rise in output The cost of all inputs in the long run Cost per unit in the long run © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

When there are significant, unexploited economies of scale
The Urge to Merge When there are significant, unexploited economies of scale Because the market has too many firms for each to operate near its minimum efficient scale Mergers often follow © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

6 LRATC for a Typical Firm in a Merger-Prone Industry Quantity
With market quantity demanded fixed at 60,000, and six firms of equal market share, each operates at point A, producing 10,000 units at $200 per unit. But any one firm can cut price slightly, increase market share, and operate with lower cost per unit, such as at the MES (point B). Other firms must match the first-mover’s price; otherwise they lose market share and end up at .a point like C, with higher cost per unit than originally. The result is a price war, with each firm ending up back at point A, only now—due to the lower price—they suffer losses. A series of mergers to create three large firms would enable each to operate at its MES (point B), with less likelihood of price wars and losses. Quantity per Month Dollars 8,000 10,000 20,000 80 200 $240 LRATC C A B Original Output Level MES © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Isoquant Analysis: Finding the Least-Cost Input Mix
Every point on an isoquant Input mix that produces the same quantity of output An increase in one input requires a decrease in the other input to keep total production unchanged Isoquants Always slope downward © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Marginal rate of technical substitution
Isoquant Analysis Higher isoquants Greater levels of output than lower isoquants Marginal rate of technical substitution The (absolute value of the) slope of an isoquant Measures the rate at which a firm can substitute one input for another while keeping output constant © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Move rightward along any given isoquant
Isoquant Analysis Move rightward along any given isoquant Marginal rate of technical substitution (MRTS) decreases Slope of the isoquant (MRTSL,N) With land measured horizontally And labor measured vertically MRTSL,N is the ratio of the marginal products, MPN/MPL © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Isoquant Analysis An isoquant Becomes flatter as we move rightward
The MPN decreases, while the MPL increases The ratio (MPN/MPL) decreases © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

A.1 Production Technology for an Artichoke Farm

A.1 An Isoquant Map 10 8 Land (hectares) Labor (workers) 2 4 6 12 14
12 14 16 18 20 22 Each of the curves in the figure is an isoquant, showing all combinations of labor and land that can produce a given output level. The middle curve, for example, shows that 4,000 units of output can be produced with 11 workers and 3 hectares of land (point B), with 5 workers and 5 hectares of land (point C), as well as other combinations of labor and land. Each isoquant is drawn for a different level of output. The higher the isoquant line, the greater the level of output. Q=6,000 F Q=4,000 A Q=2,000 B C © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Isocost lines always slope downward
If you use more of one input, you must use less of the other input in order to keep your total cost unchanged Slope of an isocost line: - PN /PL With land (N) on the horizontal axis and labor (L) on the vertical axis Remains constant as we move along the line Higher isocost lines Greater total costs for the firm © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

A.2 Isocost Lines 10 9 Land (hectares) Labor (workers) 3 5 7.5 12 15
20 Each of the lines in the figure is an isocost line, showing all combinations of labor and land that have the same total cost. The middle line, for example, shows that total cost will be $7,500 if 9 workers and 3 hectares of land are used (point C). All other combinations of land and labor on the middle line have the same total cost of $7,500. Each isocost line is drawn for a different value of total cost. The higher the isocost line, the greater is total cost. TC=$10,000 TC=$7,500 C TC=$5,000 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

The Least-Cost Input Combination
Of two inputs (L, N) for producing any level of output Is found at the point where an isocost line is tangent to the isoquant for that output level The firm’s MRTS between the two inputs (MPN/MPL) will equal the ratio of input prices (PN /PL) The marginal product per dollar of land (MPN/PN) must equal the marginal product per dollar of labor (MPL/PL) © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

A.3 The Least-Cost Input Combination for a Given Output Level 10 5
Land (hectares) Labor (workers) 3 7.5 15 20 To produce any given level of output at the least possible cost, the firm should use the input combination where the isoquant for that output level is tangent to an isocost line. In the figure, the input combinations at points J, C, and K can all be used to produce 4,000 units of output. But the combination at point C (5 workers and 5 hectares of land), where the isoquant is tangent to the isocost line, is the least expensive input combination for that output level. Q=4,000 TC=$10,000 J TC=$7,500 TC=$5,000 C K © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

The Least-Cost Input Combination
Least-cost input mix with many variable inputs Marginal product per dollar of any input is equal to marginal product per dollar of any other input © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Production and Cost CHAPTER

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