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Chapter 22

The Firm: Cost and Output

Determination

Copyright ©2014 Pearson Education, Inc. All rights reserved. 22-2

Introduction

The most expensive component of a hybrid or all-electric passenger vehicle is its set of battery packs. Automakers have found that the cost of producing a battery pack declines as more are produced.

Yet, the volume of electric cars is not great enough to make use of the scale of operation that would minimize the cost of producing a battery pack.

Reading this chapter will help you understand why the per-unit cost of battery packs varies with the scale of production of these items.


Learning Objectives

• Discuss the difference between the short run and the long run from the perspective of a firm

• Understand why the marginal physical product of labor eventually declines as more units of labor are employed

• Explain the short-run cost curves a typical firm faces


Learning Objectives (cont’d)

• Describe the long-run cost curves a typical firm faces

• Identify situations of economies and diseconomies of scale and define a firm’s minimum efficient scale


Chapter Outline

• Short Run versus Long Run• The Relationship Between Output and

Inputs• Diminishing Marginal Product• Short-Run Costs to the Firm• The Relationship Between Diminishing

Marginal Product and Cost Curves


Chapter Outline (cont’d)

• Long-Run Cost Curves• Why the Long-Run Average Cost Curve is U-

Shaped• Minimum Efficient Scale


Did You Know That ...

• Utilization of apps is growing more rapidly in the business world than among consumers?

• Firms are employing apps to manage travel plans, track equipment, and monitor employees working time.

• Businesses find that digital apps enable them to better organize the diverse resources they use to produce goods and services.


Short Run versus Long Run

• Short Run

– A time period when at least one input, such as plant size, cannot be changed

– Plant Size• The physical size of the factories that a firm owns and

operates to produce its output


Short Run versus Long Run (cont'd)

• Long Run

– The time period in which all factors of production can be varied


Short Run versus Long Run (cont'd)

• Managers take account of both the short-run and long-run consequences of their behavior

• While making decisions about what to do today, tomorrow, and next week—they keep an eye on the long-run benefits


The Relationship Between Output and Inputs

• A firm takes numerous inputs, combines them using a technological production process and ends up with output

• We classify production inputs in two broad categories—labor and capital


The Relationship Between Output and Inputs (cont'd)

Q = output / time periodK = capitalL = labor

Q = ƒ(K,L)

or

Output per time period = some function of capital and labor inputs



• Production

– Any activity that results in the conversion of resources into products that can be used in consumption



• Production Function

– The relationship between maximum physical output and the quantity of capital and labor used in the production process

– The production function is a technological relationship between inputs and output.


Example: 3D Printers Shift from Design to Production

• 3D printers have been in use since the late 1990s. Printing physical models is less expensive than paying skilled workers to construct models by hand.

• In recent years, some firms have used 3D printing to produce goods such as airline parts and dental crowns in their final forms.

• Materials used to create fine layers in 3D-print production include nylon, plastic, carbon fiber, stainless steel, and titanium.



• Average Physical Product

– Total product divided by the variable input



• Marginal Physical Product

– The physical output that is due to the addition of one more unit of a variable factor of production

– The change in total product occurring when a variable input is increased and all other inputs are held constant

– Also called marginal product


Figure 22-1 The Production Function and Marginal Product: A Hypothetical Case, Panel (a)


Figure 22-1 The Production Function and Marginal Product: A Hypothetical Case, Panel (b)


Figure 22-1 The Production Function and Marginal Product: A Hypothetical Case, Panel (c)


Diminishing Marginal Product

• The marginal product of labor may increase very rapidly at the beginning

• Beyond some point, marginal product must begin to diminish as more workers are hired

• This is not because additional workers are less qualified, but rather because each worker has, on average, fewer machines to work with


Diminishing Marginal Product (cont'd)

• Law of Diminishing Marginal Product

– The observation that after some point, successive equal-sized increases in a variable factor of production, such as labor, added to fixed factors of production, will result in smaller increases in output


Diminishing Marginal Product (cont’d)

• Production of computer servers as an example of the law of diminishing marginal profit:

• We have a fixed amount of factory space, assembly equipment, and quality control diagnostic software

– So the addition of more workers eventually yields successively smaller increases in output


Diminishing Marginal Product (cont'd)

• After a while, when all the assembly equipment and quality-control diagnostic software are being used, additional workers will have to start assembling and troubleshooting quality problems manually

• The marginal physical product of an additional worker, given a specified amount of capital, must eventually be less than that for the previous workers


Diminishing Marginal Product (cont’d)

• Point of saturation– Given the amount of fixed inputs, there is no

further positive use for more of the variable input.


Example: Evaluating the Marginal Physical Product of Oil Drilling

• Chevron uses a sonic boom technology to determine which potential drilling locations in the Gulf of Mexico will yield the most oil.

• By observing energy shifts in different areas, scientists can distinguish solid rock from ridges that line pools of oil.

• In this way, Chevron’s geophysicists can identify locations that will most likely result in the highest increase in the company’s marginal physical product.


Figure 22-2 Cost of Production: An Example, Panel (a)


Figure 22-2 Cost of Production: An Example, Panel (b)


Figure 22-2 Cost of Production: An Example, Panel (c)


Policy Example: How the U.S. Army Uses Virtual Warfare to Cut Variable Costs

• The U.S. Army has long relied on war games to keep soldiers trained for combat.

• These practice battles, however, are costly in terms of wear and tear on equipment as well as with regard to inadvertent injuries.

• To reduce its training expenses, the Army is now using digital devices such as smartphones and tablet computers that simulate field exercises with electronic games, apps, and avatars.

• This approach has slashed the variable costs of training soldiers.


Total costs (TC) = TFC + TVC

Short-Run Costs to the Firm

• Total Costs– The sum of total fixed costs and total variable costs

• Fixed Costs– Costs that do not vary with output and are fixed for a

certain period of time, i.e. rent on a building

• Variable Costs– Costs that vary with the rate of production, i.e. wages paid

to workers and purchases of materials


Short-Run Costs to the Firm (cont'd)

• Average Total Costs (ATC)– Also called average per-unit total costs

Average total costs (ATC) = total costs (TC)

output (Q)



• Average Variable Costs (AVC)

Average variable costs (AVC) = total variable costs (TVC)

output (Q)



• Average Fixed Costs (AFC)

Average fixed costs (AFC) = total fixed costs (TFC)

output (Q)


International Example: Using Cheap Power from the Sun to Reduce Average Total Costs

• A number of petroleum companies are now using heat waves from the sun to extract small pools of oil that remain after traditional drilling operations.

• Mirrors are used to focus energy waves from the sun into pipes that will direct steam into remaining pockets of oil.

• The steam pushes the oil into a position where it can be extracted.

• This method reduces the average total cost of extracting oil from the fields.



• Marginal Cost

– The change in total costs due to a one-unit change in production rate

Marginal costs (MC) = change in total cost

change in output



• Question

– What do you think—is there a predictable relationship between the production function and AVC, ATC, and MC?



• Answer

– As long as marginal physical product rises, marginal cost will fall, and when marginal physical product starts to fall (after reaching the point of diminishing marginal product), marginal cost will begin to rise


Short-Run Costs to the Firm (cont’d)

• The relationship between average and marginal costs:

– When marginal costs are less than average variable costs, the latter must fall

– When marginal costs are greater than average variable costs, the latter must rise



• There is also a relationship between marginal costs and average total costs

– Average total cost is equal to total cost divided by the number of units produced

– Marginal cost is the change in total cost due to a one-unit change in the production rate


Figure 22-3 The Relationship Between Output and Costs, Panel (a)


Figure 22-3 The Relationship Between Output and Costs, Panel (b)


Figure 22-3 The Relationship Between Output and Costs, Panel (c)


Figure 22-3 The Relationship Between Output and Costs, Panel (d)


The Relationship Between Diminishing Marginal Product and Cost Curves

• Firms’ short-run cost curves are a reflection of the law of diminishing marginal product

• Given any constant price of the variable input, marginal costs decline as long as the marginal product of the variable resource is rising


The Relationship Between Diminishing Marginal Product and Cost Curves (cont'd)

• At the point at which diminishing marginal product begins, marginal costs begin to rise as the marginal product of the variable input begins to decline



• If the wage rate is constant, then the labor cost associated with each additional unit of output will decline as long as the marginal physical product (MPP) of labor increases



• Of course, the average total cost curve and average variable cost curve are also affected.

• They will have their familiar U shape in the short run.


Long-Run Cost Curves

• Planning Horizon

– The long run, during which all inputs are variable


Long-Run Cost Curves (cont'd)

• Long-Run Average Cost Curve

– The locus of points representing the minimum unit cost of producing any given rate of output, given current technology and resource prices

• Planning Curve

– The long-run average cost curve.


Figure 22-4 Preferable Plant Size and the Long-Run Average Cost Curve


Long-Run Cost Curves (cont'd)

• Observation– Only at minimum long-run average cost curve is

short-run average cost curve tangent to long-run average cost curve.

• Question– Why do you think the long-run average cost

curve U-shaped?


Why the Long-Run Average Cost Curve is U-Shaped

• Economies of scale

• Constant returns to scale

• Diseconomies of scale


Why the Long-Run Average Cost Curve is U-Shaped (cont'd)

• Economies of Scale

– Decreases in long-run average costs resulting from increases in output

• These economies of scale do not persist indefinitely, however.

• Once long-run average costs rise, the curve begins to slope upwards.



• Reasons for economies of scale

– Specialization• Division of tasks or operations

– Dimensional factor

• Large-scale firms often require proportionately less input per unit of output

– Improved productive equipment

• The larger the enterprise, the more the firm can take advantage of larger-volume types of machinery.


Figure 22-5 Economies of Scale, Constant Returns to Scale, and Diseconomies of Scale Shown with the Long-Run Average Cost Curve



• Explaining why a firm might experience diseconomies of scale

– Limits to the efficient functioning of management

– Coordination and communication is more of a challenge as firm size increases


Example: Diseconomies of Scale at One of the World’s Top Airlines

• American Airlines is the world’s fourth largest airline company.

• It operates at a higher long-run cost per passenger mile than most other airlines. The reason is because its scale is so large.

• The company is contemplating reducing its number of flights, selling off regional routes operated by a subsidiary, and cutting back on the size of its fleet.

• At the current level of operations, American Airlines is experiencing diseconomies of scale.


Minimum Efficient Scale

• Minimum Efficient Scale (MES)

– The lowest rate of output per unit time at which long-run average costs for a particular firm are at a minimum


Figure 22-6 Minimum Efficient Scale


Minimum Efficient Scale (cont'd)

• Small MES relative to industry demand– There is room for many efficient firms.

– High degree of competition

• Large MES relative to industry demand– There is room for only a small number of

efficient firms.

– Small degree of competition


What if . . .the government required firms to reduce their long-run scales of operation to cut overall U.S. energy use?

• Requiring firms to reduce their scales of operation would compel firms to operate below minimum efficient scale.

• Consequently, average total cost would increase, and goods and services would be provided at higher costs per unit.


You Are There: Cutting Costs by Replacing Pilot Projects with Simulations

• Schneider National, a large U.S. trucking firm, has relied on pilot projects to investigate whether cost-cutting ideas actually translate into cost savings.

• Since there was a cost involved in running the pilots, there were instances where no cost-saving methods were discovered, and costs actually increased due to conducting the pilot.


You Are There: Cutting Costs by Replacing Pilot Projects with Simulations (cont’d)

• Ted Gifford, an operations research scientist, developed software to simulate the pilots, thereby eliminating the need to actually conduct the pilot projects.

• This has reduced Schneider’s total costs by tens of millions of dollars per year.


Issues & Applications: Can Electric Car Production Attain Minimum Efficient Scale?

• A significant portion of the cost of an electric or hybrid passenger vehicle is the battery pack.

• To reduce average battery cost, car companies are expanding their productive capabilities.

• This is an attempt to move down along the average cost curve to a minimum efficient scale.

• But the number of battery packs consistent with minimum efficient scale is more than what is needed to supply the number of electric cars operating in the U.S.

• Consequently, average costs will remain high.


Summary Discussion of Learning Objectives

• The short run versus the long run from a firm’s perspective

– Short run—a period in which at least one input is fixed

– Long run—a period in which all inputs are variable


Summary Discussion of Learning Objectives (cont'd)

• The law of diminishing marginal product– As more units of a variable input are employed with a

fixed input, marginal physical product eventually begins to decline

• A firm’s short-run cost curves– Fixed and average fixed cost

– Variable and average variable cost

– Total and average total cost

– Marginal cost


Summary Discussion of Learning Objectives (cont'd)

• A firm’s long-run cost curve– Planning horizon

– All inputs are variable including plant size

• Economies and diseconomies of scale and a firm’s minimum efficient scale

– Along the down-ward sloping range of the firm’s long-run average cost curve, the firm experiences economies of scale

– Along the upward sloping portion, the firm encounters diseconomies of scale

Career

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