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ECON 102.004 – Principles of Microeconomics

S&W, Chapter 6

The Firm’s Costs

Instructor:

Mehmet S. Tosun, Ph.D.

Department of Economics

University of Nevada, Reno

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Lecture Outline

• Production and types of costs

• Relationship between marginal and average costs

• Short run and long run cost curves

• Cost minimization

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Maximizing Profits

• The firm’s goal is to maximize profits.• This determines the firm’s choice of what,

how, and how much to produce.• Firms invest in long‑run projects if they

expect the results to be worth the expenditure.• Firms may have other objectives besides

profits, but firms that neglect profits too much go bankrupt.

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Income and Costs

• The firm's income is total revenue TR = pQ.

• The firm's profits are total revenue minus costs = TR - costs =pQ - costs.– The firm's costs are the money it spends.– Firms try to minimize costs without adversely

affecting the quality of their products.– Firms vary the mix of inputs they use until they

find the lowest‑cost way to produce their product.

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Production with One Variable Input

• A farmer uses a fixed amount of land, machinery, and fertilizer.

• Only labor varies.• The production function relates the input to the

output.• Increases in labor increase output but at a

decreasing rate.

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Marginal Product (a)• Marginal product (MP) is the extra output from the use of an

extra unit of input, holding other inputs fixed.• MP is the slope of the production function.

• Diminishing returns or diminishing marginal productivity: – As more labor is used, holding all other inputs constant, the marginal

product of labor diminishes.– Additional workers are not as productive as previous workers,

because of crowding of fixed inputs.

• Diminishing marginal product implies that even with constant wages, additional units of output cost more than previous units.

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Other Shapes of Production Functions

• Increasing marginal product: By doubling one input, output more than doubles.

• A firm that collects garbage expands from collecting from 1,000 houses to collecting from 2,000 houses.– It must increase its workforce but not by double, since the

average distance between houses falls.– Increasing marginal product holds for other infrastructural

goods and network goods.– The production function has increasing slope.

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Constant Returns

• Constant returns: Output rises exactly in proportion to one input.

• The production function is a straight line out of the origin, and the marginal product of labor is constant.

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Fixed Inputs

• Firms need some inputs just to get started, e.g., space, office furniture, and machines, also some workers (secretaries, lawyers).

• These are fixed inputs since they do not depend on the level of output the firm produces.

• Fixed costs are the money spent on fixed inputs and are constant at all levels of output

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Variable Inputs• The inputs that depend on output are variable

inputs.

• Labor and materials are variable inputs.

• Variable inputs generate variable costs.

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Total Costs

• Since there are fixed and variable inputs, the firm pays fixed and variable costs.

• Fixed costs are the costs of fixed inputs; e.g., a farmer buys a farm (land and equipment) for $25,000.

• Variable costs are the costs of variable inputs: labor, fertilizer, seed, and so on.

• Total costs are the sum of the variable and fixed costs: TC = TVC + TFC.

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Marginal Cost and Marginal Product

• Marginal cost is the extra cost of producing one additional unit of output.

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Marginal Cost and Marginal Product (cont.)

• Marginal cost is the slope of the total cost curve: MC = ∆TC/∆Q.

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An Example• Suppose a farmer increases labor input from 7,000

to 8,000 hours and output increases by 10,000 bushels.– One an additional hour of labor produces 10 bushels =

10,000 bushels/1,000 hours.– 10 bushels per hour of labor is the marginal product of

labor• Or one bushel every 1/10 hour of labor

• If the wage is $20 per hour, each additional bushel costs $2 to produce.

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Diminishing Marginal Product and Increasing Marginal Cost

• If w is the wage and MP is marginal product, marginal cost, MC = w/MP.– The more productive labor is, the lower the cost of producing the next unit.

• Diminishing marginal product: eventually additional units of labor are less productive than previous units.– The cost of additional units rises with diminishing marginal product.– This implies that the marginal cost curve is usually upward sloping, reflecting

diminishing marginal product.

• With diminishing marginal returns, as more workers are hired, successive workers are less productive and the output they make is more expensive.

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Average Costs (a)

• Average costs are total costs divided by output: AC = TC/Q.– Average cost is the slope of the line between

the origin and the point on the total cost curve.

• Average variable costs are total variable costs divided by output: AVC = TVC/Q.

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Average Costs (b)

• Average cost curves with fixed costs are U‑shaped.

• Inputs have diminishing marginal returns, so marginal costs are increasing with output.

• Initially average costs fall as fixed costs are spread over more units of output and before diminishing marginal productivity sets in.

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Average Costs (c)• When diminishing marginal productivity sets in, marginal

costs rise.– When marginal cost exceeds average cost, average cost rises.– For example:

• A course has three exams.• Your average on the first two exams is 80.

– The next exam is the marginal exam.

– If you score a 90 (> 80) on the third exam, your average rises.

– If you score a 50 (< 80) on the third exam, your average falls.

• In general, the position of margin relative to the average determines what happens to the average.

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The Relationship between MC and AC (a)• If MC >AC, then AC rises.• If MC < AC, then AC falls.• If MC = AC, then AC neither rises nor falls; AC is at a

minimum.• Minimum average costs occur at Q*.• So there are declining average costs out to Q*.

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Relationship between MC and AC (b)

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The Difference between the Short Run and the Long Run

• The short run is a time period during which some inputs are fixed.

• The long run is a time period during which no inputs are fixed; all inputs can be changed.

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Short‑Run Cost Curves• Those factors fixed in the short run generate short‑run

fixed costs.– Labor and raw materials are the principal variable inputs.

– They generate short‑run average cost curves that are U‑shaped.

• Short‑run marginal cost curves in many firms are approximately flat, or constant, over a wide range.– Firms can often expand production 10% by using 10% more labor and

materials.

– Eventually, worse machines must be brought on line and workers have to be paid overtime.

– Hence, at low levels of output, the short‑run marginal cost curve is flat, while at high levels, the curve gets steeper and steeper.

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Long‑Run Cost Curves• In the long run no inputs are fixed.• In the long run, the firm can change everything about itself,

including the size of the firm and its factories.• If production grows in the long run, the firm builds another

factory or plant to produce the expected long‑run output at the lowest possible average cost.

• In the long run, the firm has a variety of factory or plant sizes to choose from.– Blueprints of different factories

– The firm builds plants that will produce the desired long‑run level of output at the lowest possible long‑run average cost.

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Long‑Run Cost Curves

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Long Run Average Cost Curves and Their Slope

• Long‑run cost curves slope down initially, then get flat, and then slope up, and so look much like a saucer.– Why?

• Must ask: How does output change when all inputs change?

• This is explained by the property of returns to scale.

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Constant Returns to Scale• If all inputs increase by the same proportion and output

changes by the same proportion, this is constant returns to scale.– If all inputs double, output doubles.– This implies that average costs are constant.

• AC = TC/Q– If all inputs double, TC doubles.– If output doubles, Q doubles.– So TC/Q = AC is constant.

• The firm can scale up or down by changing its average costs.• Constant returns to scale yield constant long‑run average

costs.– There is evidence that U.S. manufacturing firms operate with

constant average costs.

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Increasing Returns to Scale

• If all inputs double, output increases by more than double.– Average costs fall as output expands.

• With increasing returns to scale, bigger is better.

• There are increasing benefits to size (the benefits are lower average costs).

• Firms with increasing returns to scale benefit from expansion and typically end up large relative to the market.

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Decreasing Returns to Scale

• If all inputs double, output increases by less than double.

• Average costs increase as output increases.– Firms with decreasing returns to scale are more

efficient at low levels of output.• They have lower unit costs at low levels of output.

• These firms typically stay small; small is beautiful.

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Long Run Average Cost Curves and Their Slope

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Economies of Scope• The cost of production depends on how much is

produced but may also depend on what other products are produced.– For example: a sheep farm produces wool but also lamb and mutton.

• If it is cheaper to produce goods together than separately, there are economies of scope.– Local and long‑distance telephone services, telecommunications,

and related goods may have economies of scope.– Some economists argued against the breakup of AT&T because they

feared a breakup would reduce efficiency by reducing economies of scope.