FIRMS, PRODUCTS, AND COSTS: AN INTRODUCTION

Types of Firms

• Sole or Individual Proprietorship

• Partnership

• Limited Liability Companies or Corporation

Individual Proprietorship

• a single person holds the entire operation as his personal property, usually managing it on a day-to-day basis.

Partnership

• may have from two to 50 or more members, as in the case of large law and accounting firms, brokerage houses, and advertising agencies. This form of business is owned by the partners themselves; they may receive varying shares of the profits depending on their investment or contribution. Whenever a member leaves or a new member is added, the firm must be reconstituted as a new partnership.

Partnership

• The distinguishing features of the partnership are the personal and unrestricted liability of each partner for the debts and obligations of the firm (whether he assented to their being incurred or not) and the right of each partner to participate in the management of the firm and to act as an agent of it in entering into legal transactions on its behalf.

Partnership• a partner may assign his share or interest in a

partnership to anyone he wishes unless the partnership agreement forbids this, but the assignment does not make the assignee a partner unless all the other partners agree. If they do not, the assignee is merely entitled to receive the financial benefits attached to the share or interest without being able to take part in the management of the firm, but neither is he personally liable for the debts of the firm.

Corporation• the limited-liability company, or corporation,

denotes incorporated groups of persons—that is, a number of persons considered as a legal entity (or fictive “person”) with property, powers, and liabilities separate from those of its members; the company is legally separate from the individuals who work for it, whether they be shareholders or employees or both; it can enter into legal relations with them, make contracts with them, and sue and be sued by them.

Corporation• formed not simply by an agreement entered

into between its first members; it must also be registered at a public office (SEC) or court designated by law or otherwise obtain official acknowledgment of its existence.

• Shares are freely transferable unless the company's constitution imposes restrictions on their transfer

The Production Function

• Land, labor, capital

The Production Function

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Production Function Utility Function

Output from inputs Preference levelfrom purchases

Derived fromtechnologies

Derived frompreferences

Cardinal(Defn: givenamount of inputsyields a unique andspecific amount ofoutput)

Ordinal

Marginal Product Marginal Utility

The Production & Utility Functions

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Q = f(L)

L

Q

•

••

•C

D

A

B

Production Set

Production Function

The Production Function & Technical Efficiency

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Definition: The feasible

but inefficient points below

the production function

make up the firm’s

production set.

The Production Function & Technical Efficiency

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The Production Function & Technical Efficiency

• The variables in the production function are flows (the

amount of the input used per unit of time), not stocks (the

absolute quantity of the input).

• Example: stock of capital is the total factory installation;

flow of capital is the machine hours used per unit of time in

production (including depreciation).

• Capital refers to physical capital (definition: goods that

are themselves produced goods) and not financial capital

(definition: the money required to start or maintain

production).

ANALYSIS

• Production Function

Q = F(K,L)• Q is quantity of output produced.

• K is capital input.

• L is labor input.

• F is a functional form relating the inputs to output.

The maximum amount of output that can be produced with K units of capital and L units of labor.

• Short-Run vs. Long-Run Decisions

• Fixed vs. Variable Inputs

Measures

• Total Product (TP): maximum output produced with given amounts of inputs.

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Definition: The marginal product of an input is the

change in output that results from a small change

in an input holding the levels of all other inputs

constant.

MPL = Q/L

• (holding constant all other

inputs)

MPK = Q/K

• (holding constant all other

inputs)

The Marginal Product

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Definition: The marginal product of an input is the

change in output that results from a small change

in an input holding the levels of all other inputs

constant.

The Marginal Product

Marginal Product of Labor: MPL = Q/L

Measures the output produced by the last worker.

Slope of the short-run production function (with respect to labor).

Marginal Product of Capital: MPK = Q/K

Measures the output produced by the last unit of capital.

When capital is allowed to vary in the short run, MPK is the slope of the

production function (with respect to capital).

Marginal Product

• Marginal Product on an Input: change in total output attributable to the last unit of an input.

Marginal Product of Labor: MPL = Q/L

• Measures the output produced by the last worker.

• Slope of the short-run production function (with respect to labor).

Marginal Product of Capital: MPK = Q/K

• Measures the output produced by the last unit of capital.

• When capital is allowed to vary in the short run, MPK is the slope of the production function (with respect to capital).

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Definition: The law of diminishing marginal

returns states that marginal products (eventually)

decline as the quantity used of a single input

increases.

Definition: The average product of an

input is equal to the total output that is to

be produced divided by the quantity of the

input that is used in its production:

APL = Q/L

APK = Q/K

The Average Product & Diminishing Returns

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Total, Average, and Marginal

• When a total magnitude is rising, the

corresponding marginal magnitude is positive.

• When an average magnitude is falling, the

corresponding marginal magnitude must be

smaller than the average magnitude.

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TPL maximized where MPL

is zero. TPL falls where

MPL is negative; TPL rises

where MPL is positive.

Total, Average, and Marginal

Decisions

• Producing on the production function– Aligning incentives to induce maximum worker

effort.

• Employing the right level of inputs (capital or labor intensive)– When labor or capital vary in the short run, to

maximize profit a manager will hire• labor until the value of marginal product of labor

equals the wage: VMPL = w, where VMPL = P x MPL.

• capital until the value of marginal product of capital equals the rental rate: VMPK = r, where VMPK = P x MPK.

ISOQUANT

• illustrates the combinations of inputs (K, L) that yield the producer the same level of output.

• The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.

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Isoquant(Defn: allpossiblecombinations ofinputs that justsuffice to produce agiven amount ofoutput)

Indifference Curve

Marginal Rate ofTechnicalSubstitution

Marginal Rate ofSubstitution

Production Function Utility Function

The Production & Utility Functions

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Example: Q = K1/2L1/2

What is the equation of the isoquant for Q = 20? 20 = K1/2L1/2 => 400 = KL => K = 400/L

Isoquants

Definition: An isoquant traces

out all the combinations of

inputs (labor and capital) that

allow that firm to produce the

same quantity of output

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Isoquants

L

K

Q = 10

Q = 20

All combinations of (L,K) along the

isoquant produce 20 units of

output.

0

Slope=K/L

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Definition: The marginal rate of technical substitution

measures the amount of an input, L, the firm would require in

exchange for using a little less of another input, K, in order to just

be able to produce the same output as before.

MRTSL,K = -K/L (for a constant level of output)

Marginal products and the MRTS are related:

MPL(L) + MPK(K) = 0

=> MPL/MPK = -K/L = MRTSL,K

Marginal Rate of Technical Substitution

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Marginal Rate of Technical Substitution

• If both marginal products are positive,

the slope of the isoquant is negative.

• If we have diminishing marginal

returns, we also have a diminishing

marginal rate of technical substitution

• For many production functions,

marginal products eventually become

negative. Why don't most graphs of

Isoquants include the upwards-sloping

portion?

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L

K

Q = 10

Q = 20

0

MPK < 0

MPL < 0

Isoquants

Example: The Economic and the

Uneconomic Regions of Production

Isoquants

Linear Isoquants

Capital and labor are

perfect substitutes

Q = aK + bL

MRTSKL = b/a

Linear isoquants imply that

inputs are substituted at a

constant rate, independent of

the input levels employed.

Leontief Isoquants

Capital and labor are perfect

complements.

Capital and labor are used in

fixed-proportions.

Q = min {bK, cL}

Since capital and labor are

consumed in fixed proportions

there is no input substitution

along isoquants (hence, no

MRTSKL).

Cobb-Douglas Isoquants

Inputs are not perfectly

substitutable.

Diminishing marginal rate

of technical substitution.

As less of one input is used in

the production process,

increasingly more of the other

input must be employed to

produce the same output level.

Q = KaLb

MRTSKL = MPL/MPK

Isocosts

The combinations of inputs that

produce a given level of output at

the same cost:

wL + rK = C

Rearranging,

K= (1/r)C - (w/r)L

For given input prices, isocosts

farther from the origin are

associated with higher costs.

Changes in input prices change

the slope of the isocost line.

Cost Minimization

• Marginal product per peso spent should be equal for all inputs:

But, this is just

r

w

MP

MP

r

MP

w

MP

K

LKL

r

wMRTSKL

Cost Minimization

Returns to scale

• If a 10% increase in all inputs yields more than a 10% increase in output, the production function has increasing returns to scale. If it yields less than a 10% increase in output, the production function has decreasing returns to scale. And if it yields exactly a 10% increase in output, it has constant returns to scale.

Returns to scale

• are important for determining how many firms will populate an industry. When increasing returns to scale exist, one large firm will produce more cheaply than two small firms. Small firms will thus have a tendency to merge to increase profits, and those that do not merge will eventually fail. On the other hand, if an industry has decreasing returns to scale, a merger of two small firms to create a large firm will cut output, raise average costs, and lower profits. In such industries, many small firms should exist rather than a few large..

Types of Cost

• Variable cost (VC)

• Fixed cost (FC)

• Total cost TC = VC + FC

• Average Cost (AC)

• Marginal Cost (MC)

• TC = FC + VC

• AFC = FC/Q

• AVC = VC/Q

• ATC = AFC + AVC

• The total variable cost curve has the same shape as the total cost curve—increasing output increases variable cost.

• The marginal cost curve goes through the minimum point of the average total cost curve and average variable cost curve.

• Each of these curves is U-shaped.

The average fixed cost curve slopes down continuously; it looks like a child’s slide – it starts out with a steep decline, then it becomes flatter and flatter.

• It tells us that as output increases, the same fixed cost can be spread out over a wider range of output.

• When output is increased in the shortrun, it can only be done by increasing the variable input.

• The law of diminishing marginal productivity sets in as more and more of a variable input is added to a fixed input.

• Marginal and average productivities fall and marginal costs rise.

• And when average productivity of the variable input falls, average variable cost rise.

• The average total cost curve is the vertical summation of the average fixed cost curve and the average variable cost curve.

• If the firm increased output enormously, the average variable cost curve and the average total cost curve would almost meet.

• The firm’s eye is focused on average total cost—it wants to keep it low.

The Relationship BetweenProductivity and Costs

• When one is increasing, the other is decreasing.

• When one is at a maximum, the other is at a minimum.

Relationship between MC and AC

• MC > AC implies AC is increasing

• MC < AC implies AC is decreasing

• Marginal cost curves always intersect average cost curves at the minimum of the average cost curve.

• The position of the marginal cost relative to average total cost tells us whether average total cost is rising or falling.

To summarize:

• If MC > ATC, then ATC is rising.

• If MC = ATC, then ATC is at its low point.

• If MC < ATC, then ATC is falling.

• Marginal and average total cost reflect a general relationship that also holds for marginal cost and average variable cost.

• If MC > AVC, then AVC is rising.

• If MC = AVC, then AVC is at its low point.

• If MC < AVC, then AVC is falling.

• As long as average variable cost does not rise by more than average fixed cost falls, average total cost will fall when marginal cost is above average variable cost,

But In Reality• Some economists have tried to construct a theory of the

firm in which the firm decides prices by a markup over costs. The attraction of this sort of theory is that, when asked to explain how they determine the prices they charge, most sellers talk in terms of markups (which they sometimes call "profit margins"). The problem with markup theories is that they have difficulty explaining the percentage size of the markup (when they bother trying to explain it at all). Grocery stores, for example, mark up different products by different percentages, and they have a much smaller average markup than furniture stores have.

• Most economists see markup pricing as a rule-of-thumb way in which businesses conduct their affairs. Firms usually do not have the information needed to compute marginal costs and revenues. Instead they find rules or guidelines that work, and stick with them as long as they perform satisfactorily. If a firm marks up a product by 50% and finds that it does not make a profit at that price, it tries another percentage. When it finally finds a markup that generates a profit, it will stick with it.

How firms decide in the long run