PRODUCTION AND ITS COSTS

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PRODUCTION AND ITS COSTS Principles of

Microeconomic Theory, ECO 284

John Eastwood CBA 213 523-7353 e-mail address:

[email protected]

http://jan.ucc.nau.edu/~jde

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ALL ABOUT COSTS

Explicit and Implicit Costs Accounting Profit and Economic Profit

Sunk Costs

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Explicit and Implicit Costs

Explicit CostsAn explicit cost is incurred when an actual monetary payment is made.

Implicit CostsImplicit costs are the value of the resources used in the production of a good for which no monetary payment is made.

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Accounting Profit and Economic Profit Accounting Profit

= Total Revenue - total explicit costs Economic Profit

= Total Revenue - opportunity costs Opportunity Costs

= Explicit costs + Implicit costs

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Normal Profit

When a firm's revenue just covers its opportunity costs, it is earning a zero economic profit.

This is also known as a normal profit. Total Cost (TC) includes all opportunity

costs, including a normal profit.

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Sunk Costs

Costs incurred in the past that cannot be changed by current decisions and cannot be recovered are said to be "sunk."

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PRODUCTION AND COSTS IN THE SHORT RUN The Short-Run Production Function Inputs And Costs In The Short Run Total, Average and Marginal Costs

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Production Functions

. . . express the relationship between the quantity of the inputs and the maximum quantity of output (q) that can be produced with those inputs.

The quantities of some inputs are variable in the short run (e.g., labor, materials)

The quantity of other inputs (e.g., capital, land) are fixed in the short run.

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Short-Run Production Function (a.k.a. TPL) . . . expresses the relationship between the

quantity of the labor and the maximum quantity of output (q) that can be produced, holding the quantity of other inputs (e.g., capital, land) constant.

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Total, Marginal, and Average Physical Products of Labor

TP q f K L N ( , , )

LAPPq

L

LMPPq

L

q q

L L

2 1

2 1

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Example:q=Sand Output (Tons/Day) L=Labor (8-hr. worker-shifts/day)

L qAPPL MPPL0 0 -- --1 102 223 364 52 13 165 70 14 186 86 14.33 16

LMPPq

L

LAPPq

L

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Table 1: q= Sand (Tons/Day) L=Labor (8-hr. worker-shifts/Day)

L qAPPL MPPL6 86 14.33 167 100 14.28 148 112 14.00 129 122 13.55 10

10 130 13.00 811 137 12.45 712 143 11.92 6

LMPPq

L

LAPPq

L

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Table 1: q= Sand (Tons/Day) L=Labor (8-hr. worker-shifts/Day)L qAPPL MPPL

13 148 11.38 514 152 10.85 415 155 10.33 316 157 9.81 217 158 9.29 118 158 8.78 019 157 8.26 -1

LMPPq

L

LAPPq

L

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The Average - Marginal Rule

When the marginal magnitude (e.g. product, cost, or utility) exceeds the average magnitude, the average must rise.

When the marginal magnitude is less than the average magnitude, the average must fall.

Marginal curve intersects average curve at a maximum or minimum.

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From Definitions to Cost Curves

The Law of Diminishing Marginal Returns– As more units of a variable input are combined

with fixed inputs, eventually the marginal physical product of the variable input will decline.

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Inputs And Costs In The Short Run

Fixed And Variable Inputs Fixed and Variable Costs Total Cost = Total Fixed Cost + Total

Variable Cost TC= TFC + TVC

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Example: w=wage; q= Sand (Tons/Day); L=Labor (8-hr. worker-shifts /Day)

L q TVC TC0 0 0 1001 10 50 1502 22 100 2003 364 525 706 86

w = $50/worker-shift

TVC = wL($/day)

TFC = $100/day

TC = TFC + TVC

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L q TVC TC7 100 350 4508 112 400 5009 122 450 550

10 130 500 60011 137 550 65012 143 600 70013 148 650 750


TVC = wL($/day)

TFC = $100/day

TC = TFC + TVC

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L q TVC TC14 152 700 80015 155 750 85016 157 800 90017 158 850 95018 158 900 100019 157 950 1050


TVC = wL($/day)

TFC = $100/day

TC = TFC + TVC

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Average Cost Concepts

Average Fixed Cost, AFC=TFC/q Average Variable Cost, AVC=TVC/q Average Total Cost, ATC=TC/q where q = the quantity of output.

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Marginal Cost, MC:

The change in total cost that results from a one unit change in output.

MCTC

q

TVC

qTVC TVCq q

2 1

2 1

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q TVC TC AVC AFC ATC MC0 0 100 -- -- -- --

10 50 150 5.00 10.00 15.00 5.0022 100 200 4.54 4.55 9.09 4.1736 150 250 4.17 2.78 6.95 3.5752 200 300 3.85 1.92 5.77 3.1370 250 350 3.57 1.43 5.00 2.7886 300 400 3.49 1.16 4.65 3.13

100 350 450112 400 500 3.57 0.89 4.46 4.17

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q TVC TC AVC AFC ATC MC122 450 500 3.69 0.82 4.51 5.00130 500 600 3.85 0.77 4.62 6.25137 550 650 4.01 0.73 4.74 7.14143 600 700 4.20 0.70 4.90 8.33148 650 750 4.39 .068 5.07 10.00152 700 800 4.60 0.66 5.26 12.50155 750 850 4.84 0.65 5.49 16.67157 800 900 5.10 0.64 5.74 25.00158 850 950 5.38 0.63 6.01 50.00

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Average - Marginal Rule (Again)

When the marginal magnitude exceeds the average magnitude, the average must rise.

When the marginal magnitude is less than the average magnitude, the average must fall.

MC cuts AVC and ATC at their lowest points.

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Total Costs Shown as Areas

TC at a given quantity, q, equals the area of the rectangle formed by the origin, q, and ATCq (along both the y-axis and on the curve.

Rectangles formed by AVC and AFC at q show TVC and TFC.

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AVC and APPL are Related

As APPL rises, AVC decreases; as APPL falls, AVC increases. Assume labor is the only variable input:

AVCTVC

q

wL

q

wqL

w

APP L

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Diminishing Marginal Returns and Marginal Cost MC and MPP are related. As MPP rises,

MC decreases; as MPP falls, MC increases.Assume labor is the only variable input:

MCTVC

q

w L

q

wqL

w

MPP L

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PRODUCTION AND COSTS IN THE LONG RUN Least-cost production Long run average (total) cost. Returns to Scale Economies of Scope Technological Change

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Equal MPP per Dollar

In the long run, all inputs may vary. For example, K may be substituted for L.

Least-cost production requires that each resource is equally productive at the margin:

L K NMPPw

MPPi

MPPn

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The Long-Run Average Total Cost Curve (LRATC)

Each possible plant size has a unique short-run ATC curve.

LRATC shows the lowest average cost at which the firm can produce any given level of output.

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How LRATC Changes with the Scale of the Firm Economies of Scale

(a.k.a. Increasing returns to scale) LRATC has a negative slope.

Constant Returns to Scale LRATC has a slope = 0.

Diseconomies of Scale (a.k.a. Decreasing returns to scale) LRATC has a positive slope.

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Constant Returns to Scale

Say we double all inputs and get double the output– q = f(K,L), and f(2K,2L)=2q– LRATC=LRTC/q– With w & i constant, LRTC doubles.– LRATC ($/unit) is the same at q and 2q.

This is Constant Returns to Scale, CRS.

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Increasing Returns to Scale

Say we double all inputs and get more than twice the output– q = f(K,L), but f(2K,2L)>2q– With w & i constant, LRTC doubles.– Output more than doubles.– LRATC = LRTC/q ($/unit) falls

This is Increasing Returns to Scale, IRS (a.k.a. Economies of Scale)

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Decreasing Returns to Scale

Say we double all inputs, but get less than twice the output– q = f(K,L), but f(2K,2L)<2q– With w & i constant, LRTC doubles.– But output less than doubles.– LRATC = LRTC/q ($/unit) rises

This is Decreasing returns to scale (a.k.a. Diseconomies of Scale )

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LRATC is the Planning Curve

Optimum Plant Size – What is the most efficient scale of operations?

Minimum Efficient Scale– What is the smallest plant that will be

competitive?

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COST CURVES SHIFT WHEN

Input prices change The production function shifts

– Technological progress occurs– The quantity of fixed inputs changes

Taxes change

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Input Prices

Higher prices for fixed inputs shift

TFC, TC, AFC, and ATC up. Higher prices for variable inputs shift

TVC, TC, AVC, ATC, and MC up.

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Technological progress affects costs in two ways: It may improve the production process It may lower input prices

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Taxes

. . . on fixed inputs . . . on variable inputs, output, revenue,

profit, etc.

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Isocosts and Isoquants

Isocost means one cost. Isocost lines are similar to budget lines. Isoquant means one quantity. Isoquants are similar to indifference curves.

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Isocost lines show bundles of (L,K) of equal cost Let TC = Total Cost L = quantity of L w = price of L K = quantity of K k = price of K The y-intercept equals: The slope equals the

relative price of L($/unit L)/ ($/unit K)= units of K per unit of L

TC wL kK

kK TC wL

KTC

k

w

kL

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Changes in the Isocost Line

Increases in TC shift the Isocost out.

The vertical intercept increases when TC increases.

Changes in relative factor prices rotate the budget line. The slope equals the relative price of L (w/k) . A lower w yields a smaller |slope|.

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Isoquant Curves

One isoquant through each point. Each isoquant slopes down to the right. Isoquants further from the origin show

higher quantities of output. Isoquants never cross. Isoquants are bowed toward the origin.

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Slope of an Isoquant

at a point equals - MRTSLK

MRTSLK is the Marginal Rate of Technical Substitution of K for L.

MRTSLK = # of units of K the firm must add to replace one unit of L.

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Along an Isoquant , Output is constant

q MPP L MPP K

MPP L MPP K

MPP K MPP L

K

LMPP

MPP

L K

L K

K L

L

K

0

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Least-Cost Production

. . . occurs once the firm reaches the lowest possible isocost attainable given its output goal.

At that point, the slopes of the isocost and the isoquant are equal.

w

kMPP

MPPL

K

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Equal MPP per Dollar

The tangency of the Isocost and the Isoquant imply that K and L are equally efficient at the margin.

w

kMPP

MPP

MPPk

MPPw

L

K

K L

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Diminishing Returns (Again)

In Figure 11, on page 189, illustrates this concept using isoquants.

K is fixed in the SR, As more L is added, the MPPL eventually

falls.

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Product and Process Technology

Better product technology results in new or improved products.

Better process technology shifts the production function upward.

TPTPoldoldqq11

qq

LL00 LL11

TPTPnewnew

qq22

LL22

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Factors that shift TP up

Better process technology.

More of the fixed factors of production.

Workers’ skills improved.

TPTPoldoldqq11

qq

LL00 LL11

TPTPnewnew

qq22

LL22

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Technology and Industrial Evolution

Mass production tech. allowed the use of task-specific capital and relatively low-skilled labor.

Early development of this technology gave the US an edge in manufacturing.

Other factors added to our comparative advantage: abundant N; long history of HS education; no bombs hit us in WWII.

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Henry Ford’s Model T

The car was an advance in product technology.

Ford’s mass production techniques advanced process technology.

Large amounts of capital were combined with labor – resulting in a high MPPL,

– and correspondingly high wages.

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Strategy: Task-specific capital & low skilled labor Long production runs can make this

strategy profitable. Much of the competition in the auto

industry focused on product technology -- adding features, changing styles -- rather than on reducing costs, and cutting price.

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Success -- for a while

The auto industry’s methods were copied by many other corporations.

Even today, US firms often lead in developing new products (e.g., VCRs and fax machines).

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Comparative Advantage Lost

Our CA could not last forever. Technology and capital travel easily across

international borders. Other countries copied our products and our

production techniques.

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Mass Production Migrates

Task-specific capital requires only low skilled labor.

Many of these countries had lower wages. The CA in auto manufacturing and other

industries began to shift abroad. US producers could compete only by

lowering wages, or producing overseas.

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Better Process Technology

R&D focused on developing process technology to reduce costs has enabled Germany and Japan to pay high wages.

Using general capital and skilled labor, firms develop new products quickly and profitably over short production runs.

Requires skilled labor -- US skills lag others.

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PRODUCTION AND ITS COSTS