PRODUCERSBusiness Organization, Costs and Production, Strategic Behavior and Game Thoery

THEORY OF THE FIRM

Any organization that turns inputs into outputs.

Every household is a firm. Child care, home maintenance

Profit-maximizing firm

Business: organization of the firm (proprietorship, partnership, corporation

Economics: Boundaries of firms : make vs buy

Separation of ownership and control

THEORY OF THE FIRM

Goal: maximize long-term value of the firm

PROFIT:

Accounting vs. economic profit

Normal rate of return

N

tti

Value1 )1(

Profit N

tti1 )1(

Cost Total - Revenue Total

THEORY OF THE FIRM

ACCOUNTINGPROFIT

EXPLICIT COST

REV

ENU

E

ECONOMICPROFIT

EXPLICIT COST

IMPLICIT COST

OP

PO

RTU

NIT

Y C

OST

REV

ENU

E

THEORY OF THE FIRM

• Economic profits or losses exist when:

a) Barriers to entry : monopoly profit

b) Unexpected changes in demand and supply : frictional profit

c) Successful invention or innovation : Schumpeterian profit

d) Extraordinary success in meeting customer needs, maintaining efficient operations : compensatory profit

THEORY OF THE FIRM

Do firms maximize profits?

Optimize vs. Satisfice

Separation of management and ownership

Internal market discipline– Optimal contract: fixed wage plus profit-contingent compensation

Labor market discipline– poor performance creates bad reputation for managers

Product market discipline firms are likely to go under if profit is not maximized.

Capital market discipline Vulnerability to corporate raid or takeover (when value of firm is lower

than its potential)

PRODUCTION

Production set is the set of all combinations of inputs (FACTORS OF PRODUCTION) and outputs that are technologically feasible.q

x1X10

J

B PRODUCTION FUNCTIONq = f(x1, x2)

PRODUCTION

Technology

Fixed proportions

Perfect substitutes

Cobb-Douglas

q = f (x1, x2 ) = minx1

a,x2

b

ìíî

üýþ

q = f (x1, x2 ) = ax1 +bx2

q = f (x1, x2 ) = Ax1ax2

b

PRODUCTIONX2

X1

A

ISOQUANT

• Downward sloping

• Higher isoquants represent higher output

• Do not cross

• Convex

PRODUCTIONX2

X1

q = f (x1 , x2 ) = ax1 +bx2

x2 =q

b-a

bx1

PRODUCTIONX2

X1

q = f (x1 , x2 ) = minx1

a,x2

b

ìíî

üýþ

b

a

PRODUCTIONX2 = CAPITAL

X1 = LABOR

J

B

q = minx1

a,x2

b

ìíî

üýþ

q = minx1

c,x2

d

ìíî

üýþ

b

a

æ

èç

ö

ø÷J

>d

c

æ

èç

ö

ø÷B

J is capital-intensive; B is labor-intensive

a

b

c

d

PRODUCTIONX2 = CAPITAL

X1 = LABOR

J

B

R(.75a+.25c, .75b+.25d)

a

b

c

d

PRODUCTION

q

x1

J

B

MP1 =Dq

Dx1

=f (x1 + Dx1, x2 )- f (x1, x2 )

Dx1

“LAW OF DIMINISHING MARGINAL PRODUCT”

PRODUCTION

Let x1 = labor; x2 = capital.

MARGINAL PRODUCT

How many units will be added to production if an additional worker is hired?

AVERAGE PRODUCT

How many units of output is typically produced by one worker?

MP1 =Dq

Dx1

=f (x1 + Dx1, x2 )- f (x1, x2 )

Dx1

AP1 =q

x1

=f (x1, x2 )

x1

PRODUCTION

OUTPUT ELASTICITY

Eqx1 =%Dq

%Dx1

=Dq / q

Dx1 / x1

=Dq

Dx1

x1

q=MP1

AP1

PRODUCTION

No. of workers Output

Marginal product of

labor

Average product of

labor

Output elasticity of labor

0 0 - - -

1 3 3 3 1

2 8 5 4 1.25

3 12 4 4 1

4 14 2 3.5 0.57

5 14 0 2.8 0

6 12 -2 2 -1

PRODUCTION

Total output

No. of workers

No. of workers

MP of laborAP of labor

PRODUCTIONX2

X1

J

q = 100B

q = f x1, x2( )

Dq =MP1Dx1 +MP2Dx2

Dq = 0

Dx2

Dx1

=MP1

MP2

TECHNICAL RATE OF SUBSTITUTION (TRS)

“LAW OF DIMINISHING TRS”

PRODUCTION

Long run (LR) vs short run (SR) All factors of production are variable in the long run.

Returns to Scale (RTS) How much is the change in output if ALL inputs change by

some proportion k?

INCREASING RTS Change in output is MORE than k

DECREASING RTS Change in output is LESS than k

CONSTANT RTS Change in output is EQUAL TO k

PRODUCTION

For some production functions:

q = f (x1, x2 )

f (kx1,kx2 ) = k t f (x1, x2 )

t > 1 INCREASING RTSt < 1 DECREASING RTSt = 1 CONSTANT RTS

EXAMPLE:q = x1

2x2

2

qNEW = kx1( )2

kx2( )2

= k4x12x2

2 = k4q INCREASING RTS

PRODUCTION

In general,

q = f (x1, x2 )

f (kx1,kx2 ) > kf (x1, x2 )

EXAMPLE:

q = x12x2

2 + x2

qNEW = kx1( )2

kx2( )2

+ kx2

INCREASING RTS

f (kx1,kx2 ) < kf (x1, x2 ) DECREASING RTS

f (kx1,kx2 ) = kf (x1, x2 ) CONSTANT RTS

Let x1 = 1, x2 = 2, k = 2. q = 6 qnew = 68 > 2(6) =12

INCREASING RTS

PRODUCTION

X1 X1 X1

X2X

2

X

2

Q=100

Q=200

Q=100 Q=100

Q=300 Q=150

3 6 3 3 66

3

6

J

B

J

B

J

B

3

6

3

6

CONSTANT RTS INCREASING RTS DECREASING RTS

COST

Cost is OPPORTUNITY COST = explicit + implicit costs

Fixed vs. variable cost

Fixed = does not vary with output

Ex. rent

Variable = depends on the output produced

Ex. wage of production worker

COST

FIXED COST

Fixed vs. quasi-fixed

Quasi-fixed = independent of output level, but incurred only with positive amount of output

Fixed vs. sunk

Sunk = non-recoverable

Example:

Office rent

Rent of machine (short-term contract)

Interest of a loan

Computer (purchase price = P80,000; resale value after 5 years = P20,000)

COST

TOTAL COST = variable + fixed

C = VC + FC

C = VC(q) + FC

Variable cost

Unit variable cost x no. of units produced

Unit variable cost may be constant or increasing with output

Increasing unit variable cost due to diminishing marginal product – presence of fixed factor

COST

AC =C

q=VC

q+FC

q

AC = AVC+AFC

C

q

C C

q q

AFC

AVCAC

COST

qq* = MES

MES = minimum efficient scale

COST

Let x1 = labor; x2 = capital (fixed).

MARGINAL COST

How much does it cost to increase production by one unit?

AVERAGE COST

How much does it usually cost to produce one unit?

MC =DC

Dq=

DVC

Dq

AC =C

q

COST

Output FC VC C AFC AVC AC MC

0 60 0 60 - - - -

1 60 20 80 60 20 60 20

2 60 30 90 30 15 45 10

3 60 45 105 20 15 35 15

4 60 80 140 15 20 35 35

5 60 135 195 12 27 39 55

COST

C

q

q

AC, MC, AVC

COST

MC =DC

Dq=

DVC

Dq=VC(q+ Dq)-VC(q)

Dq

Let q = 0, Δq = 1.

MC(1) =VC(1)-VC(0)

1=VC(1)

MC is the derivative of VC.

VC is the area under derivative of MC.

MC = AVC when AVC is minimum.

MC = AC when AC is minimum.

COST

Example: C(q) = q2 +1

VC = q2 FC =1

AVC = q AFC =1

qAC = q+

1

q

MC = AVC when AVC is minimum.

q = 2q

MC = 2q

only if q = 0.

MC = AC when AC is minimum.

q+1

q= 2q

q = 1

COST

q

AC

MC

AVC

10

COST

In the long-run, all costs are variable.

where k* is optimal fixed factor (say, plant size).

LAC is the envelope of SAC.

LRC(q) = SRC(q, k*(q))

LRC(q) £ SRC(q, k(q))

LAC(q) £ SAC(q, k(q))

COST

q

k =1

k =2k =3

k =4

q1 q2 q3

COST

qq1 q2

0 < q < q1 INCREASING RTS

q1 ≤ q ≤ q2 CONSTANT RTS

q2 < q DECREASING RTS