Production refers to the transformation of inputs or resources into outputs of goods and services

Creation of utility

Created by human labor and capital

Satisfy human wants directly or indirectly

Are comparatively scarce and have

economic value

Have a definite monetary price/cost

EnterpriseCapitalLaborLand

•Immobile•Passive•Heterogeneous

•Active•Mobile•Variable•productivity

•Structures•Equipment•Cap.goods•Money

•Innovative function •Risk•Decision making

Factors of Production

INPUTS

INPUTS

CAPITAL

EntrepreneurWorkersLand &

Structures

LABOR

Machineryplant &equipment

Natural Resources

InputsFixed InputsVariable Inputs

Short Run- At least one input is fixed

Long Run - All inputs are variable The length of long run depends on industry.

Level of production can be altered changing the proportion of variable inputs

Output = Fixed inputs + Variable inputs

• Scale of production can be altered by changing the supply of all the inputs only in the long run

Output = Total inputs(variable inputs)

Total Product - total volume of goods produced during a specific period of time

Average Product - the per unit product of a variable factor

Marginal Product - the rate at which total product increases / addition to total product resulting from a unit increase in the quantity of the variable factor

Production Function With Two Inputs

Input & output are measured in physical unitsAssumption- Technology is constant the during analysis period- All units of L & K are homogenous

K Q6 10 24 31 36 40 395 12 28 36 40 42 404 12 28 36 40 40 363 10 23 33 36 36 332 7 18 28 30 30 281 3 8 12 14 14 12

1 2 3 4 5 6 L

Q = f(L, K)

Discrete Production Surface

Total Product TP = Q = f(L)

Marginal Product MPL =TP L

Average Product APL =TP L

Production orOutput Elasticity

Q/Q L/L

Q/ L Q/L

== =ELMPL

APL

L Q MPL APL EL

0 0 - - -1 3 3 3 12 8 5 4 1.253 12 4 4 14 14 2 3.5 0.575 14 0 2.8 06 12 -2 2 -1

Total, Marginal, and Average Product of Labor, and Output Elasticity

L Q MPL APL EL

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

Total, Marginal, and Average Product of Labor, and Output Elasticity

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7

6

A

B

C

D E

F

A’

B’ C’ D’E’

F’

TotalProduct

Marginal& AverageProduct

Labor

Labor

Production Function with One Variable Input

TP

MP

AP

Law of Diminishing Returns states that when increasing amounts of Variable inputs are combined with a fixed level of another input, a point will be reached where MP will decline.

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7

6

A

B

C

D E

F

B’ C’

A’D’

E’F’

I

TotalProduct

Marginal& AverageProduct

Labor

Labor

The Law of Diminishing Returns & Stages of Production

Stage I of Labor Stage II of Labor Stage III of Labor

TP

MP

AP

GInflection pt.

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7

6

A

B

C

D E

F

B’ C’

A’D’

E’F’

I

TotalProduct

Marginal& AverageProduct

Labor

Labor

The Law of Diminishing Returns & Stages of Production

Stage I of Labor Stage II of Labor Stage III of Labor

TP

MP

AP

G

MPL is increasingMPK is negative MPL is negativeMPL & MPK Positive

Marginal RevenueProduct of Labor

MRPL = (MPL)(MR)

Marginal ResourceCost of Labor

MRCL =TC L

Optimal Use of Labor MRPL = MRCL

L MPL MR = P

2.50 4 $103.00 3 103.50 2 104.00 1 104.50 0 10

Optimal Use of the Variable Input

Assumption : Firm hires additional units of labor at constant wage rate = $20

L MPL MR = P MRPL MRCL

2.50 4 $10 $40 $203.00 3 10 30 203.50 2 10 20 204.00 1 10 10 204.50 0 10 0 20

Use of Labor is Optimal When L = 3.50

Optimal Use of the Variable Input

Assumption : Firm hires additional units of labor at constant wage rate

2.5 3.0 3.5 4.0 4.5

40

30

20

10

0

MRCL = w = $20

dL = MRPL

Units of Labor Used

$

The marginal product of labor equation for a firm is given by: MPL = 10(K/L)0.5

Currently the firm is using 49 units of capital and 100 units of labor. Capital usage is fixed, but labor can be varied. If the price of labor is $20 per unit and the firms' output sells for $4, is the firm producing efficiently in the short run? If not, explain and determine the optimal rate of labor input.

MRPL = MRCL = w

28 ≠ 20 Not efficient

L = 196

Isoquants show combinations of two inputs that can produce the same level of output.

K

Q

6 10 24 31 36 40 395 12 28 36 40 42 404 12 28 36 40 40 363 10 23 33 36 36 332 7 18 28 30 30 281 3 8 12 14 14 12

1 2 3 4 5 6 L

Isoquants

Economic Region of ProductionFirms will only use combinations of two inputs that are in the economic region of production.

WRidge line

Marginal Rate of Technical Substitution

Q/ L = MPL and Q/ K = MPK

(L) MPL = -(K) MPK

Q = f(L,K)

dQ=Q/ L *dL + Q/ K *dK= 0

dK= (-) Q/ LdL Q/ K

dK - MPL = MRTS

dL MPK

=

MRTS = -(-2.5/1) = 2.5

Marginal Rate of Technical Substitution

Absolute value of the slope of isoquant is called the MRTS

K

Perfect Substitutes Perfect Complements

6

4

2

2 4 6 8 10 12

6

4

2

2 4 6

Capital Capital

Labor Labor0 0

-1K

2L

2K1L

C

A

B

Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost.

C wL rK

C wK L

r r

C Total Cost

( )w WageRateof Labor L

( )r Cost of Capital K

10

8

6

4

2 2 4 6 8 10

Capital

Labor

1K

1L

AB C = $100, w = r = $10A

B

slope = -w/r = -1

vertical intercept = 10

4 8 10 12 14 16 20

14

10 8

4

A

A’

A”

BB” B’ B*0 Labor

Capital

Isocost Lines

Isocost Lines

AB C = $100, w = r = $10

A’B’ C = $140, w = r = $10

A’’B’’ C = $80, w = r = $10

AB* C = $100, w = $5, r = $10

MRTS = w/r

Isocost Lines

AB C = $100, w = r = $10

A’B’ C = $140, w = r = $10

A’’B’’ C = $80, w = r = $10

Optimal input combinations:Slope of isoquant = Slope of isocost line

(absolute)Slope of isoquant = (absolute) Slope of isocost line

MRTS = w r

Since MRTS = MPL/ MPK

MPL = wMPK r

MPL = MPK

w r

If MPL = 5, MPK =4, and w = r

MPL > MPK

w r

MRP(input) = MRC(input)with constant input pricesMRP(input) = input price

To maximize Profits:MRPL = w = (MPL)(MR)

MRPK = r = (MPK)(MR) MPL = MPK

w r

MPL = wMPK r

Returns to scale refers to the degree by which output changes as a result of a given change in the quantity of all inputs used in production.

•Long run function

•Both L & K are changing

Production Function Q = f(L, K)

Q = f(hL, hK)

If = h, constant returns to scale.

If > h, increasing returns to scale.

If < h, decreasing returns to scale.

Constant Returns to

Scale

Increasing Returns to

Scale

Decreasing Returns to

Scale

Cobb-Douglas Production Function

Q = AKaLb

For example: the inputs are doubled i.e. instead of K & L, we are using 2K & 2L, then by how much the production will increase.

New Q = A(2K)a(2L)b

= A(2)a+bKaLb

= 2a+bAKaLb

= 2a+bQ

Now Q = 2a+bQ

If a + b = 1, constant returns to scale.

If a + b > 1, increasing returns to scale.

If a + b <1, decreasing returns to scale.

Do the following production functions have constant, increasing or decreasing returns of scale? ( K, L, M are inputs)

a. Q = 0.5X + 2Y + 40Zb. Q = 3L + 10K + 500c. Q = K/Ld. Q = 4A + 6B + 8ABe. Q = 10L 0.5 K 0.6

A. constant returns to scale.B. diminishing returns to scale.C. Decreasing returns to scaleD. increasing returns to scale.E. increasing returns to scale

Technology – cost effective at high level of production

Specialization of labour

Diseconomies of scale Transportation cost Difficult to manage

Medical Testing Labs, Inc., provides routine testing services for blood banks in the Los Angeles area. Tests are supervised by skilled technicians using equipment produced by two leading competitors in the medical equipment industry. Records for the current year show an average of 27 tests per hour being performed on the Testlogic-1 and 48 tests per hour on a new machine, the Accutest-3. The Testlogic-1 is leased for $18,000 per month, and the Accutest-3 is leased at $32,000 per month. On average, each machine is operated 25 eight-hour days per month.

a. Does Medical Testing Lab usage reflect an optimal mix of testing equipment?

b. If tests are conducted at a price of $6 each while labor and all other costs are fixed, should the company lease more machines?

a) (27*25*8)/ 18000 = (48*25*8) / 32000 = 0.3In both instances, the last dollar spent on each

machine increased output by the same 0.3 units, indicating an optimal mix of testing machines.

b) For each machine hour, the relevant question is Testlogic-1

27 ×(25×8)× $6 > $18,000 or $32,400 > $18,000.Accutest-348 ×(25×8)× $6 > $32,000 or $57,600 > $32,000.

In both cases, each machine returns more than its marginal cost (price) of employment, and expansion would be profitable.

The marginal product of labor for international trading is given by the equation

MPL = 10K0.5/L0.5

Currently the firm is using 100 units of capital and 121 units of labor. The capital stock is constant but the labor can be varied. If the price of labor is 10/- and price of output is Rs. 2/- per unit, is the firm operating efficiently in the short run? If not, determine the optimal rate of labor input.

Exercise

Answer: not optimally, L = 400

The production function is : Q = 20K0.5L0.5

With marginal product functions

MPK = 10L0.5/K0.5 MPL = 10K0.5/L0.5

If the price of capital is Rs. 5/- and price of labor is Rs. 4/- per unit, determine the expansion path for the firm.

The firm currently is producing 200 units of output per period using input rates of L = 4 and K =25. is this an efficient input combination? Why or why not? If not, determine the efficient input combination for producing an output rate of 200.

If the price of labor increases from Rs 4 to Rs 8 per unit, determine the efficient input combination for an output rate of 200. What is the capital –labor ratio now?

Answer: K= 0.8L, L= 11.18 and K= 8.94, L = 7.905 and K = 12.65

Suppose the price of one unit of labor is $10 and price of one unit of capital is $2.50.

Use this information to determine the isocost equations corresponding to a total cost of $200 and $500.

Plot these two isocost lines on a graph If the price of labor falls from $10 per unit to $8 per

unit, determine the new $500 isocost line and plot it on the same diagram used in part (b)

Answer: K = 80- 4L and K = 200 – 4L, K = 200 – 3.2L

4. Given the production function Q = 30K0.7L0.5

and input prices r = 20 and w = 30. Determine an equation for the

expansion path What is the efficient input combination

for an output rate of Q = 200? For 500?

Answer: K = 2.1L, for 200: L = 3.15 and K = 6.62, for 500: L = 6.765 and K = 14.207

The revenue dept. of a state govt. employs certified public accountants (CPAs) to audit corporate tax returns and book keepers to audit individual returns. CPAs are paid $31200 per yr, while the annual salary of a bookkeeper is $18200. Given the current staff of CPAs and bookkeepers, a study made by the dept’s economist shows that adding one year of a CPA’s time to audit corporate returns results in an additional tax collection of $52000. In contrast, an additional bookkeeper adds $41600 per year in additional tax revenue.

If the dept’s objective is to maximize tax revenue collected, is the present mix of CPAs and bookkeepers optimal? Explain

If the present mix of CPAs and bookkeepers is not optimal, explain what re-allocation should be made. That is, should the department hire more CPAs and fewer bookkeepers or vice versa.

Answer: CPAs – 1.67 and bookkeepers – 2.29