The Supply Side of the Market The Supply Side of the Market in in - - PowerPoint PPT Presentation

The Supply Side of the Market The Supply Side of the Market in in Three Parts: Three Parts:

• I. An Introduction to Supply and
• I. An Introduction to Supply and

Producer Surplus Producer Surplus

• II. The Production Function
• II. The Production Function
• III. Cost Functions
• III. Cost Functions

Econ Dept, UMR Presents

Part II: The Production Part II: The Production Function Function

Starring Starring

N NSupply

Supply

O OProduction

Production

O OCost

Cost

N NProducer Surplus

Producer Surplus

Featuring Featuring

N NThe Law of Diminishing Marginal Product

The Law of Diminishing Marginal Product

N NThe MP/ P Rule

The MP/ P Rule

N NEconomic Cost vs. Accounting Cost

Economic Cost vs. Accounting Cost

N NEconomic Profit vs. Accounting Profit

Economic Profit vs. Accounting Profit

N NThe Unimportance of Sunk Cost

The Unimportance of Sunk Cost

Behind the Supply Curve Behind the Supply Curve

N N Necessary compensation for effort is

Necessary compensation for effort is based on cost based on cost

N N And, Cost is based on the production

And, Cost is based on the production function and input prices function and input prices

O O The production function relates inputs to

The production function relates inputs to

• utput and is governed by technology
• utput and is governed by technology

O O The input mix required for any output

The input mix required for any output times the input prices gives output cost times the input prices gives output cost

O O What we want is obtained efficiently only

What we want is obtained efficiently only if it is produced at minimum output cost if it is produced at minimum output cost

Production - Cost - Supply Production - Cost - Supply

N N Supply, Cost, and the Production Function are

Supply, Cost, and the Production Function are interdependent interdependent

N N We assume input prices are fixed

We assume input prices are fixed

N N As is Technology

As is Technology

N N Production technology relates inputs to outputs

Production technology relates inputs to outputs

N N The optimal method of production, for a profit-

The optimal method of production, for a profit- maximizing firm, is the one that minimizes costs maximizing firm, is the one that minimizes costs

N N Two periods are important for decision making

Two periods are important for decision making

O O The Short Run

The Short Run

O O The Long Run

The Long Run

Short Run vs. Long Run Short Run vs. Long Run

N N The short run is a period of time

The short run is a period of time such that there is a fixed factor of such that there is a fixed factor of production or constraint-it is the production or constraint-it is the period we are in period we are in

N N The long run is a period of time

The long run is a period of time such that there are no fixed factors such that there are no fixed factors

• f production or constraint-it is the
• f production or constraint-it is the

period we are planning period we are planning

N N Total Product

Total Product

N N Average Product

Average Product

N N Marginal Product

Marginal Product

Now we will look at the Now we will look at the production process and three production process and three ways to measure productivity ways to measure productivity

• f inputs
• f inputs

Then we will see how the production relationships link to costs

Total Product (TP) Total Product (TP)

N N A mathematical or numerical

A mathematical or numerical expression of a relationship expression of a relationship between inputs and outputs: between inputs and outputs:

O O q = f(K,L) is the function relating the

q = f(K,L) is the function relating the production of q to just two inputs: capital, production of q to just two inputs: capital, K; and labor, L K; and labor, L N N Graphically shows units of total

Graphically shows units of total product as a function of units of a product as a function of units of a variable input with other inputs variable input with other inputs fixed fixed

Average Product (AP) Average Product (AP)

N N The average amount of output

The average amount of output produced by each unit of a produced by each unit of a variable factor of production, or variable factor of production, or input input

N N Output per unit of an input, e.g.,

Output per unit of an input, e.g., AP APL

L = q/ L is the average

= q/ L is the average product of labor product of labor

Marginal Product (MP) Marginal Product (MP)

N N The additional output that can be

The additional output that can be produced by adding one more unit produced by adding one more unit

• f a specific input, ceteris paribus
• f a specific input, ceteris paribus

N N If Labor is the variable input:

If Labor is the variable input:

O OMP

MPL

L =

=

˛ ˛q/

q/ ˛

˛L (over a range)

L (over a range)

(where (where ˛

˛ refers to change in)

refers to change in) O OMP

MPL

L = dq/ dL (using calculus,

= dq/ dL (using calculus, the 1st derivative of the the 1st derivative of the production function wrt L) production function wrt L)

Calculus?--Don’t Worry Calculus?--Don’t Worry

N N Often to show the mathematical

Often to show the mathematical relationships, we will use formulas relationships, we will use formulas derived from calculus, e.g., Calculus 8 derived from calculus, e.g., Calculus 8

N N Calculus is

Calculus is not

not a prerequisite so any

a prerequisite so any formulas will be provided formulas will be provided

Consider a lawn service with a fixed Consider a lawn service with a fixed capital base, e.g, 2 mowers, 3 trimmers, etc. capital base, e.g, 2 mowers, 3 trimmers, etc.

Labor Total Marginal Average Units Product Product Product 0 0 --- --- 1 2.67 5 2.67 2 9.30 8 4.65 3 18.00 9 6.00 4 26.67 8 6.67 5 33.33 5 6.67 6 36.00 0 6.00

MPL

= dq/ dL = 6L - L2 ; APL = q/ L

TP = q = 3L2 - L3/ 3 ;

This data can be plotted as This data can be plotted as follows: follows:

5 10 15 20 25 30 35 40 1 2 3 4 5 6

Total Product

1 2 3 4 5 6 7 8 9 10 1 2 3 4 4.5 5 6 MP AP

Average Product (L) Marginal Product (L)

Number of employees/ t Number of employees/ t

The Law of Diminishing The Law of Diminishing Returns Returns

N N After a certain point, when

After a certain point, when additional units of a variable input additional units of a variable input are added to fixed inputs, the are added to fixed inputs, the marginal product of the variable marginal product of the variable input declines input declines

N N At this point, output starts

At this point, output starts increasing at a decreasing rate increasing at a decreasing rate

In the lawn service, as more In the lawn service, as more employees are added to the fixed employees are added to the fixed inputs, eventually MP falls. inputs, eventually MP falls.

Diminishing returns

Diminishing returns sets in after the sets in after the third worker is third worker is hired hired

1 2 3 4 5 6 7 8 9 10 1 2 3 4 4.5 5 6 M P A P

Number of employees/ t

Average Product (L) Marginal Product (L)

Adding More Inputs to the Adding More Inputs to the Variable Input Makes the Variable Variable Input Makes the Variable Input More Productive Input More Productive

N N More, or better tools makes Labor more

More, or better tools makes Labor more productive productive

N N An increase in capital stock increases:

An increase in capital stock increases:

O O the total product of labor

the total product of labor

O O the average product of labor

the average product of labor

O O the marginal product of labor

the marginal product of labor

Returning to our lawn service, suppose Returning to our lawn service, suppose the owners can invest in four mowers the owners can invest in four mowers rather than two rather than two

Units of Two Mowers Four Mowers Units of Two Mowers Four Mowers Labor TP MP TP MP Labor TP MP TP MP 0 0 --- 0 --- 0 0 --- 0 --- 1 2.67 5 3.67 7 1 2.67 5 3.67 7 2 9.30 8 13.33 12 2 9.30 8 13.33 12 3 18.00 9 27.00 15 3 18.00 9 27.00 15 4 26.67 8 42.67 16 4 26.67 8 42.67 16 5 33.33 5 58.33 15 5 33.33 5 58.33 15 6 36.00 0 72.00 12 6 36.00 0 72.00 12 With 4 mowers, q = 4L2 - L3/ 3 ; MPL = 8L - L2

Review: The Production Review: The Production Function Function

N N Simplifying Assumptions we use

Simplifying Assumptions we use

O O Short Run, therefore at least one input is

Short Run, therefore at least one input is fixed fixed

O O Output, q, depends on only two inputs

Output, q, depends on only two inputs

N Labor, L, the variable input

Labor, L, the variable input

N Capital, K, the fixed input

Capital, K, the fixed input

N N As the variable input is added to the fixed

As the variable input is added to the fixed input, q increases first at an increasing rate, but input, q increases first at an increasing rate, but ultimately at a decreasing rate due to the law of ultimately at a decreasing rate due to the law of diminishing marginal returns diminishing marginal returns

N N More of the fixed inputs make the variable

More of the fixed inputs make the variable inputs more productive inputs more productive

L1

Graphic View of Graphic View of Typical Short Typical Short Run Production Run Production

Function Function

q = f (K,L) K=K q = f (K,L) K=K

L2 L0 q0 q1 q/ t APL APL, MPL MPL L/ t L/ t L0 L1 L2 The “bar” means the variable is fixed

L1

First, notice the First, notice the total product total product

• curve. Output as
• curve. Output as

a function of a function of labor depends on labor depends on a given fixed a given fixed capital input. capital input. With more K, With more K, labor is more labor is more productive productive

L2 L0 q0 q1 q/ t L/ t More capital makes labor more productive q with K = K1 q with K = K2 > K1

L1

Second, find MP Second, find MP by taking the by taking the slope of TP slope of TP

L2 L0 q0 q1 q/ t MPL MPL L/ t L/ t L0 L1 L2 A B C At “A” , the inflection point, the slope is maximized; The law of diminishing returns set in at “B”, the slope also equals the average product; at “C”, the slope is zero

L1

Last find Last find Average Product Average Product by drawing a ray by drawing a ray from the origin from the origin to different to different points on TP. points on TP. The slope of The slope of these rays is AP these rays is AP

L2 L0 q0 q1 q/ t APL APL, MPL MPL L/ t L/ t L0 L1 L2 Note AP = MP at max AP

L1

Everything Everything Together: Typical Together: Typical Short Run Short Run Production Production

Function Function

q = f (K,L) K=K q = f (K,L) K=K

L2 L0 q0 q1 q/ t APL APL, MPL MPL L/ t L/ t L0 L1 L2 The “bar” means the variable is fixed

The Equal MP/ P Rule The Equal MP/ P Rule

N N A necessary condition for minimizing cost of

A necessary condition for minimizing cost of any given level of an activity is to mix the any given level of an activity is to mix the variable inputs such that their Marginal variable inputs such that their Marginal Product/ Price ratios (MP Product/ Price ratios (MPi

i/ P

/ Pi

i) are equal

) are equal

N N MP

MP1

1/ P

/ P1

1 = MP

= MP2

2/ P

/ P2

2 = . . . = MP

= . . . = MPn

n/ P

/ Pn

n for all n

for all n variable inputs variable inputs

N N If MP

If MP1

1/ P

/ P1

1 > MP

> MP2

2/ P

/ P2

2 you are getting more

you are getting more value per dollar from input 1 than from input value per dollar from input 1 than from input 2 and to produce the same level of output at 2 and to produce the same level of output at lower cost you should hire more 1 and less 2 lower cost you should hire more 1 and less 2

N N As you hire more of input 1, MP

As you hire more of input 1, MP1

1 falls, and as

falls, and as you hire less of input 2, MP you hire less of input 2, MP2

2 increases

increases

From the Short Run to the From the Short Run to the Long Run Long Run

N N In the short run at least one input is

In the short run at least one input is fixed fixed

N N In the long run all inputs may be

In the long run all inputs may be changed changed

N N An important property of the

An important property of the production function is its “Internal production function is its “Internal Returns to Scale” Returns to Scale”

Types of Internal Returns to Scale Types of Internal Returns to Scale

N N Economies of Scale

Economies of Scale: a proportional : a proportional change in change in all

all inputs leads to a larger

inputs leads to a larger proportional change in output proportional change in output

N N Constant Returns to Scale

Constant Returns to Scale: a : a proportional change in proportional change in all

all inputs leads

inputs leads to an equal proportional change in to an equal proportional change in

• utput
• utput

N N Diseconomies of Scale

Diseconomies of Scale: a proportional : a proportional change in change in all

all inputs leads to a smaller

inputs leads to a smaller proportional change in output proportional change in output

Returns to Scale Returns to Scale

N N Changing all inputs in the same proportion is

Changing all inputs in the same proportion is a “scale” change, e.g., increase all by 10%, a “scale” change, e.g., increase all by 10%, decrease all by 5% decrease all by 5%

N N Increasing Returns to Scale: %

Increasing Returns to Scale: %˛

˛q>%

q>%˛

˛R

R

N N Constant Returns to Scale: %

Constant Returns to Scale: % ˛

˛q=%

q=%˛

˛R

R

N N Decreasing Returns to Scale: %

Decreasing Returns to Scale: %˛

˛q<%

q<%˛

˛R

R (where R is all resources) (where R is all resources)

N N As we will see, cost curves in the long run are

As we will see, cost curves in the long run are based on the underlying production based on the underlying production technology, i.e., returns to scale technology, i.e., returns to scale

Returns to Scale, examples Returns to Scale, examples

N N IRTS: doubling all inputs leads to an

IRTS: doubling all inputs leads to an increase of 125% in q increase of 125% in q

N N DRTS: an increase in all inputs by 5%

DRTS: an increase in all inputs by 5% leads to a 3% increase in q leads to a 3% increase in q

N N CRTS: a decrease in all inputs by 10%

CRTS: a decrease in all inputs by 10% lead to a 10% fall in q lead to a 10% fall in q

N N If all inputs are decreased by 5% and

If all inputs are decreased by 5% and

• utput falls by 7%, %
• utput falls by 7%, %˛

˛q>%

q>%˛

˛R, therefore

R, therefore IRTS IRTS

What if all inputs change but What if all inputs change but not in the same proportion? not in the same proportion?

N N If the %

If the %˛

˛q>%

q>%˛

˛Costs we use the term

Costs we use the term Economies of Scale Economies of Scale

N N If the %

If the %˛

˛q<%

q<%˛

˛Costs we use the term

Costs we use the term Diseconomies of Scale Diseconomies of Scale

N N IRTS implies Economies of Scale but

IRTS implies Economies of Scale but Economies of scale do not imply IRTS Economies of scale do not imply IRTS

N N The same is true for the relationship

The same is true for the relationship between Diseconomies of Scale and DRTS between Diseconomies of Scale and DRTS

Economies of Scale Economies of Scale

N N Reasons for economies of scale

Reasons for economies of scale

N N Greater specialization of resources

Greater specialization of resources

O O Divide work get benefits of specialization (lower costs).

Divide work get benefits of specialization (lower costs). This was the point emphasized by Adam Smith This was the point emphasized by Adam Smith

O O Efficient Utilization of specialized technologies may not

Efficient Utilization of specialized technologies may not be possible at small scale, e.g., Airline hubs, irrigation be possible at small scale, e.g., Airline hubs, irrigation systems systems

O O Arithmetic relationships, e.g.,

Arithmetic relationships, e.g.,

N

the circumference of a pipe, which approximates

the circumference of a pipe, which approximates cost equals pi*2*radius, but the carrying capacity cost equals pi*2*radius, but the carrying capacity depends on the area which equals pi*radius squared depends on the area which equals pi*radius squared

Diseconomies of Scale Diseconomies of Scale

N N Reasons for diseconomies of scale

Reasons for diseconomies of scale

N N Coordination and control problems as firm

Coordination and control problems as firm gets large--The Principal/ Agent Problem gets large--The Principal/ Agent Problem

O O The Principal is the person in charge and the

The Principal is the person in charge and the Agent is the person charged with carrying out Agent is the person charged with carrying out the wishes of the Principal the wishes of the Principal

O O Two conditions need to be present for the P/ A

Two conditions need to be present for the P/ A problem to exist problem to exist

N Agents and Principals must have different

Agents and Principals must have different

• bjectives
• bjectives

N It must be costly for the Principal to monitor and

It must be costly for the Principal to monitor and enforce enforce

Now, let’s link production to Now, let’s link production to costs costs

N N Each production relationship has a cost

Each production relationship has a cost counterpart counterpart

O O TP:variable input

TP:variable input

• - Variable Cost
• - Variable Cost

O O AP:variable input

AP:variable input

• - Average Variable Cost
• - Average Variable Cost

O O MP:variable input

MP:variable input

• - Marginal Cost
• - Marginal Cost

O O Fixed inputs

Fixed inputs

• - Fixed (or Sunk) Cost
• - Fixed (or Sunk) Cost

O O MP/ P rule

MP/ P rule

• - Equal MC rule
• - Equal MC rule

N N The production function and the MP/ P rule

The production function and the MP/ P rule tells us the minimum cost of producing any tells us the minimum cost of producing any level of output, q: Cost = input price *inputs level of output, q: Cost = input price *inputs required required

The End The End

Go Ahead to Part III, on Costs