water resources p&m and eng. econ. microeconomics ce...

١

Water Resources P&M and Eng. Econ.

MicroeconomicsCE-448

٣

Microeconomics• Microeconomics (or price theory) is a branch of

economics that studies how individuals, organizations and firms make decisions to allocate limited resources, typically in markets where goods or services are being bought and sold.

• Microeconomics examines how these decisions and behaviors affect the supply and demand for goods and services, which determines prices, and how prices, in turn, determine the supply and demand of goods and services

• Microeconomics deals with the theory of behavior and markets for small agents, usually consumers, or firms that produce goods

٢

۴

Outlines

• Demand

– Consumer Theory

– Budget Line (Budget Constraint)

– Utility and Preference

– Indifference Curve

– Marginal Utility, Marginal Rate of Substitution

• Supply– Production function

– Marginal product

– Technical rate of substitution

۵

Consumer Theory

• How Consumers Make Choices under Income

Constraints?

• Two Components of Consumer Demand:

– Opportunities:

• What can the consumer afford?

• What are the consumption possibilities?

• Summarized by the budget constraint

– Preferences:

• What does the consumer like?

• How much does a consumer like a good?

• Summarized by the utility function

٣

۶

The Budget Line (Constraint)

• A budget line describes the limits to consumption

choices and depends on a consumer’s budget and

the prices of goods and services.

• The budget constraint measures the

combinations of purchases that a person can

afford to make with a given amount of monetary

income.

٧

Budget Constraint

• The mathematical expression for budget

constraint is:

I = PW W + PG G

• We refer to the |slope| of the budget line as the

ERS=Economic Rate of Substitution

• In this case it is PW / PG

• For Example: PW=$1, PG=$0.5, I=$4, ERS=2

۴

٨

Budget Constraint

•Figure shows

consumption

possibilities.

•Points A through E on

the graph represent

the rows of the table.

•Price of water = $1

•Price of gum = $0.5

•Income = $4

٩

Budget Constraint

The budget line

separates

combinations that

are affordable from

combinations that

are unaffordable.

۵

١٠

Budget Constraint

Changes in Prices

– Shrinkage of Consumption Possibilities

• If the price of one good rises when the prices of other

goods and the budget remain the same, consumption

possibilities shrink.

– Expansion of Consumption Possibilities

• If the price of one good falls when the prices of other

goods and the budget remain the same, consumption

possibilities can expand.

١١

Budget Constraint

On the initial budget

line, the price of

water is $1 a bottle

(and gum is 50 cents

a pack), as before.

Effect of a fall in the price of water.

۶

١٢

Budget Constraint

When the price of

water falls from $1 a

bottle to 50¢ a bottle,

the budget line

rotates outward and

becomes less steep.

١٣

Budget Constraint

When the price of

water rises from $1 a

bottle to $2 a bottle,

the budget line

rotates inward and

becomes steeper.

٧

١۴

Budget Constraint

• Prices and the Slope of the Budget Line

– You’ve just seen that when the price of one good

changes and the price of the other good remains

the same, the slope of the budget line changes.

– When the price of water falls, the budget line

becomes less steep.

– When the price of water rises, the budget line

becomes steeper.

– Recall that slope equals rise over run.

١۵

Budget Constraint

Let’s calculate the slope of

the initial budget line.

When the price of water is $1

a bottle, the slope of the

budget line is 8 packs of gum

divided by 4 bottles of water,

which equals 2 packs of gum

per bottle.

٨

١۶

Budget Constraint

When the price of water is 50

cents a bottle, the slope of the

budget line is 8 packs of gum

divided by 8 bottles of water,

which equals 1 pack of gum per

bottle.

Calculate the slope of the

budget line when water

costs 50 cents a bottle.

١٧

Budget Constraint

When the price of water is $2, a

bottle, the slope of the budget

line is 8 packs of gum divided by 2

bottles of water, which equals 4

packs of gum per bottle.

Finally, calculate the

slope of the budget line

when water costs $2 a

bottle.

٩

١٨

Budget Constraint

– You can think of the slope of the budget line as an

opportunity cost.

– The slope tells us how many packs of gum a bottle

of water costs.

– Another name for opportunity cost is relative

price, which is the price of one good in terms of

another good = ERS.

– A relative price equals the price of one good

divided by the price of another good, and equals

the slope of the budget line.

١٩

Budget Constraint

• A Change in the Budget

– When a consumer’s budget increases,

consumption possibilities expand.

– When a consumer’s budget decreases,

consumption possibilities shrink.

١٠

٢٠

Budget Constraint

An decrease in the budget

shifts the budget line

leftward.

Effects of changes

in a consumer’s

budget.

The slope of the budget

line doesn’t change

because prices have not

changed.

٢١

Budget Constraint

An increase in the budget

shifts the budget line

rightward.

Again, the slope of the

budget line doesn’t change

because prices have not

changed.

١١

٢٢

Utility

Utility is the benefit or satisfaction that a

person gets from the consumption of a good

or service.

Temperature: An Analogy

The concept of utility helps us make predictions

about consumption choices in much the same

way that the concept of temperature helps us

make predictions about physical phenomenon.

٢٣

Utility Function• Assuming two product x1 and x2 to be bought by a consumer

• A utility function u(xi) is a numerical representation of

consumer preferences.

• Marginal Utility – Change in utility due to a small change in xi.

• Marginal Rate of Substitution – The rate at which a consumer

can substitute good 1 for good 2

2

1

2

1

1

212

i

i

2

2

1

1

p

pERS

MU

MU

dx

dxMRS

x

uMU

0dxx

udx

x

u)x(du

−=

=−=

∂

∂=

=∂

∂+

∂

∂=

١٢

٢۴

Preferences in Indifference Curves

• An indifference curve connects

all the bundles that have the

same utility.

• Higher indifference curves

indicate more utility (IC2 is

preferred to IC1).

• Lower indifference curves

indicate less utility (IC1 is

preferred to IC0).

• The indifference curve map is

FULL of indifference curves.

Li's Indifference Curves

0

5

10

15

20

25

30

0 10 20

Wheat

Ric

e

I2

I1

I0

IC2

IC1

IC0

٢۵

The Marginal Rate of Substitution

• The Marginal Rate of

Substitution(MRS) tells us

how much of one good

would be willingly to trade

for an incremental unit of the

other good and remain

indifferent.

• The MRS=|slope| of the

indifference curve at a

bundle.

• Common to assume the MRS

declines as we move down

an indifference curve.

Li's Indifference Curves

0

5

10

15

20

25

30

0 10 20

Wheat

Ric

e

I2

I1

I0

١٣

٢۶

How Much Wheat and Rice?

• Consumer Problem – Optimal amount of

Product 1 and Product 2 to consume is the

amount that maximizes utility subject to

budget constraint.

• In the graph...

�Get to the highest indifference curve possible

�Stay on the budget constraint

٢٧

How to Find Best Combination

Wheat

Rice

20

10

IC0

IC1

IC2

W*

R*

• The black bundle is best.

• The blue bundle is not

the best. You have spent

all your income but is

not on the highest

indifference curve

possible.

• At (W*, R*) you are

doing the best you can

subject to your budget

constraint.

١۴

٢٨

How to Find the Best Combination

• Utility is maximized when:

– the indifference curve is just tangent to the budget line.


– you are on the budget line and

– the slope of the indifference curve equals the slope of the budget line


– MRS=ERS

٢٩

• Let MUW = marginal utility of wheat

– it measures the change in utility as we change wheat consumption by

an incremental unit while holding rice constant

• Let MUR = marginal utility of rice

– it measures the change in utility as we change rice consumption by an

incremental unit while holding wheat constant

• Common to assume that marginal utilities decline as we

increase consumption - the law of diminishing marginal utility

• The MRS = MUW / MUR

• The ERS = PW / PR

• At an optimal bundle: MRS=ERS

• Rewritten we have:

� MUW / MUR = PW / PR

� MUW/PW = MUR/PR

١۵

٣٠

MARGINAL UTILITY THEORY

٣١


The marginal utility of the

3rd bottle of water = 36

units – 27 units = 9 units.

١۶

٣٢

– Diminishing marginal utility

• We call the general tendency for marginal utility to

decrease as the quantity of a good consumed increases

the principle of diminishing marginal utility.

• Think about your own marginal utility from the things

that you consume.

• The numbers in Table display diminishing marginal

utility.


٣٣


١٧

٣۴

Part (a) graphs total utility from

bottled water.

Figure shows total utility

and marginal utility.


Each bar shows the extra total

utility gains from each additional

bottle of water - marginal utility.

The blue line is total utility curve.

٣۵

Part (b) shows how marginal utility

from bottled water diminishes by

placing the bars shown in part (a)

side by side as a series of declining

steps.

The downward sloping blue line is

marginal utility curve.


١٨

٣۶

٣٧


• Maximizing Total Utility

• The goal of a consumer is to allocate the available

budget in a way that maximizes total utility.

• The consumer achieves this goal by choosing the

point on the budget line at which the sum of the

utilities obtained from all goods is as large as

possible.

١٩

٣٨

Consumer’s Problem

• Consumer tries to maximize utility while satisfying the

budget:

Max. u(x) = u(W, R)

Subject to:

PWW + PRR <=Income (Budget) → PWW + PRR = Income

W, R >=0

٣٩

Best Choice Reconsidered• Consider the choice at PW= PR= $2/lb.

• Budget = I = $40

• The point B is optimal.

• The point A is feasible but inferior to all

points on the red budget line between

E and F.

• The point C is preferred to B but cannot

be purchased with $40 income at the

given prices; it is above the red budget

line.

• The point E is feasible but we prefer

more wheat and less rice (B).

• The point F is feasible but we prefer

less wheat and more rice (B, again).

• There is no combination that prefers to

B

Li's Best Choice of Wheat and Rice

0

5

10

15

20

25

30

0 5 10 15 20Wheat

Ric

e

I2

I1

I0

2

A

E

F

BC

٢٠

۴٠

Handling a change in Pw

• The highest indifference curve that the budget constraints permit.

• The points A, B, and C

represents the best that can

do at prices of $4, $2, and $1

for wheat.

• The equation MRS=ERS is

satisfied at each of the points.

Li's Demand for Wheat

0

5

10

15

20

25

30

0 5 10 15 20

Wheat

Ric

e

I2

I1

I0

4

2

1

CB

A

۴١

Demand for Wheat

• The table shows the

amount of wheat that

demands at each

price.

• These are the points

of tangency from the

previous slide.

Quantity Price Point

6 4 A

10 2 B

16 1 C


٢١

۴٢

Graph of Demand for Wheat

• When we connect the

points from the table in

the previous slide we get

demand for wheat.

• The points A, B, and C

correspond to the

tangencies of the budget

constraint and the

indifference curves.


0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20

Quantity

Pri

ce

A

B

C

۴٣


0

5

10

15

20

25

30

0 5 10 15 20

Wheat

Ric

e

I2

I1

I0

4

2

1

CB

A


0

1

2

3

4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Quantity

Pri

ce

A

B

C

From IC Map to Demand for Wheat

٢٢

۴۴


• Finding the Demand

Curve

– We can use marginal

utility theory to find a

consumer’s demand

curve.

– Figure shows demand

curve for bottled water.

۴۵


When the price of water is $1

a bottle, we buy 2 bottles of

water a day. We are at point A

on our demand curve for

water.

When the price of water falls

to 50¢ , we buy 4 bottles of

water a day and moves to

point B on our demand curve

for bottled water.

٢٣

۴۶

Supply

• Objectives:

�So far, we have studied consumer’s behavior

� In this lecture, we will study the supply side of the

market (firms…)

� It will be easier because many concepts used

when studying the firm have a clear counterpart

in the previous chapters dedicated to the

consumer

۴٧

Utility function Production function

Goods Inputs

Indifference curve Isoquant

Marginal rate of substitution

Marginal rate of technical substitution

Max utility Max profits

Min expenditure Minimize costs

٢۴

۴٨

Production Function

• A firm produces a particular good (y) using

combinations of inputs (xi)

• The most common used inputs are capital (k)

and labor (l)

• One could think in introducing different inputs:

skilled labor, unskilled labor, raw materials,

intermediate products, technology…

۴٩

Production Function

٢۵

۵٠

Production Function

• The firm’s production function for a

particular good (y) shows the maximum

amount of the good that can be produced

using alternative combinations of inputs (for

example, capital (k) and labor (l))

y = f(k,l)

۵١

Marginal Productivity

• (equivalent to marginal utility). The marginal productivity

(also called marginal physical product) is the additional output

that can be produced by employing one more unit of that input

while holding other inputs constant.

• Given by the first derivative of the production function with

respect to the input under consideration

k

yMP capital ofty productivi marginal k

∂

∂==

ll

∂

∂==

yMP labor ofty productivi marginal

٢۶

۵٢

Isoquant Maps

• To illustrate the possible substitution of one

input for another, we use an isoquant map

• An isoquant shows those combinations of k

and l that can produce a given level of

output (y0) (remember… indifference

curves)

f(k,l) = y0

۵٣

Isoquant Maps

l per period

k per period

• Each isoquant represents a different level of output

– output rises as we move northeast

y = 30

y = 20

Increasing production

٢٧

۵۴

Technical Rate of Substitution (TRS)

• The rate of technical substitution (TRS) shows the

rate at which labor can be substituted for capital while

holding output constant along an isoquant (slope of

the isoquant)

0

for

yyd

dkkRTS

=

−=

ll )(

۵۵

TRS and Marginal Productivities

• Take the total differential of the production function:

0dkMPdMPdkk

fd

fdy k =⋅+⋅=⋅

∂

∂+⋅

∂

∂= ll

ll

• Along an isoquant dy= 0, so dkMPdMP k ⋅−=⋅ ll

kyy

lkMP

MP

d

dk)k for ( TRS

0

l

ll =

−=

=

• Rate at which labor can be substituted for capital while

holding output constant along an isoquant

٢٨

۵۶

Firm Problem: to Max. Revenue, R

• Amount of money that a firm receives for selling an

amount of a product for a particular price p.

• Marginal Revenue is the change in revenue for a

change in the output or the quantity sold

dy

dpyp

dy

dp

p

R

y

R

dy

dR

pyR

+=∂

∂+

∂

∂=

=

۵٧

Example: Given a demand

function of the form:

bya)y(p −=

How the revenue is changed if the

quantity sold is reduced by one?

Revenue is given by the quadratic

function

by2ady

dR

:Thus

byaypyR 2

−=

−==

water resources p&m and eng. econ. microeconomics ce...

Documents