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O-Level Singapore/O-Level/Pure Physics Tuition/Physics Tutor

Temperature

1. Temperature (T) is a measure of how hot or cold an object is. It is an indication of the amount of heat energy of an object.

2. The SI unit of temperature is the kelvin (K). However, the degree Celsius (°C) is more commonly used.

3. A thermometric property is a physical property that changes according to temperature. To define a temperature scale, a thermometric property that varies linearly with temperature is used.

4. In the Celsius scale, two fixed points are used: ice point and steam point. They are 0°C and 100°C respectively. Each interval on the thermometer measures 1°C.

5. A thermometer is a device used to measure the temperature of an object.

6. Using a thermometric property that varies linearly with temperature, the value of the unknown temperature T is determined by the following equation:

T = (XT – X0)/(X100 – X0)

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A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

Mathematical Induction

Proof by Induction involves the following steps:

STEP 1: Let Pn be the statement

STEP 2: Prove P1 is true [Note that for some cases,
(By substituting into LHS and RHS of the statement to prove that P1 is true)

STEP 3: Assume Pk is true for a

STEP 4: Prove “ Pk+1 is true also true”

STEP 5: Conclude the proof:
If Pk is true, then Pk+1 is also true
By mathematical induction,Pn is true for x is element Z+

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A-Level Economics Tuition Singapore/H2/H1 Economics Tuition

Date : 3 July 2014

Topic 2.2 Macroeconomic Aims, Problems/Issues, Consequences and Policies

Syllabus

Macroeconomic Problems and their Causes
• Undesirable rates of economic growth
• High inflation rate
• High unemployment rate
• Persistent or large balance of payments deficit

Outcome
• Explain the meaning of undesirable rates of economic growth, high inflation rate, high unemployment rate and persistent or large balance of payments deficit.
• Analyse the causes and consequence of macroeconomic problems.

Macroeconomics Lecture 1 : Undesirable Rates of Economic Growth

1.1 Recap : Economic Growth

Economic Growth is the increase in an economy’s level of real output over time.

Rate of Economic Growth is the percentage increase in national output over a 12-month period.

Aim of governments : High and sustained rates of economic growth.

Reason : To advance the standard of living of the people.

4.2 Recap : Actual Growth Vs Potential Growth

Actual economic growth is the annual percentage increase in national output i.e. the rate of growth in actual output. Published statistics on growth rates (such as that in Table 1) are examples of actual economic growth.

Potential economic growth is the speed at which the economy could grow. It is the annual percentage increase in the capacity (potential) of the economy to produce or develop i.e. the rate of growth in potential output.

Potential economic growth may be achieved by :

• Increase in the quantity of available resources such as labour, land, capital and entrepreneurship.

• Improvement in the quality of the available resources.

Actual and Potential Growth may be illustrated by 2 models :
• PPC
• AD/AS

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A-Level Physics Tuition Singapore/H2 Physics Tuition/JC Physics Tutor

Hi A-level/H2/JC Physics Tuition students

Two types of Error

1) Systematic Error

A systematic error is one that occurs according to some definite pattern. Errors of this type occur according to some fixed rule or pattern such that they yield a consistent over-estimation or underestimation of the true value of the measured quantity.

Sources of Systematic Errors:

(a) Incorrect calibration of an instrument
e.g. bias caused by friction or wear in its moving parts.

(b) Construction faults in the instrument These instrumental faults caused zero errors when the indicator or pointer of the instrument
is not at the ‘zero’ position before the start of a measurement. An example is the off-centre pivoting of the pointer of the ammeter.

(c) Non-constancy of experimental conditions
e.g. change of temperature and pressure which affects the value of the quantity measured and has not been properly taken into account.

(d) Biasness of the observer e.g. tendency of some persons to press a stopwatch a fraction of a second too early or to overestimate or underestimate the fraction of a scale division.

(e) Incorrect experimental procedure or technique
e.g. parallax error that occur due to wrong positioning of the eye when taking readings.

2. Random Error

A random error is one that occurs without a fixed pattern. It has an equal chance of being negative or positive and it causes a set of measurements done under the same conditions to have an equally likely chance of being greater or less than the true value.

Examples of random error:

(a) Random variations in external experimental conditions
e.g. disturbances caused by mechanical vibrations, tremors produced by the wind

(b) Non-constancy of experimental specimen
e.g. non-uniform diameter of cylindrical specimen

(c) Random human error
e.g. misjudgment in the interpolation of the smallest division of the scale of measuring instruments, error due to starting and stopping of a stopwatch in reaction to visual observation

Since random error have an equal probability of being positive or negative, it can be reduced by taking a large number of independent readings of a quantity. Their mean or average is then almost entirely free from random errors and gives the best estimate for the value of the quantity being measured.

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A-Level Biology Tuition Singapore/H2 Biology Tuition/JC Biology Tutor

TOPIC 2: DNA AND GENOMICS – Part 2

LEARNING OUTCOME

(b)Describe the process of DNA replication and the experimental evidence for semi-conservative replication.

ESSAY ANSWER

PROCESS OF DNA REPLICATION

Before DNA replication occurs, free deoxyribonucleotides are synthesized in the cytoplasm and transported into the nucleoplasm via pores in the nuclear envelope. DNA Replication starts at specific sites known as origins of replication. The enzyme helicase causes DNA to unwind at the origin of replication through catalysing the breakage of hydrogen bonds between the complementary bases of the two polynucleotide chains.

This causes the two DNA strands to separate. The separated strands of DNA interact with single stranded binding protein (SSBP). The role of the single stranded binding protein is to stabilize the separated single-stranded so that the unwound region can serve as a template. Each separated strand of DNA can now act as a template for DNA synthesis. The template strand is also known as the parental strand.

At each DNA template, DNA synthesis is initiated by the synthesis of an RNA primer. An RNA primer is a short RNA chain consisting of about ten ribonucleotides. Its sequence is complementary to its corresponding DNA template strand. This RNA primer is needed at the beginning of all new DNA chains because the enzyme responsible for the synthesis and elongation of DNA, DNA Polymerase III, needs a free 3’ OH group to add the new complementary nucleotide. The RNA Primer is synthesized by the enzyme primase. After the RNA primer has been synthesized, DNA
Polymerase III catalyses DNA synthesis and elongation by catalysing the formation of a phosphodiester bond between new deoxyribonucleotides and the last ribonucleotide of the RNA primer.

Elongation of new DNA strands occurs in the 5’ to 3’ direction. Nucleotides are added one by one to the growing end of the new strand by complementary base pairing to the bases of the ‘old’ strand. Complementary base pairing involves the formation of hydrogen bonds between complementary bases (A to T; C to G). Nucleotides are joined
via the hydrolysis of two phosphates from the NTPs. This releases energy to drive the polymerization of the nucleotides. DNA polymerase III selects free deoxyribonucleotides that are complementary to those on the parental strand.

The leading daughter strand is synthesized continuously from the parental strand. The lagging daughter strand is synthesized discontinuously from the parental strand, forming of Okazaki fragments. As DNA Polymerase requires a 3’ OH end to elongate DNA, every Okazaki fragment must be “primed”. Hence, the lagging strand has more
than 1 primer. The primers are later excised, replaced with DNA. This is aided by DNA polymerase I. DNA Ligase catalyses the formation of a phosphodiester bond between two Okazaki fragments. DNA Polymerase I also completes a proof reading function of the newly synthesized strand of DNA.

The two separate strands of DNA winds back into a double helix after DNA
Polymerase I has completed its action.

EXPERIMENTAL EVIDENCE FOR SEMI-CONSERVATIVE REPLICATION

Meselson and Stahl used two different isotopes for nitrogen in their experiments: 14N, the ordinary isotope of nitrogen and15N, the heavy isotope of nitrogen.

In this experiment, Escherichia coli was cultured in a medium that contained nucleotide precursors labeled with heavy isotope 15N, for several generations. Nitrogen (N) is incorporated in the nitrogenous bases of these nucleotides. This causes all DNA in the bacteria to be labeled with 15N. This same group of bacteria was then transferred to medium with only 14N, a lighter isotope.

Two DNA samples were taken from this flask, one at 20 minutes and one at 40 minutes, after the 1st and 2nd replications, respectively Meselson and Stahl could distinguish DNA by their weight/ by centrifuging DNA extracted from the bacteria. DNA containing only 15N is denser (heavier) than DNA containing only 14N. Due to the weight difference, 15N would form a band below 14N in caesium chloride solution. Hybrid DNA (14N-5N),
consisting of one 14N strand and one 15N strand, would form a band halfway between the 14N DNA band and 15N DNA band.

The results from the “First Replication” were a single DNA band was precisely halfway between those of 14N DNA and 15N DNA. Hence, only14N15N DNA was found in these first generation cells. The results from the “Second Replication” were two bands of DNA, one above the other This indicated that half of the DNA molecules were of hybrid type
(14N-15N) and the other half were pure 14N DNA.

Meselson and Stahl compared their results to those predicted by each of the three models in the first replication in the 14N medium produced 1 band of hybrid (14N-15N)DNA. This result eliminated the conservative model. The second replication produced 1 light and 1 hybrid DNA bands, a result that eliminated the dispersive model and supported the semi-conservative model. From these results, Meselson and Stahl concluded that DNA replication is semi-conservative.

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A Level GP/General Paper Tuition Singapore

Use of figurative language

Writers often make use of figurative language or figures of speech in order to convey their meaning more effectively. Figurative language is impactful because it allows a writer to explain abstract ideas by linking them (drawing an analogy) to more concrete, familiar, everyday items. For instance, an abstract concept like life is often described as a journey where there are different paths that a person can take. Similarly, another abstract concept like love is often compared to roses.

So, figurative language comprises of two parts: (1) the abstract idea that the writer intends to describe, and (2) the more concrete meaning of the word/phrase in context. Figurative language can take many forms, including metaphors, similes and idioms (this list is not exhaustive). In P2, answers to questions involving the use of figurative language require first an explanation of the analogy, followed by an explanation of how the abstract idea is related to or linked to it. The two parts should not be described or elaborated using the exact same words because that means the meaning of the metaphor has not been fully contextualized or explained

Example 1

1. Like the rings embedded within a tree’s trunk which one can only see by slicing the trunk open, it’s only by dissecting the concept of tolerance that one becomes aware of the magnitude of meanings nestled within it. (lines 13-15)

Explain why the author compares ‘the concept of tolerance’ to ‘a tree trunk’.

a) A tree trunk, despite appearing as a solid whole, actually contains patterns and layers only visible when it is cut open.
Key Idea: Additional information about the tree can be obtained when it is sliced open
b) Similarly, tolerance as a concept appears simple and uncomplicated but upon closer examination is revealed to be complex and nuanced.
Key Idea: Explain the complexity present in Tolerance

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A-Level Chemistry Tuition Singapore/H2 Chemistry Tuition/JC Chemistry Tutor

Trends in First Ionisation Energies

(A) Across a period of the Periodic Table, the ionisation energies generally increase.

Reason:
• Nuclear charge increases as the proton number increases.
• Successive members of the period has one electron added to the same outermost shell, thus, the increase in screening effect is negligible.
• Effective nuclear charge increases.
• More energy is required to remove the more tightly held electrons, hence ionisation energy generally increases.

(B) Down a group of the Periodic Table, the ionisation energies generally decrease.

Reason:
• Nuclear charge increases as proton number increases.
• Electrons are added to a higher principal quantum shell which is further away from nucleus.
• Weaker electrostatic forces of attraction between the nucleus and valence electrons.
• Less energy is required to remove the valence electrons, hence ionisation energy generally decreases

(C)TRENDS IN THE ATOMIC RADIUS OF ELEMENTS

Across a period,
• nuclear charge increases
• shielding effect is relatively constant (number of inner core electrons is the same across a period)
• effective nuclear charge increases, resulting in electrons being pulled closer towards the nucleus
• atomic radius generally decreases.

Down a group,
• nuclear charge increases
• electrons are added to a higher principal quantum shall
• valence electrons are increasingly further away from the nucleus
• weaker electrostatic forces of attraction between valence electrons and nucleus
• atomic radius generally increases.

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O-Level Additional Mathematics Tuition Singapore

Quadratic Inequalities

1. A quadratic expression is an expression of the form ax^2 + bx + c, where a, b and c are constants and a # 0.
For example: 4x^2 — 2x + 1

2. A quadratic function is a function with rule being a quadratic expression. For example: y = x^2 — 3x + 1 or f(x) = x^2 — 3x + 1

3. A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b and c are constants and a # 0.
For example: 2x^2 + 5x — 10 = 0

4. A quadratic inequality is an inequality that can be expressed in one variable on one side and zero on the other such that
ax^2 + bx + c < 0, where a, b and c are constants and a # 0.

For example: 4x^2 — 2x + 1 < 0 and (x — 1)(x + 3)< 0

5. Steps to solve a quadratic inequality:
(a) Make the right-hand side (RHS) of the inequality zero by bringing all the terms to the left-hand side (LHS).
(b) Factorise the expression on the LHS.
(c) Use one of the following methods to find the solution.
(i) Sketch the quadratic curve, OR
(ii) Use the sign test

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O Level E Maths Tuition Singapore/Tuition O Level E Maths/Tutor

Substitution into Algebraic Expressions

If a = 2, b=5, c = -3, find the value of each of the following:
i. a^2 + b^3 – 2c^3
ii. (2a – b + 4c) (2b – c^2)

Solution i

a^2 + b^3 – 2c^3
= 2^2 + 5^3- 2(-3)^3
= 4 + 125 – 2(-27)
= 183

Solution ii

(2a – b + 4c) (2b – c^2)
= [(2 x 2) – 5 + 4 (- 3)] [2 x 5 – (-3) (-3)]
= (4 – 5 – 12) (10 – 9)
= (-13 ) (1)
= -13

Solving Linear Equations in One Unknown

To solve an equation, we can add or subtract the same number to each side.

We can also multiply or divide each side by the same number.

Example 1 :
a — 6 = 7
(a— 6)+6 = 7+ 6
Hence, a = 13

Example 2 :
a+ 3 = 16
(a+ 3)— 3 = 16 —3
a = 13

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O-Level Singapore/O-Level/Pure Physics Tuition/Physics Tutor

Pressure

1. Pressure p is the force F acting on a surface divided by the area A of the surface.

P = F/A

2. The SI unit of pressure is pascal (Pa) or newton per square metre (N m-2).

3. Pressure p at a certain depth h of a liquid with density p under the influence of gravitational field strength g is given by the following relationship:

p = hpg

4. According to Pascal’s Principle, an extra pressure applied at any part of a body of liquid will be experienced throughout the liquid. In a hydraulic press, an extra pressure applied at one end will be experienced by the other end.

5. According to the Principle of Conservation of Energy, the work done at one end of a hydraulic press is equal to the work done at the other end.

Fx x dx= Fy x dy
(where F is the force applied on/by the piston d is the distance moved by the piston)

6. Atmospheric pressure is exerted due to the weight of the atmosphere. Its average value at sea level is 1.013 x 10^5 Pa.

7. The barometer is a simple device used to measure atmospheric pressure. The height of liquid level in the vacuum-filled tube increases if the atmospheric pressure increases

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O-Level Singapore/O-Level/Physics and Chemistry Tuition/Physics Tutor

EXPERIMENTAL CHEMISTRY – Do you Know?

Use of distillation

To obtain pure water from sea water

The porcelain boiling stones are used to smoothen the boiling.
The first few drops of liquid are discarded to make sure that any possible impure liquid that may have a boiling point slightly lower than that of the required liquid is not collected.
The running tap must not be turned off before the flame is extinguished to avoid breakage of the condenser if overheated.
The thermometer shows a constant temperature during the distillation process when pure solvent is being collected at the boiling point of the solvent.

Fractional distillation

Separation of a mixture of miscible liquids with different boiling points can be done through fractional distillation.

Uses of fractional distillation

1. Separation of liquid air into oxygen, nitrogen and other useful gases.
2. Separation of crude oil into petrol, kerosene and other useful components of crude oil.
3, Separation of femented liquor into ethanol and water

Do you Know?
The pure liquid that has the lowest boiling point will distil off first. This is because the glass beads in the fractionating column condense the liquids with the higher boiling points back into the flask, allowing the pure liquid with the lowest boiling point to vapourise and distil off as the first distillate

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O Level Chemistry Tuition Singapore/Chemistry O Level Tuition/Tutor

O Level Chemistry Tuition Singapore/Chemistry O Level Tuition/Tutor

EXPERIMENTAL CHEMISTRY – Do you Know?

Use of distillation

To obtain pure water from sea water

The porcelain boiling stones are used to smoothen the boiling.
The first few drops of liquid are discarded to make sure that any possible impure liquid that may have a boiling point slightly lower than that of the required liquid is not collected.
The running tap must not be turned off before the flame is extinguished to avoid breakage of the condenser if overheated.
The thermometer shows a constant temperature during the distillation process when pure solvent is being collected at the boiling point of the solvent.

Fractional distillation

Separation of a mixture of miscible liquids with different boiling points can be done through fractional distillation.

Uses of fractional distillation

1. Separation of liquid air into oxygen, nitrogen and other useful gases.
2. Separation of crude oil into petrol, kerosene and other useful components of crude oil.
3, Separation of femented liquor into ethanol and water

Do you Know?
The pure liquid that has the lowest boiling point will distil off first. This is because the glass beads in the fractionating column condense the liquids with the higher boiling points back into the flask, allowing the pure liquid with the lowest boiling point to vapourise and distil off as the first distillate

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O-Level Singapore/O-Level/Pure Physics Tuition/Physics Tutor

Pressure

1. Pressure p is the force F acting on a surface divided by the area A of the surface.

P = F/A

2. The SI unit of pressure is pascal (Pa) or newton per square metre (N m-2).

3. Pressure p at a certain depth h of a liquid with density p under the influence of gravitational field strength g is given by the following relationship:

p = hpg

4. According to Pascal’s Principle, an extra pressure applied at any part of a body of liquid will be experienced throughout the liquid. In a hydraulic press, an extra pressure applied at one end will be experienced by the other end.

5. According to the Principle of Conservation of Energy, the work done at one end of a hydraulic press is equal to the work done at the other end.

Fx x dx= Fy x dy
(where F is the force applied on/by the piston d is the distance moved by the piston)

6. Atmospheric pressure is exerted due to the weight of the atmosphere. Its average value at sea level is 1.013 x 10^5 Pa.

7. The barometer is a simple device used to measure atmospheric pressure. The height of liquid level in the vacuum-filled tube increases if the atmospheric pressure increases

If you need help in the above topics, please contact Angie @96790479 or Mr Ong @98639633

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A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

Hi A-Level/H2 Math Students

Graphing Techniques & Curve Sketching

1. y = f(x) —> f(x + a)

Translation
The graph of y = f (x) is translated -a units parallel to the x-axis.

2. y = f(x) —> f(x – a)

Translation
Translation The graph of y = f (x) is translated a units parallel to the y-axis.

3. y = f(x)—> f(ax)

Scaling
The graph of y = f(x) is scaled 1/a units parallel to the x-axis.

3. y = f(x)—> af(x)

Scaling
The graph of y = f(x) is scaled a units parallel to the y-axis.

4. y = f(x) —>f(ax+b)

Translation then scaling
The graph of y = f (x) is translated -b units parallel to the x-axis and then scaled 1/a units parallel to the x-axis.

5. y = f(x) —> af(x) + b

Scaling then translation
The graph of y = f (x) is scaled a units parallel to the y-axis and then
translated b units parallel to the y-axis.

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A-Level Economics Tuition Singapore/H2/H1 Economics Tuition

Lesson Plan for JC1 H1/H2 on 24th May 2014

Market Failure Part 1

1. Introduction and Definitions

a) Market failure: A situation where resource allocation concerning what, how, for whom and how much to produce based on the market mechanism fails to achieve efficiency or equity among various income groups or both.

b) Partial Market Failure: Describes a situation whereby resource allocation through market forces alone results in a level of production that is less than or more than that which is deemed socially desirable

c) Complete Market Failure: Describes a situation whereby resource allocation through market forces alone results in zero production of the good or service.

d) Concept Map to Link (a) to (c)

e) Economic efficiency is achieved when society has already allocated resources in such a way that it is not possible to change the existing resource allocation to make someone better off without making someone else worse off. When economic efficiency is achieved, we say that society’s welfare has been maximized.

f) To achieve economic efficiency, society needs to achieve allocative and productive efficiency.

g) Allocative efficiency is achieved when the right amount of goods and
services are produced from society’s point of view. There is no under or over production. This is achieved when a firm produces a level of output up to the point where Marginal Social Benefit (MSB) gained on the last unit by society equals to the Marginal Social Cost (MSC) of producing that last unit of output.

In other words, MSB = MSC

h) MSB is the total benefits to society as a result of the consumption of an additional unit of good. MSB is the summation of marginal private benefit (MPB) and marginal external benefit (MEB).

i) MSC is the total costs to society as a result of the consumption or production of an additional unit of good. MSC is the summation of marginal private cost (MPC) and marginal external cost (MEC).

j) Concept Map and Equation for linking (g) to (i)

k) Demand and supply diagram to illustrate allocative efficiency.

l) Underproduction (MSB > MSC)

m) Overproduction (MSB < MSC)

n) Productive efficiency is achieved when all the firms in all industries use the least-cost or best combination of inputs to produce a given level of output. At any given level of output, the average cost of production cannot be lowered any further in the long run. This implies there is no wastage of resources. In order to achieve this, a firm must produce along any point on the LRAC.

o) Concept map to link everything.

p) Why do markets fail?

i. The price mechanism is based on self-interest of consumers and
profit motive of producers.

2. Types/Causes/Forms of Market Failures

a) Partial Market Failure due to negative externality in production
i. Definition of externality

Externality is a third party effect on someone not directly involved in
production and/or consumption of a good/service. These third parties
are not compensated for the damages inflicted on them.

ii. Definition of negative externality

Negative externality is a third party cost or adverse effect on
someone not directly involved the production and/or consumption of
a good/service. These third parties are not compensated for the
damages inflicted on them.

iii. Example of negative externality

 Release of toxic materials from a factory upstream into the
river. This results in a decrease of catch by downstream
fisherman and hence the income of these fisherman. iv. Important Concepts for discussing negative externality
 MSC
 MPC = Costs that firm incurs in producing an additional unit of
output. Examples include wages, rental, and cost of raw
materials and implicit costs.
 MEC = Costs incurred by third parties and not compensated
from an additional unit of output.
 Equation

v. Intuitive Ideas and Story Based Discussion

 To begin with let us consider the producer side.
 In a free market without government, a producer pursues his
self-interest of maximizing profits.
 Thus he only takes into account his private costs.
 Suppose the firm produces chemical products. The private
cost in this case would comprise the cost of labour, raw
materials and capital equipment for producing the chemicals.
 Next, let us move on to consumer side.
 A consumer is willing and able to pay only on the basis of the
satisfaction he can obtain from the chemicals. This satisfaction
is the private benefit he derives from the consumption of the
good.
 In a free market without government, the producer will
manufacture chemicals up to the point where his profits are
maximized and may pollute the environment.
 The pollution will then give rise to third party costs known as
external cost or negative externalities. The example of these
external costs can manifest in the form of negative health
effects and the medical bills incurred. Most importantly, these
costs are not reflected in the financial accounting record of
the firm.
 Thus the true cost or social cost or total cost of the production
is underestimated.
 If the social cost is underestimated, that means from a
society’s point of view, resource allocation alone will result in
overproduction of the chemical.
 Overproduction violates the concept of allocative efficiency,
and this in turn violates the concept of efficiency and thus
causes market failure.  In short, social welfare is not maximized or there is welfare loss.

vi. Putting everything into a graph (COPY ON ROUGH PAPER PLEASE!)
 Graph with correct labels and annotations
 Assumptions
 No positive externality
 Firms operate in perfect markets with no government intervention
 Keywords
 Divergence
 Private equilibrium
 Social Equilibrium
 Overproduction
 Allocative inefficiency
 Total deadweight loss
 Market Failure

vii. Government Policies to correct negative externalities
 Taxes
 Policy Statement = Government could impose a tax on
production that is equal to the marginal external cost at
the last unit of output determined by MPB = MPC.
 Impact on graphs
 Analysis Keyword = internalize the external cost
 Examples = Road taxes pegged to engine capacity to
encourage the use of fuel efficient vehicles.
 Merits and Limitations
 Market forces are allowed to operate and consumer
sovereignty is protected
 Incentive to reduce pollution
 Incidence of tax and price elasticity
 Production levels and price elasticity
 Lack of knowledge on damages from pollution
 Manpower costs to assess collect and enforce the tax.

TO BE CONTUNUED NEXT LESSON!
 Rules and Regulation
 Tradeable Pollution Permits

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