LESSON 1 (Refer to TUT101 for assessment guidelines)
Benchmark model of resource allocation: positive
and normative approaches
INTRODUCTION
Public economics should be the concern of all South Africans, rich or poor because it will
influence everyone's economic position in one way or another. Rich people may be more
concerned with the rates of personal income tax, company tax and capital gains tax and what
they will get in return for their taxes, while poor people, on the other hand, maybe far more
interested in the increases in grants (e.g. social pensions and child support) or expenditure on
health, housing and education.
Public economics focuses on the government's role in a market economy (refer to chapter 1 in
the textbook, Calitz, Siebrits and Steenekamp or CSS). Will governmentʼs involvement in the
economy promote efficiency, equity and economic growth? To be able to analyse the
government's actions we need economic tools to determine whether such actions will promote
efficiency and equity. In this lesson, the focus falls on the benchmark model, which is a very
valuable tool to determine whether the actions of the government will promote efficiency or
inefficiency.
In life, we tend to look at matters in relative terms. We know someone is tall because someone
else is short, and person A is rich relative to person B who is poor – we are making
comparisons. In economics, we also think in relative terms, for example, when prices are
studied. We know that the price of diamonds is high because in comparison the price of
doughnuts is low. This relationship is often expressed as a ratio Pdiamonds/Pdoughnuts. When we
compare things and view matters in relative terms, we are benchmarking.
You will recall from your first-year Economics that we aim to study the economic problem
(scarcity and unlimited wants) and to find solutions to this problem. Several possible economic
systems attempt to solve this problem. The second chapter of the textbook mainly explains and
illustrates how the perfectly competitive market system solves the economic problem in a
(Pareto) efficient manner. The perfectly competitive market (or neoclassical general
equilibrium model) with its very restrictive assumptions is our benchmark economic system
(or model). Make sure that you understand this well because we are going to use this tool
repeatedly in subsequent chapters to determine whether government intervention promotes
allocative efficiency or not.
After you have studied this lesson (and the prescribed sections in chapter 2 in CSS), you will
have a better understanding of how to use a neoclassical general equilibrium model as a
benchmark to evaluate the role of government in the economy. You should, therefore, be able
to:
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Open Rubric
explain the basic assumptions of the benchmark model
explain the benchmark model and allocative efficiency
define a Pareto optimal allocation of resources
define X-efficiency and its relationship with economic growth
provide an overview of market failure
distinguish between broad approaches to rectify market failures
distinguish between direct and indirect government intervention
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explain government failure
CONTENTS
1.1
Assumptions of the benchmark model
When we study public economics, a logical beginning is to consider the role of government in
the economy. Surely, if we cannot identify a role for government there should be no need to
study public economics! A highly theoretical economic model is used as a starting point,
namely the “benchmark model”, which shows how a perfectly competitive economic system
will ensure allocative efficiency. If we can prove that this system cannot solve some of the
economic issues without the help of government, we have set the scene for studying
government from an economics perspective.
If you recall the microeconomics you have studied at the second-year level, we now continue
where you left off. To retrace our steps we begin with the assumptions of the perfectly
competitive model (see box 2.1 of CSS).
1.2
The benchmark model and allocative efficiency
In section 2.2 of CSS, it is shown that in a perfectly competitive economy allocative efficiency
will occur if three conditions hold, namely equilibrium in production, equilibrium in
consumption and simultaneous equilibrium for producers and consumers. Once you have
studied section 2.2 you should be able to define Pareto optimality and discuss the conditions
for allocative efficiency with the aid of equations [2.4], [2.5] and [2.6] as well as figure 2.4.
Note that the condition for simultaneous equilibrium MRPTxy = MCx/MCy = Px/Py = MRSaxy =
MRSbxy (equation [2.6] will reoccur in later chapters (eg when we discuss the efficiency of a
tax). A good understanding of these conditions is, therefore, essential for grasping important
issues in later chapters. First, consider Condition 1.
Condition 1 refers to efficiency in production and can be summarised as follows:
•
It is a situation where it is impossible to increase the production of one commodity without
thereby decreasing the production of another commodity.
Under perfect competition, each firm (or sector) will try to maximise output (reach the highest
possible isoquant in figure 2.2) and minimise costs (reach the lowest possible isocost curve in
figure 2.2). Equilibrium is only possible when firms face the same equilibrium factor prices (=
(wage (w))/(implicit rental value of capital (r))). This occurs where the isoquants are tangent
such as point f in figure 2.2. At this point labour and capital are used Pareto optimally –
production of good X cannot be increased by reallocating labour or capital without reducing
the production of good Y. There are many such points and when these points are linked a
contact curve is obtained.
The contract curve can be used to derive the familiar production possibility curve (PPC). The
slope of the tangent to the PPC measures the marginal rate of product transformation (MRPT).
The slope of PPC also measures the marginal cost of producing one good (X) relative to
producing the other good (Y) and can be expressed as a ratio (MCx/MCy). Therefore, at all
points on the PPC the following condition holds:
MRPTxy = MCx/MCy
Under perfect competition, good X is produced where the MCx = Px and good Y is produced
where MCy = Py. Because the MRPT is equal to the marginal cost ratio it follows that
MRPTxy = MCx/MCy = Px/Py (see equation [2.5] in CSS).
Condition 2 refers to efficiency in consumption (or exchange) and can be summarised as
follows:
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It is a situation where it is impossible to increase the utility of one consumer without thereby
reducing the utility of another consumer.
Under perfect competition, consumers will maximise utility (reach the highest indifference
curve in the figure below) subject to his/her preferences and budget constraint (or budget line
in the figure below).
Note: The figure below is simply a reproduction of the Edgeworth-Bowley box diagram drawn
inside the PPC of figure 2.4 in CSS. Note the differences between this figure and figure 2.2. In
the diagram below the consumption of good X and good Y by two individuals (a and b) are
represented in the diagram, that is, consumer equilibrium. Utility functions (indifference
curves) and budget lines are plotted inside the box diagram. In contrast, figure 2.2 represents
the production by two suppliers combining capital and labour to produce two goods X and Y,
that is, production equilibrium. Isoquants (or equal output curves) and equal-cost curves
(isocost curves) are plotted inside the box diagram.
Consumers face the same relative price ratio (Px/Py). If the price ratio differs between
consumers they can increase utility through the exchange. For example, at point Z the price
ratios differ and by exchanging/bargaining consumer (a) can reach a higher indifference curve
Ua without reducing the utility of person (b) (who remains on indifference curve Ub3) until
point F' is reached. Equilibrium occurs where the budget line (or price line vv') is tangent to
the indifference curves at a point such as F'. At this point, consumption is Pareto efficient since
one person (a) cannot be made better off through exchange (trade) without making the other
person (b) worse off. Again there are many such points and by linking these points we obtain
a contract curve for consumption.
The slope of the budget (price) line at point F' is equal to the relative price ratio Px/Py and the
slope of the tangent to the indifference curves at point F' is equal to the marginal rates of
substitution, that is, MRSaxy = MRSbxy. Because the slope of the budget line and the slope of
the tangent to the indifference curves are equal it implies that
MRSaxy = Px/Py = MRSbxy (see equation [2.6] in CSS)
0b
Good Y
v
Ub3
Z
F'
Ua3
Ua1
Ua2
v'
0a
Good X
Condition 3 requires that consumption and production equilibrium are achieved simultaneously
to ensure efficiency in the output mix (or market efficiency). We can summarise market
efficiency (or the top-level equilibrium) as follows:
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•
•
•
In a competitive market,
producers will maximise profits where MRPTxy = MCx/MCy = Px/Py
consumers will use their budgets so that MRSaxy = Px/Py = MRSbxy
the equilibrium price Px/Py is the same for producers and consumers (i.e. the relative price
ratio is the common denominator in both equilibrium conditions) and therefore
MRPTxy = MCx/MCy = Px/Py = MRSaxy = MRSbxy (see equation [2.6] in CSS)
Assume that the market produces the combination F on the PPC in figure 2.4. The indifference
curves of the two consumers are drawn within the dimensions of the box – we insert the
Edgeworth-Bowley box diagram above within the PPC and obtain figure 2.4 (reproduced
below). If the top-level equilibrium condition is to be met, the slopes of vv' and tt' must be the
same, that is, the lines must be parallel. If the lines are not parallel it means that the price ratios
for consumption and production differ implying Pareto inefficiency. It would then be desirable
to increase the output of one product and/or reduce that of the other until the two ratios are the
same again. At a point such as B in the diagram below we notice that line kk' is not parallel to
tt' or the MRSxy differs from the MRPTxy. By producing more of good X and less of good Y
a Pareto efficient output mix can be obtained.
M
Good Y
t
Y2
F = 0b
v
k
t'
Ub3
Z
B
F'
Ua3
k'
Ua1
Ua2
N
0a
v'
X2
Good X
ACTIVITY 1
State the equilibrium conditions for Pareto efficiency using mathematical equations. Outline
the three conditions for a top-level general equilibrium with the aid of diagrams and explain
why it represents a Pareto-optimal allocation of resources. Use a diagram to illustrate
simultaneous equilibrium. How would the initial distribution of income impact on the
equilibrium?
For an explanation of this activity, see video clip 1, 2 and 3.
1.3
X-efficiency and economic growth
X-inefficiency (or technical inefficiency) means that firms are not maximising profit or factors
of production (labour and capital) are not maximising their welfare. A position inside the PPC
such as R in figure 2.5 is indicative of X-inefficiency. Non-maximising behaviour is found
under conditions of monopoly (see chapter 4) and may occur in some developing countries
where lack of market information and organisational slack lead to economies not reaching their
full potential (producing on the PPC). Economic growth (dynamic efficiency) can be illustrated
as an outward shift of the PPC. Note the causes of economic growth in section 2.3 (CSS).
1.4
Market failure: An overview
In section 2.4 you will find a summary of different market failures, which are discussed in
much more detail in later chapters. These failures relate to the non-applicability of some of the
assumptions of perfect competition noted in section 2.1 of the textbook. This implies that under
certain circumstances the perfectly competitive economic system will not ensure allocative
efficiency in the real world. Market failure allows for government intervention and, thus, a role
for government in a market economy.
1.5
Enter the public sector: General approaches
In this section and the next section, you will see that the role of government is viewed from
two sides. The one approach is to consider the possible functions of government. Another
approach is to consider the nature of government intervention (this is done in sec 2.6).
Generally, a distinction is made between three functions: allocative, distributive and
stabilisation. Make sure that you understand what each of these functions entails. Note,
however, that the descriptions of these topics in this section are mere introductions to what
follows in later chapters. This section nevertheless provides a concise summary of the
government's possible role in the economy.
1.6
Direct versus indirect government intervention
The second approach to the role of government is to look at government intervention. Two
types of interventions can be distinguished: direct (e.g. producing goods and services) and
indirect (e.g. regulations). Note that since it is difficult, if not impossible, to quantify the
resource use of indirect interventions, the true size of government may be underestimated.
1.7
Concluding note on government failure
The final section of this chapter ponders an important caveat. Although markets fail, the
government in its attempts to correct the shortcomings of the market may also fail. This may
imply that instead of promoting efficiency government may contribute to inefficiency.
LOOKING BACK
Now that you have worked through this lesson you must be able to explain which conditions
must prevail for a perfectly competitive market to ensure an efficient allocation of resources.
However, you also became aware that market failure, as well as a government failure, may
occur. In the following lessons, you will learn how we use benchmark tools to analyse some of
the budget proposals of the Minister of Finance.