Resumen completo (2017)
Apunte InglésUniversidad  Universidad Pompeu Fabra (UPF) 
Grado  International Business Economics  1º curso 
Asignatura  Microeconomics I 
Año del apunte  2017 
Páginas  30 
Fecha de subida  08/10/2017 
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Subido por  lnavarrete 
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PART 1: CONSUMER CHOICE AND DEMAND
TOPIC 1. THE ELEMENTS OF THE PROBLEM
1.1. THE REASON FOR CHOICE: PREFERENCES
INTRODUCTION
The consumer theory states that people choose the best things (preferences) they can afford (budget
constraint). For this we assume that consumers know what they prefer, the they can rank consumption
bundles. We call the objects of consumer choice consumption bundles; complete list of the goods and
services involved in the choice problem.
The word complete deserves emphasis: when you analyse a consumer’s choice problem, make sure that
you include all of the appropriate goods in the definition of the consumption bundle. If we are analysing
consumer choice at the broadest level, we would want not only a complete list of the goods that a
consumer might consume, but also a description of when, where, and under what circumstances they
would become available. Notice we don’t value the same 10$ today and 10$ tomorrow, an umbrella in a
sunny day or in a rainy day, two apples / 1 DVD / 2 weeks of vacation in Menorca…
PREFERENCE RELATION
Given two consumption bundles (X1, X2) and (Y1, Y2), the consumer can rank them as to their desirability:
Strictly preferred: in the sense that she definitely wants the xbundle rather than the ybundle. (>,<)
Indifference: means that the consumer would be just as satisfied, according to her own preference,
consuming xbundle as she would be consuming the ybundle. (~)
Weakly prefers: if the consumer prefers or is indifferent between the two bundles. (~<)
RATIONAL PREFERENCES
Complete: we assume that two bundles can be compared. It’s hardly objectionable, at least for the kinds of
choices economists generally examine. It’s simply to say that the consumer is able to make a choice
between any two given bundles: one might imagine extreme situations involving life or death choices.
Reflexive: we assume that any bundle is at least as good as itself.
Transitive: if the consumer thinks that X is at least as good as Y and that Y is at least as good as Z, then the
consumer thinks that X is at least as good as Z.
INDIFFERENCE CURVES
An indifference curve is the line through (X1, X2) consisting of all bundle of goods that leave the consumer
indifferent to (X1,X2). With rational preferences, indifference curves representing distinct levels of
preference cannot cross.
The general procedure for drawing indifference curves: we consider a bundle (X1,X2), for a given change in
the amount off good 1 (increment X1), how does the amount of good 2 have to change (increment X2) to
make the consumer just indifferent between (X1 + increment X1, X2 + increment X2) and (X1,X2) ?
PERFECT SUBSTITUTES
Two goods are perfect substitutes if the consumer is willing to
substitute one goods for the other at a constant rate. Suppose, for
example, that we are considering a choice between red pencils
and blue pencils. The consumer only cares about the total number
of pencils, not about their colours. Thus the indifference curves
are straight lines with a slope of 1; if for example, we start at (10,10) in order to me give up one blue pen
you have to give one black pen more (11,9). That’s why they have a constant slope.
PERFECT COMPLEMENTS
Two goods are perfect complements if they are always consumed
together in fixed proportions. For instance, the right shoes and
left shoes. Having only one out of a pair of shoes doesn’t do the
consumer a bit of good. Thus, the indifference curves are Lshaped. Suppose we pick the consumption bundle (10,10). Now
add 1 more right shoe, so we have (11,10). By assumption this
leaves the consumer indifferent.
BADS
A bad is a commodity that the consumer doesn’t like. For
instance the amount of light and noise in an apartment. The
direction of increasing preference is down and to the right –
that is, toward the direction of decreased noise and increased
light. Thus, the slope is positive, in order to give up one unit of
light I have to have one less unit of noise.
NEUTRALS
A good is a neutral good if the consumer doesn’t care about it. For example, I don’t care about X2 (school
district, since I don’t have kids). Therefore, if I change the amount
of good X2, in order to me to be indifferent X1 has to be the same
amount. Consequently, the general shape is a vertical line, if X2 is
the neutral. The more X1 the better, but adding X2 doesn’t affect
the consumer one way or the other.
SATIATION
We sometimes want to consider a situation involving
satiation, where there is some overall best bundle for the
consumer, and the closer he is to that best bundle, the
better off he is in terms of his own preferences. An example
would be with icecream and cake. Suppose that the
consumer has some most preferred bundle of goods
(X1,X2) and the farther away he is from that bundle, the worse off he is. In this case we say that (X1,X2) is
a satiation point or a bliss point. In this case the indifference curves have a negative slope when the
consumer has “too little” or “too much” of both goods, and a positive slope when he has “too much” of
one of the goods. When he has too much of one of the goods, it becomes a bad – reducing the consumption
of the bad good moves him closer to his “bliss point”. If he has too much of both goods, they both are bads,
so reducing the consumption of each moves him closer to the bliss point.
WELLBEHAVED PREFERENCES
A wellbehaved preference involves monotonicity and convexity.
First, we will typically assume that more is better, that is, that we are
talking about goods, not bads. Monotonicity means that a bundle that has
more quantity is preferable. This implies that they have a negative slope.
For instance: A = 8 apples, 5 peers ; B = 5 apples, 5 peers ; C = 10 apples,
4 peers. We know that A>B, but we don’t know if A?C.
Secondly, we assume that the set of bundles weakly preferred to
(X1,X2) is a convex set. Convexity implies that averages are better
than extremes. Strictly convexity means that the weighted average
bundle is strictly preferred to the two extreme bundles.
MARGINAL RATE OF SUBSITITUTION
The slope of the indifference curve is the marginal rate of
substitution = ΔX2 / ΔX1 = it’s the rate at which consumer is just
willing to substitute on good for the other. For the monocity
behavior MRS is usually negative when the consumer likes both
goods, since reducing the consumption of one good implies getting
more of another for. It will not be negative if there were bads or
neutrals. For convex indifference curves the MRS decreases in absolute terms as X1 increases: diminishing
marginal rate of substitution. This means that the amount of good 1 that the person is willing to give up for
an additional amount of good 2 increases as the amount of good 1 increases. Stated in this way, convexity
of indifference curves seems very natural: it says that the more you have of one good, the more willing you
are to give some of it up in exchange for the other good.
EXAMPLES
1.2. REPRESENTATION OF PREFERENCES: UTILITY
The utility is a way to describe the preferences of consumers. All that mattered about utility as far as choice
behaviour was concerned was whether one bundle had a higher utility than another – how much higher
didn’t really matter. A utility function assigns numbers to bundles such that morepreferred bundles are
assigned higher numbers than lesspreferred bundles.
ORDINAL UTILITY
The ordinal utility is the term used to emphasize that the only important thing of utility assignment is how
it orders the bundles of goods, the magnitudes of utility function is only important insofar as it ranks the
different consumption bundles; the size of the utility difference between any two consumption bundles
doesn’t matter. Therefore, there are different ways to assign utilities:
Since only the ranking of the bundles matters, there can be no
unique way to assign utilities to bundles of goods. What
matters is the ordering of utilities not the absolute value. U2
and U3 are monotonic transformations, is a way of
transforming one set of numbers into another set of numbers in a way that preserves the order of the
numbers. Multiplying by 1 is not an example of monotonic transformation since it doesn’t preserve the
order. Thus, a monotonic function always has a positive rate of change = positive slope = increasing
function. We can say that a utility function is a way to label indifference curves. Since every bundle on an
indifference curve must have the same utility, a utility function is a way of assigning numbers to the
different indifference curves in a way that higher indifference curves get assigned larger numbers. Seen
form this point of view a monotonic transformation is just a relabelling of indifference curves.
Example: Consumer 1, 2 and 6 have A > B > C.
Consumer 3 and 5 have A ~ B > C.
Consumer 4 has A ~ B ~ C
CONSTRUCTIING A UTILITY FUNCTION
To construct some other example we only have to equal the
utility function to a number k and that will be our indifference
curve. For instance: X1X2 = k. And X1^2*X2^2 is a monotonic
function of the first one so the ordering is the same, the
indifference curve is the same, the only thing changed is that
k is now k^2.
PERFECT SUBSTITUTES
The case of the red and blue pencil. All that mattered to the consumers was the total number of pencils.
Therefore the utility function could be X1 + X2 or any other monotonic transformation: (X1 + X2)^2. In
general, preference for perfect substitutes can be represented by a utility function of the form aX1 + bX2,
being a and b positive values. The slope of the typically indifference curve is given by a/b.
PERFECT COMPLEMENTS
The left shoe and the right shoe case. In these preferences, the consumer only cares about the number of
pairs of shoes he has, so it’s natural to choose the number of pairs of shoes as the utility function. Thus,
the utility function for perfect complements takes the form min (a*X1, b*X2), where a and b are positive
numbers that indicate the proportions in which the goods are consumed.
QUASILINEAR PREFERENCES
The general equation for an indifference curve takes the
form X2 = u – f(X1), where u is a different constant for each
indifference curve. This equation says that the height of each
indifference curve is some function of X1 plus a constant k.
COBBDOUGLAS PREFERENCES
The general equation is X1^c * X2^d, where c and d
are positive numbers. CobbDouglas indifference
curves look just like the nice convex monotonic
indifference curves that we referred to as “wellbehaves indifference curves”. Another example could
be ln(A*X1^c*X2^d) = clnX1 + dlnx2. The indifference
curves for this utility function will look just like the
ones for the first CobbDouglas function, since the
logarithm is a monotonic transformation.
MARGINAL UTILITY
The marginal utility is the rate of change with respect to good 1: how does this consumer’s utility change
as we give him or her a little more of good 1? We write it as MU1:
Note that the amount of good 2 is held fixed in this calculation. It is important to realize that it depends on
utility function transformation, which means that marginal utility itself has no behavioural content.
MARGINAL RATE OF SUBSTITUTION
The marginal rate of substitution (MRS) can be interpretated as the rate at which a consumer is just willing
to substitute a small amount of good 2 for good 1. Intuitively the willingness to exchange good 2 for one
unit of good 1, given that the level of utility stays constant. Geometrically is equivalent to the slope of the
indifference curve. The MRS is independent of the particular transformation of the utility function you
choose to use.
EXERCISE
1.3. LIMITS OF CONSUMER CHOICE: BUDGET CONSTRAINT
The budget constraint can be written as:
The budget set is the set of affordable
consumer bundles at prices p1 and p2, and a certain
income. The
budget line is the set of
bundles that cost exactly, these are the bundles of goods
that just exhaust the consumer’s income. The slope of the
budget line measures opportunity cost of good 1 – how
much of good 2 you must give up in order to afford more
of good 1.
THE NUMERAIRE
The budge line is defined by two prices and one income, but one of these variables is redundant. We could
peg one of the prices, or the income, to some fixed value and adjust the other variable so as to describe
exactly the same budget set. The numeraire price is the price set to 1 – the price relative to which we’re
measuring the other price and the income.
EXAMPLE
TOPIC 2. THE CHOICE
2.1. THE FORMAL PROBLEM OF MAXIMIZATION OF PREFERENCE
Consumers choose the best things they can afford. We put preference
and budget constraint together to determine what consumers will
choose. The consumer problem is to choose the consumption bundle X
that is best according to preferences subject to the constraint that the
total cost of X is no greater than the consumer’s income.
OPTIMAL CHOICE WITH WELL BEHAVED PREFERENCES
The optimal choice implies that the optimal consumption position is where the indifference curve is tangent
to the budget line (usually, what is always true is that at the optimal point the indifference curve can’t cross
the budge line). Moreover, the budget is exhausted. When preferences are wellbehaved and solutions are
interior, the tangency condition is fulfilled.
With wellbehave preferences the slope of the indifference curve = the slope of the budget line – at interior
optimum; which means that the MRS has to be equal to p1/p2. – What would happen if the MRS were
different from the price ration. Suppose that the MRS is 1/2 and the price ratio is 1/1. Then this means
that the consumer is just willing to give up 2 units of good 1 in order to get 1 unit of good 2, but the market
is willing to exchange them on a onetoone basis. Thus the consumer would certainly be willing to give up
some of good 1 in order to purchase a little more of good 2. Whenever the MRS is different form the price
ratio, the consumer cannot be at his or her optimal choice.
OPTIMAL CHOICE WITH PERFECT SUBSTITUTES
We have three possible cases. If p2 > p1, then the
slope of the budget line is flatter than the slope of the
indifference curves. In this case, the optimal bundle
is where the consumer spends all of his or her money
on good 1. If p1 > p2, then the consumer purchases
only good 2. Finally, if p1 = p2, there is a whole range
of optimal choices—any amount of goods 1 and 2
that satisfies the budget constraint is optimal in this
case.
OPTIMAL CHOICE WITH PERFECT COMPLEMENTS
Note that the optimal choice must always lie on the diagonal
where the consumer is purchasing equal amounts of both
goods, no matter what the prices are.
X1* = X2 * = m/ p1+p2.
OPTIMAL CHOICE WITH CONCAVE PREFERENCES
The optimal choice for these preferences is always going to
be a boundary choice.
Note: depending on the slope of budget line/ exact format
of IC, optimal choice could be: X1* = O and X2* = m/p2. But
if concave preferences then the consumer specializes.
OPTIMAL CHOICE WITH CALCULUS
Choose the consumption bundle X that is the best according to the utility function.
Subject to the constraint that the total cost of X is no greater than the consumer’s income. Which means
that we have to choose X that maximizes utility and it’s subject to the budget constraint.
The optimal choice must satisfy the condition
And also the budget constraint
There are two methods to maximize utility analytically:
1. Substituting the constraint (BL) into the objective function (U).
2. Lagrange multiplier method.
2.2 DERIVATION OF THE DEMAND FUNCTION
The consumer’s demand functions give the optimal amounts of each of the
goods as a function of the prices and income faced by the consumer.
Important property of CobbDouglas: consumer spends fixed proportion of
income in each good.
In the example of BOB
(See more detail in the example of Cob Douglass, more easily explained).
COMPARATIVE STATISTICS
Studying how a choice responds to changes in the economic environment is known as comparative statics.
The comparative statics questions in consumer theory therefore involves investigating how demand
changes when prices and income changes.
With normal goods
With inferior goods: for example, when my income increases I decrease
my consumption of lowcost
products
and
increase my consumption
of brands.
INCOME CHANGES
We have seen that an increase in income corresponds to shifting the budget line outward in a parallel
manner. We can connect together the demanded bundles that we get as we shift the budget line outward
to construct the income offer curve. This curve illustrates bundles of goods that are demanded at the
different levels of income. If both goods are normal goods then the income expansion path (=income offer
curve) will have a positive slope. We will have at the axis X1 and X2, and price will be fixed.
If we hold the prices of goods 1 and 2
fixed and look at how demand for one
good changes as we change income, we
generate a curve known as the Engel
curve. The Engel curve is a graph of the
demand for one of the goods as a
function of income, with all price being
held constant. Axis will be Xi and M
(income).
REMARK: Engel curves are not necessarily straight lines. There are nonhomothetic preferences.
ORDINARY GOODS AND GIFFEN GOODS
Now let’s consider price changes. Suppose that we
decrease the price of good 1 and hold the price of
good 2 and money income fixed. Then what can
happen to the quantity demanded of good 1?
Intuition tells us that the quantity demanded of
good 1 should increase when its price decreases.
Indeed, this is the ordinary case. When the price of
good 1 decreases, the budget line becomes flatter.
Or said another way, the vertical intercept is fixed
and the horizontal intercept moves to the right. The
optimal choice of good 1 moves to the right as well:
the quantity demanded of good 1 has increased.
It is logically possible to find wellbehaved preferences for
which a decrease in the price of good 1 leads to a reduction
in the demand for good 1. Such a good is called a Giffen good.
Suppose that the two goods that you are consuming are gruel
and milk and that you are currently consuming 7 bowls of
gruel and 7 cups of milk a week. Now the price of gruel
declines. If you consume the same 7 bowls of gruel a week,
you will have money left over with which you can purchase
more milk. In fact, with the extra money you have saved because of the lower price of gruel, you may decide
to consume even more milk and reduce your consumption of gruel. The reduction in the price of gruel has
freed up some extra money to be spent on other things—but one thing you might want to do with it is
reduce your consumption of gruel! Thus, the price change is to some
extent like an income change. Even though money income remains
constant, a change in the price of a good will change purchasing power,
and thereby change demand.
PRICE OFFER CURVE AND THE INVERSE DEMAND CURVE
Suppose that we let the price of good 1
change while we hold p2 and income
fixed. Geometrically this involves pivoting
the budget line. We can think of
connecting together the optimal points to
construct the price offer curve. This curve
represents the bundles that would be
demanded at different prices for good 1.
We can depict this same information in a
different way. Again, hold the price of
good 2 and money income fixed, and for each different value of p1 plot the optimal level of consumption
of good 1. The result is the demand curve. The demand curve is a plot of the demand function, x1(p1, p2,
m), holding p2 and m fixed at some predetermined values. Ordinarily, when the price of a good increases,
the demand for that good will decrease. Thus the price and quantity of a good will move in opposite
directions, which means that the demand curve will typically have a negative slope. In terms of rates of
change, we would normally have
which simply says that demand curves usually have a negative
slope. However, we have also seen that in the case of Giffen goods, the demand for a good may decrease
when its price decreases. Thus it is possible, but not likely, to have a demand curve with a positive slope.
SUBSTITUTES AND COMPLEMENTS
SUMMARY
TOPIC 3. REVEALED PREFERENCES AND SLUTSKY EQUATION
3.1. REVEALED PREFERENCES
3.2. SLUTSKY EQUATION
Economists are often concerned with how a consumer’s behaviour changes in response to changes in the
economic environment; particularly we are interested in people’s reaction to changes in relative prices
(incomeprice). We decompose the effect of a price change into simpler pieces to determine behaviour of
whole.
When a price of good changes there are two sorts of effects:

Substitution effect: the change in demand due to the change in the rate at which you can change one
good for another; increase demand for cheaper good, substituting away from other goods.

Income effect: the change in demand due to the fact that total purchasing power of your income is
altered; with the same income, consumer can now buy more (raise in purchasing power).

The total price effect on demand = substitution effect + income effect.
The Slutsky decomposition means that we will decompose the total price effect on demand into a pure
substitution effect and a pure income effect.
How can we separate substitution effect and income effect? First step: we will let the relative prices change
and adjust money income so as to hold purchasing power constant. Second step: let purchasing power
adjust while holding the relative prices constant.
The price of good 1 has declined. This means that the budget
line rotates around the vertical intercept m/p2 and becomes
flatter. Two steps: first pivot the budget line around the
original demanded bundle and then shift the pivoted line
out to the new demanded bundle. This “pivotshift”
operation is a way to decompose the change in demand
into: the first step—the pivot—is a movement where the
slope of the budget line changes while its purchasing power
stays constant, while the second step is a movement where
the slope stays constant and the purchasing power changes.
Step 1 Substitution effect: Let us calculate how much we
have to adjust money income in order to keep the old bundle
just affordable. Let m’ be the amount of money income that
will just make the original consumption bundle affordable;
this will be the amount of money income associated with the
pivoted budget line.
Step 2 Income effect: we know that a parallel shift of the budget line is the movement that occurs when
income changes while relative prices remain constant. We simply change the consumer’s income from m’
to m, keeping the prices constant at (p’1, p2).
Step 3 Total effect:
Note: substitution effect must be negative (quantity moves in opposite direction of prices) due to revealed
preference. Income effect can be negative or positive (depends on whether normal or inferior good).
3.3 THE LAW OF DEMAND
The law of demand. If the demand for a good increases when income increases, then the demand for that
good must decrease when its prices increases.
This follows directly from the Slutsky equation: if the demand increases when income increases, we have a
normal good. And if we have a normal good, then the substitution effect and the income effect reinforce
each other, and an increase in price will unambiguously reduce demand.
TOPIC 4. CONSUMER WELFARE
4.1. CONSUMER SURPLUS
The consumer surplus measures the net benefit from consuming n units of the good: the difference
between your willingness to pay and the actual price added up over all units purchased.
Your demand curve can be seen as your willingness to pay curve; for all units you consume, you actually
pay the market price. The difference of how much you’re willing to pay for an extra unit of good and how
much you’re actually paying is a measure of your benefit from purchasing one more unit.
When demand is continuous, area under the
demand curve is an approximate measure of
utility/consumer welfare (the difference is the
income effect).
Exception: quasilinear utility area under demand
curve is the exact measure (no income effect). In
the special case of quasilinear utility there is “no
income effect” since changes in income don’t
affect demand, which means that the reservation
prices are independent of the amount of money
the consumer has to spend on other goods. Using
the area under the demand curve to measure
utility will only be exactly correct when the utility function is quasilinear.
We are interested in the change of consumer surplus
that results from some policy change. The triangle T
measures the value of the lost consumption of the xgood. And R measure the loss from having to pay more
for the units he continues to consume.
Other ways of measuring utility changes or welfare changes different from consumer surplus are:
compensating and equivalent variation. They measure utility and utility changes in monetary units. There
is no need to know demand curve of consumers.
The compensating variation in income measures the change in income necessary to restore the consumer
to his original indifference curve. It’s the change in income that will just compensate the consumer for the
price change. (expost).
The equivalent variation in income measures how much money would have to be taken away from the
consumer before the price change to leave him as well off as he would be after the price change. So, it
measures the maximum amount of income that the consumer would be willing to pay to avoid the price
change.
The compensating and equivalent variations are just two different ways to measure “how far apart” two
indifference curves are. In each case we are
measuring the distance between two
indifference curves by seeing how far apart
their tangent lines are. In general, this
measure of distance will depend on the
slope of the tangent lines, that is, on the
prices that we choose to determine the
budget line.
However, the compensating and
equivalent variation are the same
in one important case—the case
of quasilinear utility. In this case
the
indifference
curves
are
parallel, so the distance between
any two indifference curves is the
same no matter where it is
measured.
4.2. PRODUCER SURPLUS
The supply curve measures the amount that will be supplied at each price. The area above the supply curve
measures the surplus enjoyed by the suppliers of a good.
The difference between the minimum amount she would be willing to sell the x∗ units for and the amount
she actually sells the units for is the net producer’s surplus. Just as in the case of consumer’s surplus, we
can ask how producer’s surplus changes when the price increases from p’ to p’’. In general, the change in
producer’s surplus will be the difference between two triangular regions and will therefore generally have
the roughly trapezoidal shape. The R measures the gain from selling the units previously sold anyway at p’
at the higher price p’’. The T region measures the gain from selling the extra units at the price p’’.
EXAMPLE
4.3. AGGREGATE DEMAND
4.4. ELASTICITY OF DEMAND
The elasticity measures how responsive is the demand to changes in prices.
(The slope of the demand function presents some problems because it depends on the units in which you
measure price and quantity).
Therefore, we use want to use a
measure of price responsiveness
which is independent of unit of
measurement – comparable across
different goods. The price elasticity
of demand is defined to be the percent change in quantity divided by the percent change in price.
For instance,
If a good has an elasticity of demand greater than 1 in absolute value we say that it has an elastic demand.
If the elasticity is less than 1 in absolute value we say that it has an inelastic demand. And if it has, exactly,
1 we say that is has unit elastic demand. An elastic demand curve is one for which the quantity demanded
is very responsive to price: if you increase the price by 1 percent, the quantity demanded decreases by
more than 1 percent. When are you hurt more by a price increase? When your demand is very inelastic.
In general, elasticity of demand for a good depends on availability of close substitutes, and goods with
closer substitutes have more elastic demand. Time horizon also affect price elasticities.
EXAMPLE
PART 2. THE FIRM AND THE SUPPLY FUNCTION
TOPIC 5. TECHNOLOGY
5.1. TECHNOLOGICAL CONSTRAINT
We will examine the constraints on a firm’s behaviour, when a firm makes choices it faces many constraints.
These constraints are imposed by its customers, by its competitors and by nature. Nature imposes the
constraint that there are only certain feasible ways to produce outputs from inputs. The technology is a
process by which inputs are converted into an output. Usually several technologies will produce the same
product. But only a certain combination of inputs are feasible ways to produce a given amount of output.
Technology is a list of feasible production plans.
Inputs to production are called factors of
production. They are often classified as: land,
labor, capital goods1 or physical capital (inputs
to production that are themselves produced
goods:
machinery,
computers,
buildings,
vehicles…) and raw materials. We will usually want to think of inputs and outputs as being measured in flow
units: a certain amount of labor per week and a certain amount of output a week
The production set is the set of all combinations of inputs and outputs that comprise a technological feasible
way to produce. Suppose, for example, that we have only one input, measured by x, and one output,
measured by y. To say that some point (x, y) is in the production set is just to say that it is technologically
possible to produce y amount of output if you
have x amount of input. The production set
shows the possible technological choices facing a
firm.
The production function is the upper boundary of
the production set and it measure the maximum
possible output you can get from a given amount
of input.
1
Different from financial capital: Money.
Of course, the concept of a production function applies equally well if there are several inputs. If, for
example, we consider the case of two inputs, the production function f(x1, x2) would measure the
maximum amount of output y that we could get if we had x1 units of factor 1 and x2 units of factor 2. In
the twoinput case there is a convenient way to depict production relations known as the isoquant. An
isoquant is the set of all possible combinations of inputs 1 and 2 that are just sufficient to produce a given
amount of output. Isoquants are similar to indifference curves. But there is one important difference
between indifference curves and isoquants. Isoquants are labeled with the amount of output they can
produce, not with a utility level. Thus the labeling of isoquants is fixed by the technology and doesn’t have
the kind of arbitrary nature that the utility labeling has.
5.2. DIFFERENT TYPES OF TECHNOLOGY
FIXED PROPORTION
Suppose that we are producing holes and that the only
way to get a hole is to use one man and one shovel.
Extra shovels aren’t worth anything, and neither are
extra men. Thus the total number of holes that you can
produce will be the minimum of the number of men and
the number of shovels that you have. We write the
production function as f(x1, x2) = min{x1, x2}.
PERFECT SUBSITUTES
Suppose now that we are producing homework and the
inputs are red pencils and blue pencils. The amount of
homework produced depends only on the total number
of pencils, so we write the production function as f(x1,
x2) = x1+x2.
COBBDOUGLAS FUNCTION
If the production function has the form f(x1, x2) = A(x1^a * x2^b), then we say that it is a CobbDouglas
production function. This is just like the functional form for CobbDouglas preferences that we studied
earlier. The numerical magnitude of the utility function was not important, so we set A = 1 and usually set
a + b = 1. But the magnitude of the production function does matter so we have to allow these parameters
to take arbitrary values. The parameter A measures, roughly speaking, the scale of production: how much
output we would get if we used one unit of each input. The parameters a and b measure how the amount
of output responds to changes in the inputs.
PROPERTIES OF TECHNOLOGY
Technologies are positive monotonic: if you increase the amount of at least one of the inputs, it should be
possible to produce at least as much output as you were producing originally. This is sometimes referred
to as the property of free disposal: if the firm can costlessly dispose of any inputs, having extra inputs
around can’t hurt it.
We will often assume that the technology is convex. This means
that if you have two ways to produce y unit of output, then their
weighted average will produce at least y units of output.
5.3. MARGINAL PRODUCT AND MARGINAL RATE OF TECHNICAL SUBSTITUTION
The marginal product is how much extra output you get from increasing the input factor i, holding factor j
fixed.
The marginal product is decreasing. More and more of a single product produces more output, but at a
diminishing rate law of diminishing returns.
The technical rate of substitution is the slope of the isoquant, if you increase the input of good 1 a little bit
how much input of good 2 has to vary to get the same level of production as before? How much extra of
factor 2 do we need if we are going to give up a little bit of factor 1?
So, it measures the rate at which the firm will have to substitute
on input for another in order to keep output constant.
The technical rate of substitution is diminishing, means that the slope of the isoquant must decrease in
absolute value as we move along the isoquant in the direction of increasing X1. Which means that the
isoquant will have the same sort of convex shape that wellbehaved indifference curves have.
Diminishing marginal product is an assumption about how the marginal product changes as we increase
the amount of one factor, holding the other fixed. Diminishing TRS is about how the ratio of the marginal
product  the slope of the isoquant  changes as we increase the amount of one factor and reduce the
amount of the other factor and reduce the amount of the other factor so as to stay on the same isoquant.
5.4. RETURNS TO SCALE
What happens to the production level when we increase the amount of all inputs proportionately = jump
to a higher isoquant?
Constant returns to scale multiply the amount of both inputs in the production function by t > 1 then the
amount produced will be t times higher than before
Increasing returns to scale we scale up both inputs by some factor t and we get more than t times as
much output
Decreasing returns to scale we scale up both input by some factor t and we get less than t times as much
output. The usual way in which diminishing returns to scale arises is because some input is being held fixed,
it’s a really shortterm phenomenon.
Technology can exhibit different kinds of returns to scale at different levels of production.
5.5. THE LONG AND THE SHORT RUN
In the short run there will be some factors of production that are fixed; a firm is restricted in some way in
its choice of at least one input level.
In the long run all factors can be varied; a firm is unrestricted in its choice of all input levels.
TOPIC 6. BENEFIT MAXIMIZATION AND COST MINIMIZATION
In this chapter we will assume there is a competitive market where the individual producers take the prices
as outside their control. Input and output process are fixed and firm has to choose quantity.
6.1. THE FORMAL PROBLEM OF PROFIT MAXIMIZATION
Notice that costs should include all factors of production, valued at market
price, including compensation for the owner of the firm – opportunity costs.
Economic costs are often referred to as opportunity cost, the name come from the idea that if you’re using
your labour, your land in one application you forgo the opportunity of employing it elsewhere. Therefore,
those lost wages are part of the cost of production. The economic definitions of profit require that we value
all inputs and output at their opportunity cost. Profits as determined by accountant do not necessarily
accurately measure economic profits, as they typically use historical costs – what a factor was purchased
for originally – rather than economic costs – what a factor would cost if purchased now.
Output and input levels are typically flows (labor hour per week and so many machines hours per week will
produce so much output per week). Consequently, profit is typically a flow also.
SHORT RUN PROFIT MAXIMIZATION
The condition for the optimal choice of factor 1 is not difficult to
determine. If x* is the profitmaximizing choice of factor 1 then the
output price times the marginal product of factor 1 should equal the price of factor 1. In other words, the
value of the marginal product of a factor should equal its price.
( if value of MP greater than its costs, then profits can be increased by increasing output a little bit.)
( if vale of MP smaller than its costs, then profits can be increased by decreasing output a little bit.)
Isoprofits are all the combinations of inputs and output that gives the same level of profits.
The profitmaximization problem is then to
find the point on the production function that
has the highest associated isoprofit line. As
usual it is characterised by a tangency
condition: the slope of the production
function should equal the slope of the
isoprofit line. So, since the slope of the
production function is the marginal product
we have that:
COMPARATIVE STATICS
We can use this graph to analyse how a
firm’s choice of inputs and outputs
varies as the prices of inputs and
outputs vary. This gives us one way to
analyse the comparative statics of firm
behaviour.
LONG RUN PROFIT MAXIMIZATION
If the firm has made the optimal choices of factors 1 and 2, the
value of the MP of each factor should equal its price. At the
optimal choice, the firm’s profits cannot increase by changing the
level of either input.
The only reasonable longrun level of profits for a competitive firm that has constant returns to scale at all
levels of output is a zero level of profits.
6.2. THE FORMAL PROBLEM OF COST MINIMIZATION
Our strategy will be to maximize profits by minimizing costs, otherwise there could be a cheaper way of
producing, meaning that profits were not maximized. There are two pieces:

Minimizing costs of producing y

Finding y that maximizes profits
MINIMIZING COSTS OF PRODUCING Y
The solution to costminimization problem, the minimum costs necessary
to achieve the desired level of output, will depend on w1, w2, and y, so we
write it as c(w1, w2, y). This function is known as the cost function.
The isoquants gives us the technological constraint. And the isocost lines is a curve
that contains all of the input bundles that cost the same amount.
Thus our costminimization problem can be rephrased
as: find the point on the isoquant that has the lowest
possible isocost line associated with it. The slope of the
isoquant must be equal to the slope of the isocost curve,
in other words, the technical rate of substitution must
equal the factor price ratio.
The average cost function is simply the cost per unit to produce y units of output:
If the technology exhibits constant returns to scale, the cost per unit of output will be constant no matter
what level of output the firm wants to produce.
If the technology exhibits increasing returns to scale, then the costs will increase less than linearly with
respect to output, so the average costs will be declining in output: as output increases, the average costs
of production will tend to fall.
If the technology exhibits decreasing returns to scale, then average costs will rise as output increases.
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