Topic 1 Microeconomics:
The Budget Constraint:
The budget constraint is one of the two subjects that allow us to
recognize the optimal consumption bundle (quantity of good x and y
preferably consumed).
The budget constraint represents the limit set by income that
consumers have to face while consuming goods.
The budget constraint is graphically represented by the Budget
Constraint line.
Or
Where represent the slope of the
B.C. line.
The slope of the budget constraint line also represents the rate of
exchange between the two goods, so, the opportunity cost of x with
reference to y.
The B.C. line divides the cartesian plane’s quadrant in three regions:
A. The grey area is the
so-called “Budget
Set”, the bundles that
lay in it are the ones
we can afford.
B.The bundles that are
above the budget
constraint line are
those we cannot
afford.
C. The bundles that lay
ON the budget
constraint line are
those Just affordable.
, Income (m) Changes Effects
As income changes from m to m’ the budget constraint will shift in in
parallel, maintaining the same slope but increasing the consumption
possibilities.
—>
Parallel Shift, Same slope
Price Changes Effects
When the price of one of the two good changes, the budget constrain
line will pivot on the axis of the good whose price has not changed.
The slope in this case will change.
—>
Pivot on unchanged price axis, different slope.
Preferences:
Take two commodities x and y and a reference bundle Z, made up of a
given quantity of x and a given quantity of y.
Z=(x,y)
The set of all bundles equally preferred to Z are represented on the
cartesian plane, as the points of a curve, called the indifference curve.
The symbol we use to indicate two bundles to be indifferent (= equally
preferred) is —> Z ~ Z’
Of course the bundles are only indifferent (~) if they lay on the same
indifference curve.
A~B~C~D
All of the points on the indifference curve are
equally preferred to the consumer.
, Properties of the indifference curve
I. There are infinite indifference curves
II. Higher indifference curves are preferred to lower ones
III. Indifference curves do not cross each other
IV. Indifference curves are Monotonic:
This property of the indifference curve implies that more is always
preferred to less and, as a consequence, the indifference curves are
negatively sloped
If more is preferred to
less, it implies that the
bundles indifferent to Z
must be somewhere near
area B and area A.
Since related to the slope of the indifference curve, we can say that
monotonicity is strictly related to the first derivative.
Monotonic —> Negatively Sloped —> First Derivative
V. Indifference curves are Concave:
This property is caused by the consumer choice being more inclined to
balance bundles rather than extreme ones.
If we in fact draw a straight line between the two extremes of an
indifference curve we can not that the bundle that lays in the middle
point of that line will be preferred to the other two.
, Convex Preferences —> Concave Curves —> Second Derivative
This is however not always true, the contrary can exist, for instance in
the case of drug addicts, in which the curve would be convex, due to
the preference of extreme bundles over balanced ones.
Preferences Symbol
To say that x’ is preferred to x’’ we write:
Well Behaved Preferences
A preference is said to be well behaved if it is both monotonic and
convex
Marginal Rate of Substitution,
MRS:
Take an indifference curve I, the marginal rate of substitution is the
absolute value of the slope of the curve at a specific point, and
indicates the rate at which the consumer is willing to exchange one
good for the other.
The marginal rate of substitution can be interpreted as the relative
subject value of x with reference to y. In laymen’s terms if you give up
a little amount of x, how much of good y will you need to be equally
satisfied to the previous bundle?
If and only if the curve is convex, the MRS will decrease as the
quantity of y increases.
The marginal rate of substitution can be also computed as the absolute
value of the derivative of x2 over the derivative f x1.
The Budget Constraint:
The budget constraint is one of the two subjects that allow us to
recognize the optimal consumption bundle (quantity of good x and y
preferably consumed).
The budget constraint represents the limit set by income that
consumers have to face while consuming goods.
The budget constraint is graphically represented by the Budget
Constraint line.
Or
Where represent the slope of the
B.C. line.
The slope of the budget constraint line also represents the rate of
exchange between the two goods, so, the opportunity cost of x with
reference to y.
The B.C. line divides the cartesian plane’s quadrant in three regions:
A. The grey area is the
so-called “Budget
Set”, the bundles that
lay in it are the ones
we can afford.
B.The bundles that are
above the budget
constraint line are
those we cannot
afford.
C. The bundles that lay
ON the budget
constraint line are
those Just affordable.
, Income (m) Changes Effects
As income changes from m to m’ the budget constraint will shift in in
parallel, maintaining the same slope but increasing the consumption
possibilities.
—>
Parallel Shift, Same slope
Price Changes Effects
When the price of one of the two good changes, the budget constrain
line will pivot on the axis of the good whose price has not changed.
The slope in this case will change.
—>
Pivot on unchanged price axis, different slope.
Preferences:
Take two commodities x and y and a reference bundle Z, made up of a
given quantity of x and a given quantity of y.
Z=(x,y)
The set of all bundles equally preferred to Z are represented on the
cartesian plane, as the points of a curve, called the indifference curve.
The symbol we use to indicate two bundles to be indifferent (= equally
preferred) is —> Z ~ Z’
Of course the bundles are only indifferent (~) if they lay on the same
indifference curve.
A~B~C~D
All of the points on the indifference curve are
equally preferred to the consumer.
, Properties of the indifference curve
I. There are infinite indifference curves
II. Higher indifference curves are preferred to lower ones
III. Indifference curves do not cross each other
IV. Indifference curves are Monotonic:
This property of the indifference curve implies that more is always
preferred to less and, as a consequence, the indifference curves are
negatively sloped
If more is preferred to
less, it implies that the
bundles indifferent to Z
must be somewhere near
area B and area A.
Since related to the slope of the indifference curve, we can say that
monotonicity is strictly related to the first derivative.
Monotonic —> Negatively Sloped —> First Derivative
V. Indifference curves are Concave:
This property is caused by the consumer choice being more inclined to
balance bundles rather than extreme ones.
If we in fact draw a straight line between the two extremes of an
indifference curve we can not that the bundle that lays in the middle
point of that line will be preferred to the other two.
, Convex Preferences —> Concave Curves —> Second Derivative
This is however not always true, the contrary can exist, for instance in
the case of drug addicts, in which the curve would be convex, due to
the preference of extreme bundles over balanced ones.
Preferences Symbol
To say that x’ is preferred to x’’ we write:
Well Behaved Preferences
A preference is said to be well behaved if it is both monotonic and
convex
Marginal Rate of Substitution,
MRS:
Take an indifference curve I, the marginal rate of substitution is the
absolute value of the slope of the curve at a specific point, and
indicates the rate at which the consumer is willing to exchange one
good for the other.
The marginal rate of substitution can be interpreted as the relative
subject value of x with reference to y. In laymen’s terms if you give up
a little amount of x, how much of good y will you need to be equally
satisfied to the previous bundle?
If and only if the curve is convex, the MRS will decrease as the
quantity of y increases.
The marginal rate of substitution can be also computed as the absolute
value of the derivative of x2 over the derivative f x1.
