Economic Principles

Question 1

i.

The marginal utility of a good provides the rate of increase or decrease in the utility

from that good as the total consumption of it rises. It is not a measure of the total utility of a

good; the marginal utility is based in the idea that, for goods that can be consumed

repeatedly (like a bottle of water, whose content is drinkable in a series of gulps), the utility

derived from the nth gulp in inferior to the utility derived from the very first gulp. The

marginal utility provides a rate of this decrease in utility as the consumption increases.

ii.

Whenever consumers are faced with the task of choosing among different baskets

(which are essentially a collection of goods and services), their choices are dictated by

rational criteria. Let's assume that all such rational behaviour conforms to three

assumptions:

1. preferences are complete, which means the consumer is able of ranking the

baskets;

2. preferences are transitive, which means they are internally consistent with each

other;

3. more is always preferred to less.

In order to decide which basket to choose, consumer must rank the baskets. The

ranking criteria is the utility derived from each basket; The consumer will rationally choose

the basket from which he or she gets the most utility.

Consumers can usually rank the utility of the basket in a qualitative way – saying

they prefer one basket to the other, but not by how much. This measure is the qualitative

utility derived from that basket – consumers can say which brings them the most utility, but

not by how much. This means there is no information about the strength of the preference.

When consumers can actually rank the intensity of the utility, we get information

about the rate of preferences. This means that we are is a position to say that one basket

is preferred to another by, for instance, ten percent more.

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Economic Principles

iii.

This example considers that the economic agent wants to have a Coca-Cola for every

BigMac he consumes.

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0,5 1 1,5 2 2,5 3 3,5 4 4,50

0,51

1,52

2,53

3,54

4,5

Perfect ComplementsU=3min(x,y)

U=3U=6U=9

BigMacs , x

Coc

a-C

olas

, y

0 2 4 6 8 10 120

0,20,40,60,8

11,21,41,61,8

Perfect SubstitutesU=x+6y

U=6U=8U=10

Pen, x

Penc

il, y

Economic Principles

Satiated Preferences

iv.

Consider that a consumer obtains a fixed amount of utility from a basket composed

of two goods, x and y, and he or she is presented with the opportunity of substituting a

certain amount of one good for a certain amount the other. The rate at which the consumer

is willing to substitute one product for the other, while maintaining the utility constant, is the

Marginal Rate of Substitution.

v.

The following chart depicts a generic utility function for two goods, x and y, such that

Uxy = xy:

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X2

X1

Economic Principles

The Marginal Rate of Substitution of x for y on any specific point on the indifference

curve is given by the slope of a line tangent to that point. Consider the lines tangent to

points A to E in the example above: their slopes equal the absolute value of the MRSxy at

each point:

This shows that along the same utility curve (along which the consumer always gets

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0 2 4 6 8 10 12 14 16 180

2

4

6

8

10

12

14

16

18

U=4

X

Y

A

C

DE

B

Point Good X Good YA 1 16 16B 2 8 4C 4 4 1D 8 2 0,25E 16 1 0,06

Slope/MRSxy

Economic Principles

the same utility), when a consumer has a lot of good x and little of good y, he is prepared

of giving up lots of x for a little more y; but as he gets more y he is less willing to give up

any of x for a greater amount of y – hence the diminishing slope of the utility curve and the

diminishing Marginal Rate of Substitution of x for y. mar. This circumstance only holds for

utility functions that, like the one depicted here, are bowed towards the origin.

Question 2

i. a = 0.5, b = 0.5 and u = 1,2,3,4,5.

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0 1 2 3 4 5 60

5

10

15

20

25

30

Indifference CurvesU(x1,x2)=x1 a*x2 a; a=b=0,5

U=1U=2U=3U=4U=5

x1

x2

Economic Principles

ii. a = 0.2, b = 0.8 and u = 1,2,3,4,5.

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0 1 2 3 4 5 60

5

10

15

20

25

Indifference CurvesU(x1,x2)=x1 0,2*x2 0,8

U=1U=2U=3U=4U=5

x1

x2

Economic Principles

Question 3

This is a Cobb-Douglas function, so it has 2 useful properties:1. MRSx1,x2 and MRSx2,x1 are both positive2. Diminishing rate of substitution with the utility functions bowing towards the origin.

The optimal basket will be on the budget line; so:

Px1x1+Px2x2=I

Since u(x1,x2)=x1a+x2

b, we getlnu(x1,x2)=alnx1+blnx2

MRSx1,x2=u(x1,x2)=x1a+x2

b, dx1 = a/x1andMRSx2,x1=u(x1,x2)=x1

a+x2b dx2 = b/x2

Since, at the maximum point in the logarithmic function MRSx1,x2=MRSx2,x1

a/x1=b/x2

x2=(bx1)/a and x1=(ax2)/b

And we can substitute it in the first equation:Px1x1+Px2x2=IPx1x1+(Px2bx1)/a=Ix1=(aI)/(aPx1+bPx2) – Demand Curve for x1, depending on price

Px1x1+Px2x2=I(Px1ax2)/b+Px2x2=Ix2=(bI)/(aPx1+bPx2) – Demand Curve for x2, depending on price

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Economic Principles

Question 4

Suppose two goods, x and y, with x being the good whose demand curve we are

trying to determin, and y being a composite good, with a price of 1. These two goods

account for all the goods the individual buys, and the individual will maximize his utility,

spending all of his income in buying those goods. The resulting bundle of goods bought

will therefore depend on the income of the individual and on the relative prices of the

goods – and, since y is a composite with a price of 1, it will depend on the price of x and

on the individual's income.

We will assume the individual's income is 20.

Our objective is to derive the individual's budget curve for various prices of x.

Imagining the price of y and the individual's income both remain constant, chart 1 shows

three budget curves for three different possible prices of x: Px=10, Px=5 and Px=2.

The chart displays the budget lines at each of these prices of x, and it also displays

the individual's indifference curves for each of the budget lines – U1, U2 and U3.

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0 2 4 6 8 10 120

5

10

15

20

25

Budget Lines

BL1BL2BL3

Units of x

Uni

ts o

f y

U1 U2

U3

Economic Principles

The point at which each of the indifference curves touches (is tangent) to the

respective budget line gives us the number of units of x and y that the subject will acquire

for that price, maximizing his utility in the process. These numbers of units of x and their

respective prices may than be plotted into a demand curve for that individual:

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0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,50

2

4

6

8

10

12

Demand Curve for Good x

Quantity

Pric

e

Economic Principles

Question 5

The uncompensated (Marshallian) demand curve gives us information about the

amount of a good demanded for a certain level of price, keeping the subject's income

constant. This way, it's the utility of the subject that may vary along the line. Thanks to the

uncompensated demand curve, it is possible to observe the income effect and the

substitution effect.

On the other hand, the compensated (Hicksian) demand curve gives us information

about the amount of good demanded for a level of price, keeping the subject's utility

constant. This means that, to keep the subject in the same utility curve as the price of the

good changes, it's the income that must change, meaning the consumer is “compensated”.

The compensated demand curve cannot depict the income effect, but it gives information

about the substitution effects, should it occur.

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