José Raúl Cárdenas Arnaiz Faculty of Economics BUAP Microeconomics Course I autumn

2021
Exercises of Unit 2: FIRST PART
Choose the correct option
1. The budget line shows:

R=a) Combinations of affordable goods for the individual, given an income and the prices of the
goods, whose expenditure is equal to the income.

2. In the case of two goods, the slope of the budget line indicates:

R=b) The price of one good measured in units of the other, referred to as relative price or cost of
opportunity

3. Which of the following expressions describes the budget constraint when a tax is applied?
per unit on the quantity of good x1?

R=a) (P1 t X1 P2 X2 m

4. If an individual only consumes two goods, A and B, and spends all their income acquiring 20 units.
5 of A and 5 of B, or 10 units of A and 10 of B. Also consider that the price of one unit of A is
10.

a) Calculate the consumer's income.

20A + 5B = 10A + 10B 10(20) + 10(20) = 300

20(10) + 5B = 10(10) + 10B 20(10)+5(20)=300
200 - 100 = 10B - 5B m=300
B=20 The consumer income is $300

b) Represent the budget constraint on a graph.

Budget Line
120

100

80

60

40

20

0
0 5 10 15 20 25
José Raúl Cárdenas Arnaiz Faculty of Economics BUAP Microeconomics Course I autumn
2021

5. If two goods can be acquired in a market, where the price of good 1 is 50, the price of good 2 is
50 and the consumer has an income of 200 to acquire these goods. Solve the following:

a) Write the budget line.

P1x1 + P2x2 = m
X1(50) + X2(50) = 200

b) If the individual spends all their income on acquiring good 1, how many units could they buy?

M/x1 = 200/50 = 4 I could buy 4 units of good 1.

c) If the individual spends all their income on acquiring good 2, how many units could they buy?

m/x2 = 200/50 = 4 I could buy 4 units of good 2.

d) Graph the budget constraint.

Budget line
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

e) Good 1 is granted a subsidy at a rate of 5%, while the other remains

constant. Write the equation of your new budget constraint and graph it.

RP InicialX1(50) + X2(50) = 20 5% of 50 = 2.5

We add a value rate of 5% (P1+t) X1 + P2X2 = m

RP New = (50 + 2.5) X1 + P2 (50) = 200

José Raúl Cárdenas Arnaiz Faculty of Economics BUAP Microeconomics Course I autumn
2021

New RP with 5%
60

50

40

30

20

10

0
0 10 20 30 40 50 60

f) What happens if the consumer's income decreases to 180 while the prices of both goods...
Do they keep it at 25? Write the budget constraint in this case and graph it.

P1x1 + P2x2 = m
X1(50) + X2(50) = 200

X1(25) + X2(25) = 180 180/25 = 7.2 - This means that despite reducing their income, they can still
acquire 4 units of a good at a maximum of 7.2 each.

RP
8

0
0 1 2 3 4 5 6 7 8
José Raúl Cárdenas Arnaiz Faculty of Economics BUAP Microeconomics Course I autumn
2021
If a consumer has a budget such that, if they spent it all, they could acquire either 8 units
24 units of good x1 and 24 units of good x2 or 32 units of good x1 and only 6 units of good x2.

a) Represent these two consumption baskets on a graph and generate the budget line.

b) Say what the relative price is.

b) If the consumer spends all their income on acquiring good x1, how many units can they buy?

c) If you spend all your income on acquiring good x2, how many units of that good can you buy?

d) What will be the equation corresponding to the budget line if the price of x1 is 3.

f) Note the change in the budget line if the price of good x1 increases to 12.

g) What will the new budget line be if, starting from the previous section, a tax is applied?
unit of 3 to good x1?

Test Type Questions. (Mark your answer with an X) second part

7. Identify the axiom that ensures that indifference curves do not cross.

Completitud

8. If a consumer's preferences are represented by the utility function

u(x; y) = min(2x; y), his income is m = 12 and the prices of the goods are Px = Py = 1; then his basket
The best is:

(6; 6) (12; 0) (0; 12) (4; 8)

9. Say what type of preferences are modeled in the previous exercise.

R=Convex
Choose the correct option
10. A representative agent likes good X1but does not support good X2, although he is willing to
consume one unit of good X2if you receive in exchange seven units of good X1.
a) Develop the utility function that describes the individual's preferences regarding the two goods.

b) Determine the marginal utility of good x1 and good x2, respectively.

José Raúl Cárdenas Arnaiz Faculty of Economics BUAP Microeconomics Course I autumn
2021

c) Calculate the Marginal Rate of Substitution.

11. Individual A has a utility function given by u(x,y) = X2+ 2XY + Y2For his part, the individual
B has a utility function v(x,y) = X + Y.

a) Calculate the RMS corresponding to each individual.

b) Do these utility functions represent the same preferences?

c) Is A's utility function a monotonic transformation of B's? Why?

12. If preferences are regular, what happens with the marginal rate of substitution (MRS) in choice?
of the consumer?

a) It is equal to the quotient of the Marginal Utilities and equal to the ratio of the prices.
b) It is equal to the product of the Marginal Utilities.
It is equal to the quotient of the Marginal Utilities but different from the price ratio.
It is equal to the quotient of the prices and equal to the product of the Marginal Utilities.

13. For the following utility function U (x1, x2) = X1+ X2when P1= 10; P2= 5; m = 200, in equilibrium
determine the quantity demanded of both goods.

a) X1= 20; X2= 0

b) X1= 10; X2= 20 X1(10) (10) = 100
c) X1= 0; X2= 40 X2 (5) (20) = 100
d) It cannot be determined. m = 200 = X1 + X2

14. Assuming the following utility function u = min {X1, 2 X2when P1= 8; P2= 4; m=200, determine
the quantity demanded of both goods.

a) X1= 12.5; X2= 25 X1(8) (10) =80

b) X1= 20; X2= 10 X2 (4) (30) = 120
c) X1= 10; X2= 30 m= 200 = X1 + X2
d) X1= 15; X220

NOTE: YOU MUST JUSTIFY THE ANSWERS TO EACH QUESTION BY MAKING THE
PROCEDURES THAT MADE HIM CONCLUDE HIS SOLUTION