# CAE 2 (2017)

Pràctica InglésUniversidad | Universidad de Barcelona (UB) |

Grado | Administración y Dirección de Empresas - 1º curso |

Asignatura | Microeconomía |

Año del apunte | 2017 |

Páginas | 7 |

Fecha de subida | 19/06/2017 |

Descargas | 0 |

Subido por | jbayona75 |

### Vista previa del texto

CAE 2
1. Maria’s breakfast consist in coffee and cookies and her budget is 8€.

a) Cookies cost 2€ and coffee also 2€. What combinations can she consume?
Represent budget line and find her optimal basket.

With a budget of 8 euros and if the price of both goods is 2 euros, she would be
able to do all combinations except the one in black bold.

Coffee (2€)
0
0
0
1
1
2
2
2
3
3
4
Cookies
(2€)
0
2
4
2
3
0
1
2
1
2
0
Total euros
Total utility
0
4
8
6
8
4
6
8
8
10
8
0
28
40
48
54
28
48
56
54
62
40
The budget line is the red one, and taking into account the total utility of both
goods we can see that her optimal basket is the pink point (2,2) which suppose
a cost of 8 euros, her total basket, and produce a total utility of 56, which is the
higher possible (in the table is the one in pink bold).

CAE 2
b) If the prince of cookies increases at 4€ and coffee is kept at 2€. What are the
baskets on the budget line and her new best?
Now less combinations will be done as the price of cookies has increased, the
ones that can’t be done are the ones in black bold.

Coffee (2€)
0
0
0
1
1
2
2
2
3
3
4
Cookies
(4€)
0
2
4
2
3
0
1
2
1
2
0
Total euros
Total utility
0
8
16
10
14
4
8
12
10
14
8
0
28
40
48
54
28
48
56
54
62
40
Now the budget line has passed from the red line to the green one. With this
new budget line, her optimal basket is now the orange point (2,1), which also
suppose a cost of 8 euros, her total budget, and produce the higher utility able,
which is 48 (the one in pink bold in the table).

CAE 2
c) Compare the results in sections a) and b), when cookies price increase, what is
the effect on the quantity consumed? Describe the substitution effect and the
income effect.

Comparing the results we see that the cookies quantity consumed has
decreased from 2 to 1 as its price has increased.

The substitution effect says that if the price of one good increase, consumers
will use the other as an alternative. In this case we can’t see this effect because
the limited budget made Maria unable to buy more coffee, so the quantity
bought was the same for this good even the price of the other has increased.

The income effect says that as price increase, demand decreases, so the
income effect here is the change in cookies quantity demanded, which is 1.

CAE 2
2. Utility function:
U(x,y) = x · y
Income= 100€
Price x= 5€
Price y= 10€
a) Find the consumer equilibrium by the Method of Lagrange.

U (x,y)= x · y
st 5·x + 10·y = 100
L= x · y – λ (100 - 5x - 10y)
∂L/∂x= y + 5λ;
y + 5λ= 0;
y = (-5λ)
∂L/∂y= x + 10λ;
x + 10λ= 0;
x= (-10λ)
∂L/∂λ= 100 – 5x – 10y;
100= 5x + 10y
100= 5 · (-10λ) + 10 · (-5λ); 100= -100λ;
λ= -1
y = (-5 · -1) = 5
x = (-10 · -1) = 10
b) Find the consumer equilibrium by the Method of Equalising the Weighted
Marginal Utilities.

(dU/dx) / (dU/dy) = px/py;
y/x = 5/10;
x=2y
c) Represent graphically the consumer equilibrium.

CAE 2
3. Total utility of a consumer:
U(x1,x2) = x1 · x2 + x1
Price x1= 3€
Price x2= 2€
a) If the consumer chooses the combination of goods x1 = 2 and x2 = 3, can it be an
optimal consumtion bundle?
MRSx1x2 = Px1/Px2;
Px1/Px2 = 3/2
MRSx1x2 = MUx1 / MUx2;
MUx1 = x2 + 1
MUx2 = x1
MRSx1x2 = (3 + 1) / 2 = 4/2
4/2 ≠ 3/2
As the condition for being a optimal consumption bundle isn’t accomplished, the
combination of goods proposed is not the optimal.

b) Keeping constant the price of good 2 (P2 = 2) what should be the price of good 1 for
the previous election to be optimal (good one = 2 and good two = 3)?
To be optimal it has to fulfill the condition expressed before:
MRSx1x2 = Px1/Px2
So, as we found before, MRSx1x2 = 4/2, which means that, for the combination of
goods x1 = 2 and x2 = 3 to be optimal, the price of good 1 must be 4.

MRSx1x2 = Px1/Px2;
4/2 = 4/2
CAE 2
4. Draw the utility function and represent the indifference curves that corresponds to
the following:
a) Cars and ties are complementary perfects, but a ratio of 1:4 (for each car Maria
wants exactly 4 ties).

(Cars vertical axis and ties horizontal axis)
b)
Maria’s soft drink utility only gets utility from caffeine ingested. She can choose soft
drink A or B, which contains twice the caffeine than first. (1:2)
(Drink A vertical axis and drink B horizontal axis)
c) The consumption of soda water gives utility to Mary, while water has no utility to her.

(Soda water vertical axis and water horizontal axis)
CAE 2
d) Maria likes burger but no soup. In order to incentive her, her mother said that for
every bowl of soup she can eat two burgers.

(Soup vertical axis and burgers horizontal axis)
5. John spends his income in gasoline and sandwiches. Find baskets achievable and
the optimal basket for John if the gasoline price is 5€, the sandwich price 10€ and
his income is 50€.

Quantity of
gasoline
Total utility
gasoline
Price
gasoline
Quantity of
sandwich
Total utility
of sandwich
Price of
sandwich
Total price
Total utility
0
1
2
3
4
5
0
80
150
210
260
300
0
5
10
15
20
25
0
2
4
6
8
10
0
70
130
180
220
250
0
20
40
60
80
100
0
25
50
75
100
125
0
150
280
390
480
550
His baskets achievable are the ones in blue and his optimal basket is the one in blue
bold.

...