# CAE 2 (2017)

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 Universidad 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 Puntuación media Subido por jbayona75

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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.
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