4. Utility (2016)

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 Universidad Universidad Pompeu Fabra (UPF) Grado International Business Economics - 1º curso Asignatura Microeconomics I Año del apunte 2016 Páginas 4 Fecha de subida 27/04/2016 Descargas 7 Puntuación media Subido por avillagrasa

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Resumen del libro completado con apuntes de clase.

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avillagrasa 1st year IBE - 3rd Term Microeconomics I IV. Utility Index The utility function ........................................................................................................... 2 Monotonic transformations ............................................................................................. 2 Constructing utility function ............................................................................................. 2 Perfect substitutes ........................................................................................................ 3 Perfect complements ................................................................................................... 3 Quasilinear preferences ............................................................................................... 3 Cobb-Douglas preferences ........................................................................................... 3 Marginal utility ................................................................................................................. 3 Marginal utility and MRS .............................................................................................. 4 Summary ........................................................................................................................... 4 1 avillagrasa 1st year IBE - 3rd Term Microeconomics I The utility function Utility function: it assigns numbers to bundles. So the bundle we prefer the most will have the highest value. They are the indifference curves but with given values.
We only care about how to rank the bundles, but not how much better a bundle is respect another. Because of this we will care about ordinal utility (order of the bundles) rather than cardinal utility (how much better is a bundle).
Monotonic transformations F(u) is a monotonic transformations if u1>u2 implies f(u1)>f(u2). This does only mean that a function is a monotonic transformation as long as it keeps the order of the preferences.
When we perform a monotonic transformation the graph of the indifference function doesn’t change, we only change the numbers.
The image above shows a monotonic transformation, as the indifference curve with the highest value (2) now also has the highest value (4). < Constructing utility function We will plot different indifference curves. Then we will find the value of the bundles to rank them.
Ex: 1. Assume (2,3)>(4,1)~(2,2) 2. Assign utilities: U(2,3)=6>U(4,1)=U(2,2)=4 3. Graph the indifference curve passing through (2,2) and (4,1) and the one passing through (2,3) more at the right (because it’s better).
We will be given an utility function and then we just have to fix a level of utility and plot the indifference curves for different values of good 1 and good 2.
2 avillagrasa 1st year IBE - 3rd Term Microeconomics I Perfect substitutes They are of the form u(x1,x2)=ax1+bx2, where a and b are the value we give to good 1 and 2. This implies that the slope is -a/b.
Apart from the above expression x1+x2 we can use any other monotonic transformation of it.
Ex: if you have to be given 2 units of good 2 to compensate giving up 1 unit of good one, u(x1,x2)=2x1+1x2, and the slope is -2.
Perfect complements In this case the good is consumed in a fixed proportion, therefore the utility function is of the from u(x1,x2)=min{ax1,bx2}, where a and b are the proportions in which the goods are consumed.
Ex: you consume 2 teaspoons of sugar (x2) for 1 cup of tea(x1). Then the utility function is: u(x1,x2)=min{1x1,1/2x2} MONOTONIC TRANSFORMATION (x2)  min{2x1,x2}.
Then, do (3,4), (3,10) and (8,9) lie in the same indifference curve? A. u(3,4)=min{6,4}=6 B. u(9,8)=min{18,8}=8 C. u(3,10)=min{6,10}=6 Quasilinear preferences They keep on shifting upwards when the utility level (k) increases. Their form is: u(x1,x2)=k=v(x1)+x2. And as we can see, the utility is linear for good 2 but it is function (which might be nonlinear) for good 1.
Cobb-Douglas preferences They are used because they are the standard well-behaved curves. The utility function is: u(x1,x2)=x1c·x2d= x1α·x21-α Marginal utility It is the rate of change of utility respect to having more quantity of goods. In other words, if how much utility do we have when we increase a bit the quantity of good 1 (keeping good 2 fixed) or good 2 (keeping good 1 fixed). The formal formula is: Utility good 1: Utility good 2: 3 avillagrasa 1st year IBE - 3rd Term Microeconomics I However it doesn’t give any behavioral content as different monotonic transformations will give us different results.
Marginal utility and MRS With the marginal utility we can measure the MRS. To do it we will use: Note that it has a negative sign, so to make things easier we might refer to the MRS by its absolute value.
The marginal utility is the quantity of good 1 we are willing to give up to get a unit of good 2 and maintain the same utility level (be in the same indifference curve).
Summary    The utility function represents the order of preferences Any monotonic transformation will represent the same preferences The MRS can be calculated in terms of the utility function 4 ...