2. Preferences and Utility Functions

MIT 14.01 Principles of Microeconomics, Fall 2018
Instructor: Prof. Jonathan Gruber

This video focuses on the demand curve, derived from how consumers make choices, and the supply curve, which is how firms make production decisions.

Chapters
00:00 Title slate
00:11 Lecture Start
01:13 Model Assumptions
05:54 Indifference Curves
09:23 Four Properties
13:27 Real Example ( job search )
15:28 Utility Functions
18:31 Margin Utility
24:49 Marginal Rate of Substitution
30:13 Why graph's not concave
32:37 (Q) Addictives & MRS
34:31 Price of Different Sizes of Goods

License: Creative Commons BY-NC-SA

[hollykm]

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[pallabibiswas]

Notes:
Demand curve – how consumers make choices
Decision making – Utility maximisation. Consumer preferences – what people want and budget constraints – what they can afford.
Step 1 – Preferences – how do we model people’s taste – Unconstrained choices, money is no object, how do we think about what we want.
Preference assumptions. Models are based on simplifying assumptions. Are they roughly consistent with reality or not?
Completeness – We have preferences over any set of goods we choose from. Can’t say I don’t know how I feel about this.
Transitivity – If we prefer A to B and we prefer B to C then we prefer A to C.
Non-satiation/More is better – More is always better than less.
Graph of people’s preferences. Indifference curves. Graphical maps of preferences. Suppose parents gave money before semester. Spent on two things – buying pizza or eating cookies. 2 dimensional decision case. Consider 3 choices A. 2 pizzas and 1 cookie B. 1 pizza and 2 cookies C. 2 pizzas and 2 cookies. Assume – We are indifferent between these packages. Equally happy with all the packages. And also assume we prefer option C as more is better.

One indifference curve between A & B because those are the points among which you’re indifferent. Indifference curve represents all combinations of consumption among which you are indifferent. You are indifferent between A & B and therefore they lie on the same curve.
4 properties that you have to follow from these assumptions:
Prop 1 – Consumers prefer higher indifference curves = More is better. Package that has at least more of 1 thing than the other so you prefer it. As the curve shifts out you are happier because more is better
Prop 2 – Indifference curves are downward sloping. Comes from Principle of non-satiation.

Why does it violate the principle of non-satiation?
You cannot be Indifferent about 1 of each or 2 of each.
Prop 3 – Indifference curves never cross.

Because in B & C, B is strictly better but they’re also on the same curve as A. You’re indifferent with A for both B & C but you can’t be indifferent between B & C because B is strictly better than C. Indifference curves crossing violates transitivity.
Prop 4 – Only 1 indifference curve through every possible consumption model/ Only one indifference curve through every bundle. You can’t have 2 indifference curves in the same bundle because of Completeness. If this did happen you wouldn’t know how you felt. You may feel indifferent but you can’t say you don’t know how you feel.
Example – year op as a grad student who had to decide where he would accept the job. I am indifferent but I care about 2 things – school location and economics department quality (quality of my colleagues and the research that’s done there) One is from Princeton and the other is Santa Cruz (not as good as economics department). 3rd offer – IMF research institution in DC and had a lot of good colleague and DC is way better than Princeton. Worst quality than Princeton and worst location than Santa Cruz but it was still better in combination than these two institutions.
Utility Functions – Mathematical representation – Every individual has a stable well behaved underlying mathematical representation of your preferences which we call utility function. 2 dimension – how do we mathematically represent between pizza vs cookies. Utility function is no. of slices of pizza vs no. of cookies. U√P*C. What is Utility? It doesn’t mean anything. Its not a cardinal but an ordinal concept. Assume you can rank your choices in many dimensions. Weigh different assumptions so you can rank them when you need to choose.
Marginal utility – 1 cookie and then the value or utility of the next cookie. Marginal decisions. Once you eat an cookie, do you want the next unit/cookie/pizza? Key feature – Diminishing Marginal Utility – the more of you’ve had of a good the less you would want the next unit.

No. of cookies holding constant pizza. If you’re having 2 pizza slices and you want to say what’s my benefit from the next cookie. Left axis – violating the above we graph utility. Eg. If you have 1 cookie your utility is 1.4; square root of 2 times 1. If you have 2 cookies the utility goes up = square root of 4 which is 2. You’re happier with 2 cookies but you are less happy with the second cookie as you were with the first cookie.

The 1st cookie gave you 1.14 utility. What’s your happiness is measured in this graph of marginal utility. The next cookie’s utility is 2.059. Each additional cookie makes you less and less happy. Makes you happy as more is better but less happy as the 1st cookie. Remember you always want more cookies. You can say that the 11th will make you barf. But in economics you can give it away or save it for later, worst case you can throw it out, but you always think more is better. Utility function can never be negative, as its an ordinal concept, and is always positive as you get some benefit from the next unit.
Indifference curves are the graphical representation of what comes out of utility function. Slope of the indifference curve is called marginal rate of substitution. The rate at which you’re willing to substitute one good for another. Substitute cookies for pizza. dp÷dc = marginal rate of substitution.

I am indifferent between point A & B. Over here 1 slice of pizza = 1 cookie. Marginal rate of substitution is -2. I am ready to give 2 pizzas for 1 cookie. When we move from B to C the MRS is -½. Now I’m willing to give only 1 slice of pizza for 2 cookie, because we don’t want cookie as much due to diminishing marginally utility. MRS is always diminishing, it has to. Slope will always be falling. How MRS relates utility function; MRS=DP÷DC= -MUc÷MUp (c – cookie and p - pizza). MRS tells you how relative marginal utility evolves as you move down the indifference curve. When you start at point A, you have lots of pizza and not a lot of cookies; here your marginal utility is small. Marginal utility are negative functions of quality, the more you have it the less you want it. As you move along the indifference curve, you’re more willing to give up the good on the x-axis to get the good on the y-axis. Implies that indifference curves are convex to the origin. They’re not concave, they’re either convex or straight. It can be linear.

What would happen if indifferent curves were concave to the origin?
From point A to B leaves you indifferent so You can give 1 slice of pizza to get 1 cookie, starting to give 4 pizzas for 1 cookie. From 2 and 3 you are willing to give 2 pizzas for 1 cookie. This violates principle of MU and MRS as pizzas should be more valuable as you have less pizza now.
Addictive decisions – Smoking. Utility function shifts as you get more addictive. The next will be still be worth less. But as we’re addicted the first cigarette will be worth more and more to you. When you wake up feeling crappy the first cigarette will be good to you but the next morning you wake up feeling crappier and wanting the first cigarette more as people get habituated to certain levels. For drugs its not about diminishing MU but different underlying products used in the drug.
Example – Prices of different sizes of goods. Starbuck tall coffee for $2.25 and the next one for 70 more cents. McDonald – Small is $1.22 but for 50 more cents you can double the size. Why do they give twice as much for much less than twice as much money? Its all about diminishing MU, you’re desperate for the first soda on a hot day, but not twice as much for the next glass. Those prices reflect market’s reaction to diminishing MU. If you think about demand and supply, the demand for 1st 16 ounces is higher than the demand for the 2nd 16 ounces, but the cost to produce the drink is the same. Since the demand for the next 16 ounces doesn’t shift twice as much, you can only charge 50 cents for the next 16 ounces. Price increments get smaller because of diminishing MU. Buying in bulk from Costco is not much less than buying single units from supermarkets as the price gap between the soda example. Even though you might get thirstier later in the day for another glass of soda, they won’t let you walk in with the first cup you bought from them. Eg. Fenway small soda - $6, bigger soda - $8, refillable soda cup - $10. Can you bring the $10 refillable cup back to additional games? No.

[tarafahey]

01:13 Model Assumptions
05:54 Indifference Curves
09:23 - - > Four Properties
13:27 - - > Real Example ( job search )
15:28 Utility Functions
18:31 - - > Margin Utility
24:49 Marginal Rate of Substitution
30:13 - - - > Why graph's not concave
32:37 - - - > (Q) Addictives & MRS
34:31 Price of Different Sizes of Goods

[edvzxzf]

Microeconomics L-2
A. Utility Curves
A.1.Assumptions
A.1.1. Completeness - You can mark preference on any item. Inversely, you cannot say you feel 'indifferent' about it.
A.1.2. Transitivity - If A preferred over B and b over C then A is preferred over C.
A.1.3. Insatiable - More is better than less.

A.2. Draw Utility curves now: Ordinal and not cardinal metric (i.e., you cannot be certain about by how much A is bigger than B but definitely rank A and B)

A.3. Properties
A.3.1. Only one utility curve for a bundle - Completeness property (i.e., preferences cannot be uncertain or non-existent).
A.3.2. Utility curves cannot cross each other - Transitivity (if crossed, A=B and A=C but A>C).
A.3.3. Utility curves are negatively slopped - Insatiability (If positively slopped, More is equally preferable to less).
A.3.4. Not concave to the origin - Violates Marginal diminishing utility (If concave, you'll be willing to substitute more goods of one type by an equal number of competitive goods when you have less of it).

B. Marginal Utility
B.1. The utility of the next unit of A relative to the amount of A you have now. Basically del(U)/del(A).
B.2. Properties:
B.2.1. Utility will increase but Marginal utility will be diminishing (Not concave to the origin).
B.2.2. Though the Marginal utility is decreasing, the value must be non-negative. (Design Utility eqn accordingly).
B.2.3. MRS (Marginal rate of substitution) = slope of the Utility curve = Marginal Utility of Item on the x-axis/Marginal Utility of item on the y-axis.
B.2.4. Explanation of 3: delta A (the number of items A willing to be exchanged) is inversely proportional to the Marginal Utility of A at the given point for a given amount of item B.

C. Other discussions:
C.1. For additive items, it's not that the Marginal utility is increasing (it's diminishing in this case too) but the Utility function shifts.
C.2. Why are price increments less than the proportional increment in the amount? - Refer Point 3 and 4 in Marginal utility.


(Will be adding notes as I progress in the course based on my understanding of the material).

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respected professor teaches in very simple manner believe me i am a biology student

[ThanhTriet]

For those of you doing the assignments and feeling like you've missed a lot with the math behind demand curves, you definitely have. If you're looking for a more in depth class that covers the math (which is quite important), I recommend the 2011 version of this course also on MIT open courses. The optional textbook also covers it if you prefer to read.

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Definitions and Notes
1. Assumptions: more is always better, there are no budget constraints for this class's thought experiments.

2. Indifference curves: An indifference curve is a graph showing combination of two goods that give the consumer equal satisfaction and utility. Each point on an indifference curve indicates that a consumer is indifferent between the two and all points give him the same utility.

3. Four properties of Indifference curves:
(i) People prefer higher IC
(ii) Indifference curves never intersect.
(iii) Indifference curves are downward sloping
(iv) Only 1 I.C through every bundle

4. Preferences: In economics and other social sciences, preference is the order that a person gives to alternatives based on their relative utility, a process which results in an optimal "choice". Preferences are evaluations, they concern matters of value, typically in relation to practical reasoning.

5. Utility: Economists use the term utility to describe the pleasure or satisfaction that a consumer obtains from his or her consumption of goods and services. It is a subjective measure of pleasure or satisfaction that varies from individual to individual according to each individual's preferences

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