Consumer Choice Under Certainty Part I Agenda: What is Rational? What does “rational” mean to an economist? Preferences and the Marginal Rate of Substitution Budgets and budget lines Putting it together: the optimal bundle! A. Graphical approach B. Numerical example

What is Rational?

What does “rational” mean to an economist? Preferences are complete Preferences are transitive “All models are wrong, but some are useful.” -- George Box Test Yourself: 1. What is a NORMATIVE theory? 2. Is Neoclassic Economics a Normative theory? Why or why not?

4 Assumptions about consumer preferences: 1. Completeness: we can rank all possible combinations of goods and services. x is preferred to y for all x and y that are elements of X “…to rule out… Buridan’s ass” Good message here about modeling rigor – in order for the models to be solvable and not result in trivial solutions we sometime have to make what appear to be trivial, or worse implausible assumptions. Again, all models are wrong. Web link talks about “tension between formal and informal ways of thinking” Bring back positive – we’re trying to explain why people do what they do – and normative – if we know why they do what they do we can change the incentives to get different, more desirable, outcomes. Read more: http://www.buridansass.com/index.php/about/

We’ve thought about things and we can make consistent choices. 4 Assumptions about consumer preferences: 2. Transitivity – we’re consistent in our preferences If we prefer hamburgers to hot dogs, and hot dogs to sausage, then we must prefer hamburgers to sausage. Completeness, and 2.Transitivity are mathematically what we mean by “rational”. We’ve thought about things and we can make consistent choices. Good football counterexample: if the cowboys beat the eagles and the eagles beat the giants it does NOT mean that the cowboys will beat the giants. Define “lexographic preferences”

4 Assumptions about consumer preferences: 3. More is better – local non-satiation – we are not indifferent over a wide range of options. x y  “The distance between y and x” Need notation and picture from Mass collel “utility function is monotonically increasing” This does NOT mean all preferred bundles have more of everything! Read more: http://en.wikipedia.org/wiki/Local_nonsatiation

4 Assumptions about consumer preferences: 4. Convexity – variety is the spice of life Any linear combination Convex Set X x z y NOT Convex Set X x z y Cannot overestimate how huge an assumption this is! Key to most mathematical economics. Necessary for optimization

A ~ B From these 4 assumptions we can draw… Indifference Curves! “is indifferent to” An Indifference Curve links all bundles that offer the same level of utility Test Yourself: 1. Write out three preference relationships suggested by this graph. 2. Draw a linear combination of two bundles and use it to explain why this indifference curve is consistent with convex preferences.

What’s Wrong?? 1. Not transitive: E~D, D~F, BUT F > E! Class Activity: name the violations of assumptions illustrated on this graph Transitivity More to less Convexity Write in notation 1. Not transitive: E~D, D~F, BUT F > E! 2. Does not exhibit more better than less: G~F, G~H 3. Not convex

Marginal Rate of Substitution (MRS) The change in Food at bundle A divided by the change in Shelter at bundle A that keeps you on the SAME Indifference Curve. See Frank p. 68 Key point: the marginal rate of substitution is not constant! Test Yourself: What is the MRS at bundle C? At bundle D? Why is MRS at A > MRS at B? Draw a line whose slope equals the MRS at point C.

Preferences are reflected in the shapes of indifference curves! Who would be willing to pay more for rice? Mohan is willing to give up more potatoes for a unit of rick, so he likes rice more. Who likes rice more? Test Yourself: Draw YOUR indifference curve for two goods (e.g. pizza & beer) and compare it to a friend’s indifference curve for the same two goods. Can you tell who likes what more?

The Budget Constraint Price of X increases Price of X decreases M = “money” Y = “composite good” = $1 per unit But that doesn’t mean the person who likes rice more will buy more rice – it depends on their budgets After this slide break for graphing exercise. Slope of budget line Price of X increases Price of X decreases Income decreases

Putting it Together: The Optimal Bundle! Why not here? Tangent: where a line touches a curve at one point. The rate of change of the curve = the rate of change of the line Why not here? This is the KEY slide for Objective #2: First the intuition: consume at the highest utility you can! People prefer more to less. Then the math: Tangency occurs where the rate of change of the indifference curve = the rate of change of the budget line Marginal rate of substitution Slope of the budget line Check your understanding: Why is it Px/Py and not Py/Px?

No, you are not maximizing utility! Test Yourself: Performance Objective #2 At your current consumption ,your marginal rate of substitution between buying clothes and going out to eat is 3. If on average you spend $20 for each new item of clothing and $25 each time you go out to eat with friends, are you maximizing your utility? If not, what should you do. Please support your answer with BOTH math and a graph, and please put clothing on the Y axis. Answer: No, you are not maximizing utility! 3 ≠ $25/$20 Buy less clothes and go out to eat with your friends more! Current consumption MRS = 3 clothes Optimal consumption MRS = 5/4 Out to eat