Consumer Choice Under Certainty Part II Agenda: VI.Review of the key consumption relationship VII. Our FIRST numerical example! VII. Utility functions – play dough economics VIII. The Key Relationship

Putting it Together: The Optimal Bundle! Tangent: where a line touches a curve at one point. The rate of change of the curve = the rate of change of the line Check your understanding: Why is it P x /P y and not P y /P x ? Why not here? Marginal rate of substitutionSlope of the budget line

Putting it Together: The Optimal Bundle Numerical Example You love coffee and bagels for breakfast. You’re willing to give up two cups of coffee for one bagel (with cream cheese). The price of coffee is $1 and the price of a bagel is $2. You have $6 to spend on breakfast and you can buy fractions. Please put coffee on the Y-axis. 1. What is the marginal rate of substitution? A: 2 coffee/1 bagel 2. What is the budget constraint? A: $1C + $2B = $6 Test yourself: draw the budget line – what are the X and Y intercepts and what do they mean? 3. What your optimal breakfast?

REMEMBER the Process of Problem Solving! Step #1: Where do you need to go? What does the answer look like? A QUANTITY of Coffee AND a QUANTITY of Bagels (B,C) Step #2: What do you know? $1C + $2B = 6 Step #3: Use what you know to get where you need to go! This is just math: two equations & two unknowns!

1. Cross multiply & simplify to express C in terms of B. 2. Substitute into the Budget Constraint! 3. Substitute the answer for B into the Budget Constraint. 2 suggestions: 1.Use $ for prices so you keep your units clear! 2.Check your answer by substituting your answer into the budget constraint!

What if you were ONLY willing to have coffee and bagels for breakfast at a ratio of one (1) bagel to two (2) cups of coffee? In other words, coffee and bagels are perfect complements to you! What is your optimal breakfast? Hint: The MRS must stay constant at 2 no matter what the prices are! What do these indifference curves look like? MRS is the rate at which we substitute Y (coffee) for X (bagels) Your answer MUST have a ratio of 2 coffee per bagel!

Utility Functions A function is a mapping from X to one Y We can draw indifference curves from a utility function BUT we can NOT draw a utility function from indifference curves! Utility is ordinal, not cardinal! Functional forms

Indifference curves Utility curves Budget constraint Different notation Same meaning! Indifference Curves & Utility Functions

A little math…a lot of different interpretations! The ratio of marginal utilities equals the price ratio, or Marginal benefit = Marginal cost The marginal utility per dollar for each good must be equal The marginal rate of substitution equals the slope of the budget line The opportunity cost per dollar for each good must be equal

You like coffee and bagels with the marginal utility of coffee = 1/2 bagels and the marginal utility of bagels = 2 coffee. The price of coffee is $1 and the price of a bagel is $2. You have $6 to spend on breakfast and you can buy fractions. What is your optimal bundle? Putting it Together Again: Optimal Bundle Example revisited What is the key relationship that defines the optimal bundle? How can you check that this is correct?

THE INTUITION We consume to the point where the marginal cost (price) = the marginal benefit Next up… Slutsky! The Key Relationship