1. Choice Under Certainty Review

2. Completeness, transitivity, convexity and more preferred to less.
In WORDS: What are these curves called and what do they reflect (what do they mean?) Y X
Indifference curves: bundles of X and Y on the same curve make us equally happy.
Bundles on indifference curves to the top right make us more happy.
In WORDS: What are the assumptions that allow us to draw indifference curves that look like this graph?
Completeness, transitivity, convexity and more preferred to less.

3. Write in NOTATION and draw a GRAPH to depict a budget line:
Write in NOTATION and WORDS the slope of the budget line
Negative the price ratio between goods X and Y.

4. Write in NOTATION and draw a GRAPH to depict an optimal bundle using indifference curves.
Write in NOTATION and WORDS the optimal bundle using a utility function
The ratio of marginal utilities, or the Marginal Rate of Substitution (MRS) is equal to the price ratio.

5. Write in NOTATION and WORDS what this graph depicts.
Note: the original optimal bundle is A Y X
The Slutsky Substitution Equation shows that the total change in the quantity of X demanded when the price of X changes (from A to D) is composed of two parts: a substitution effect (from A to C) and an income effect (from C to D).
Write in WORDS whether this graph depicts a Normal or an Inferior good and how you know?
Normal: positive income effect . (decline in purchasing power → decline in quantity)

6. With these prices and a budget of $100 could you consume B?
Draw a GRAPH to of an indifference curve and label the point A where the marginal rate of substitution is 2 A B
Label the point B where the marginal rate of substitution is 1/2
Y=2X, therefore the opportunity cost of X = ½ Y
8(1/2)X + 4X = 100
8X=100
X = 12.5
The opportunity cost of Y is 2X
8Y + 4(2)Y=100
16Y = 100
Y = 6.25
If the price of Y is $8 and the price of X is $4 which bundle should you consume?
B because slope of budget line is Px/Py = 4/8 = 1/2
With these prices and a budget of $100 could you consume B?
Yes
Should you?
No, you can do better with Y=6.25 and X = 12.5

7. How much more money would you need to buy the original bundle (5,10)?
What prices would make the depicted bundle optimal with a budget of $100?
TEST YOURSELF! Use the marginal utilities and original prices to calculate the original bundle!
X = $10, Y = $5
If MUx = 2Y and MUy = 2X and the price of X increased to $20, what would be the new optimal bundle?
Optimal MRS: Y = 4X
5(4)X + 20X = 100, X = 2.5
5Y + 20*2.5=100, Y = 10
How much more money would you need to buy the original bundle (5,10)?
($20 -$10)*5=$50
With a budget of $150, Px=$20 and Py=5 what is the compensated bundle?
5(4)X + 20X = 150, X = 3.75
5Y + 20*3.75=150, Y = 15
What is the total effect, substitution effect and income effect of the price change?
Original – New: (5,10) – (2.5, 10) = (-2.5, 0) total effect
Original – Compensated: (5,10) – (3.75, 15) = (-1.25, 5) substitution effect
Compensated – New: (3.75, 15) – (2.5, 10) = (-1.25, -5) income effect

8. In WORDS: What does this curve depict?
A Demand Curve
In NOTATION write mathematical expression for this curve
What UNITS are on the X and Y axis?
Y = price ($)
X = quantity (#)

9. In WORDS: What is this curve called and what does it reflect (what does it mean?)
Utility Function: It maps how much utility, or “happiness” we get from different amounts of the good on the X axis (in this graph, M or money).
In NOTATION write an expression for the optimal bundle where the ratio of marginal utilities equals the ratio of prices.

10. No substitution effect!
Draw a GRAPH to illustrate indifference curves for perfect substitutes.
Draw a GRAPH and write NOTATION to illustrate the substitution and income effects for perfect complements.
No substitution effect!

11. In WORDS: What assumption does this equation reflect?
Convexity
What part of the convexity notation reflects a linear combination?
Set X x z y
Draw a GRAPH to illustrate convexity.

12. Write NOTATION and an example in WORDS to illustrate the transitive assumption.
Draw a GRAPH of indifference curves that violate the transitive property Y X

13. Good Luck!!