Choice Under Certainty Review

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.

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.

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.

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)

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

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

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 (#)

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.

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!

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.

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

Good Luck!!