Preferences and Utility & Demand

Question 1

Describe the basic economic model of consumer behavior

Answer 1

consumers choose the best bundle of goods that they can afford

“can afford”– within their budget constraint
“best bundle” – the bundle that maximizes their utility

Question 2

if x ≻ y , then … [explain]

Answer 2

bundle x is strictly preferred to bundle y ; meaning x ⪰ y and not x ~ y // x ⪰ y and not y ⪰ x. In other words, If I think x ≻ y then I think x is at least as good as y but I am not indifferent between the two bundles.

Question 3

if x ⪰ y , then … [explain]

Answer 3

bundle x is weakly preferred to y ; I think x is at least as good as y (x must not be lower quality* than y).

Question 4

if x ~ y , then … [explain]

Answer 4

consumer is indifferent between bundle x and bundle y ; meaning x ⪰ y and y ⪰ x. I would be just as satisfied with consuming bundle x or bundle y because I think x is at least as good as y and y is at least as good as x

Question 5

Describe Utility

Answer 5

Utility is a mechanism for describing consumer preferences through ordering and ranking bundles by assigning numbers to every bundle. In Utility functions, more preferred bundles get larger numbers or an indifference between two bundles are equal in magnitude.

Question 6

Explain monotonic transformations and functions

Answer 6

a monotonic transformation of a utility function is a utility function that represents the same preferences* as its original utility function.
It transforms one set of numbers assigned to a bundle into another set of numbers in a way that preserves the order of numbers, represented by f(u). Typically, one multiplies u by some positive number, addition, or raising by odd number

Question 7

We say that preferences are well-behaved if they satisfy what assumptions

Answer 7

my Crazy Train Runs More South
Preferences are complete, transitive, reflexive, have monotonicity, and strictly convex

Question 8

What does it mean when a preference is complete

Answer 8

Any two bundles can be compared

Question 9

What does it mean when a preference is transitive (transitivity)

Answer 9

if some bundle is compared to another bundle which itself has its own bundle comparison, the original bundle will take on the properties of that other comparison (my way or the highway» if a=b & b=c -> a=c)

Question 10

What does it mean when a bundle is reflexive

Answer 10

Any bundle is at least as good as itself
x1,x2 ⪰ x1, x2

Question 11

What does it mean when a preference has monotonicity

Answer 11

More is better, any curve/area north east of the indifference curve is better off for the consumer. But since the consumer must give up some of one good to obtain another good that means the indifference curve’s slope is negative

Question 12

What does it mean when a preference is strictly convex

Answer 12

Any average case of two extreme cases is always better than the latter. Also, the slope of the indifference curve gets flatter as x1 increases

Question 13

if preferences can be represented by a utility function, they must be ___ and ___

Answer 13

complete and transitive

Question 14

Write the utility function for typical indifference curves

Answer 14

u(x1,x2) = k
such that k = x1 * x2

Question 15

write the utility function for perfect substitutes

Answer 15

u(x1, x2)= ax1 + bx2
positive slope

Question 16

write the Cobb Douglas utility function

Answer 16

u(x1,x2) = x1^c*x2^d

Question 17

write the utility function for perfect compliments and explain

Answer 17

u(x1,x2)=min{ax1,bx2}

the consumer cares for the number of pairs such that pairs = minimum, or where ax1=bx2. A and b are the proportions in which goods are consume.

Question 18

write and explain utility function for quasilinear cases

Answer 18

u(x1,x2)= f(x1) + x2 , where f(x1) in a nonlinear function of x1, like f(x1)= ln(x1)

Question 19

Define the marginal rate of substitution and write the equation

Answer 19

Between goods 1 and 2, the marginal rate of substitution defines how much of good 2 you are willing to give up for one extra, infinitely small unit of good 1.

MRS is the slope of an indifference curve at a given bundle of goods & the ration of marginal utilities of good 1 and good 2.
MRS = (du/dx1) / (du/dx2)

Question 20

Try an example problem of calculating the marginal rate of substitution
- Slide 144
-Slide 147

Answer 20

:)

Question 21

How is the marginal rate of substitution related to the assumption of strict convexity in well behaved preferences ?

Answer 21

If preferences are strictly convex, the MRS gets smaller in magnitude as x1 increases (magnitude= fractional value gets closer and closer to zero)

Question 22

Utility functions are a way of describing choice behavior because…

Answer 22

If a consumer is more likely to choose bundle X over bundle Y, then bundle X gives that consumer more utility

Question 23

write the equation for budget constraints

Answer 23

px1 +px2 ≤ m

if assuming monotonicity means all money will be spent, then

px1 +px2 = m

Question 24

Derive the budget line equation

Answer 24

px1 +px2 = m ->

x2 = -p2/p1(x1) + m/p2 (linear relationship like y= mx+b)

Question 25

What occurs to a budget line function when we decrease prices and income?

Answer 25

An increase in m -> shifts budget line right A decrease in m -> shifts budget line left A decrease in p1 -> makes the budget line steeper An increase in p1-> makes the budget line flatter (play around with p2)

Question 26

Describe an "interior solution"

Answer 26

With well behaved preferences, the slope of the indifference curve (MRS) equals the slope of the budget constraint. Meaning the optimum choice bundle for the consumer is where the budget line is tangent to the indifference curve * this is not a sufficient condition for all sets of preferences; There could be points of the budget constraint where its suboptimal (two optimum points, one bad point) with nonconvex preferences.

Question 27

Describe "corner solution"

Answer 27

Contrary to well behaved preferences, this is where either x1 or x2 = 0 as a consumer's optimum choice bundle, and MRS does not equal the slope of the budget line. However, the indifference curve of interest to our optimum point does not "cross" the budget line.

Question 28

Try constrained optimization problems -Slide 174 and write the recipe

Answer 28

Recipe: Find the MRS by taking the ratio of each good's marginal utility Set the MRS equal to the slope of the budget line to form the first equation Use the budget constraint as the second equation use algebra to solve 2 equations with 2 unknowns

Question 29

write the demand function for Cobb Douglas Preferences and explain its components

Answer 29

x1 = c/(c+d) * m/p1 The amount of money spent on good 1 will always equal c/c+d percent of the consumers income, meaning the equation can be written as x1p1= c/c+d * m

Question 30

write the inverse demand function for Cobb Douglass

Answer 30

p1 =c/(c+d) * m/x1 where income and price is fixed.

Question 31

Compare and Contrast the demand function versus the inverse demand function

Answer 31

the demand function tells us quantities as a function of prices and/or income the inverse demand function expresses prices as a function of quantities (income held constant) / derives the demand curve

Question 32

Try an example problem for deriving the demand curve from a utility function - Slide 219

Answer 32

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Question 33

Define the price offer curve

Answer 33

a graph of how the bundles demanded change with the price

Question 34

Define the income offer curve

Answer 34

a graph depicted the bundles of goods that are demanded at different levels of income.

Question 35

Try an example problem for deriving the income offer curve and engel curve - Slide 227

Answer 35

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Question 36

Define the Engel curve

Answer 36

a plot of income against demand

Question 37

Explain normal goods in respect to changes in the demand function

Answer 37

as income increases, quantity demanded increase dx1/dm > 0 examples: new clothing

Question 38

Explain inferior goods in respect to changes in the demand function

Answer 38

as income increases, quantity demanded decreases dx1/dm < 0 examples: low quality food, like bologna

Question 39

Explain ordinary goods in respect to changes in the demand function

Answer 39

as price decreases , quantity demanded increases dx1/dp1< 0 examples: kitchen utensils

Question 40

Explain Giffen goods in respect to changes in the demand function

Answer 40

as price decreases, quantity demanded decreases dx1/dp1> 0 All Giffen goods are inferior goods but not all inferior goods are giffen

Question 41

Given the demand function x1=x1(p1,p2,m), we define substitutes as goods for which...

Answer 41

dx1/xp2 > 0 ; here the demand for good 1 goes up when the price of good 2 goes up , like if the price of pens increase, I consume more pencils (pens and pencils case)

Question 42

Given the demand function x1=x1(p1,p2,m), we define compliments as goods for which...

Answer 42

dx1/xp2 < 0 ; here the demand for good 1 goes down when the price of good 2 goes up. If the price of coffee increases, I consume less sugar because I want them together

Question 43

Describe the self-fulfilling prophecy of goods that are close substitutes if the price of one good were to go down (Coke and Pepsi example Slide 253)

Answer 43

if the price of one subtitute were to decrease-- like in the Pepsi Coke example if the recipe for Coke were sold to other soda manufacturers, then Coke's value would decrease-- so would the profits of the other good decrease because the price and demand of the other substitute would decrease