1. Walter Nicholson Christopher Snyder
Amherst College
Christopher Snyder
Dartmouth College
PowerPoint Slide Presentation | Philip Heap, James Madison University
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2. 2 Utility and Choice CHAPTER
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3. Chapter Preview
Want to develop a theory of choice which we can use to show how people make choices or decisions.
Two factors influence people’s choices.
Preferences: what goods do you like
Constraints: how much money do you have, what are the prices of the goods you buy
Importance of Ceteris Paribus assumption.
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4. Utility
Utility is the pleasure or satisfaction that people get from their economic activity.
Utility = U(X,Y; other things)
Utility depends on the amount of X and Y and other things.
Assume that the other things are held constant.
Measuring Utility
Problem with ceteris paribus.
Problem with unit of measurement.
Cardinal vs. ordinal utility.
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5. Three Assumptions About Preferences
Complete
Given two options, a person can state which option they prefer or whether they find both options equally attractive.
Transitivity
Preferences are internally consistent.
If I prefer A to B, and prefer B to C, then I must prefer A to C.
More is Better
Economic “goods” and “bads”.
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6. More is Better
Combinations of X and Y in the green area are preferred to (X*, Y*)
Quantity of Y
per week
(X*, Y*) is preferred to combinations of X an Y in the red area.
What can you say about these points? ? Y* ?
Quantity of X
per week X*
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7. Indifference Curves
We want to find a way to compare points in the two ? regions from the last picture.
Two goods: soft drinks and hamburgers.
Indifference curve
A curve that shows all the combinations of two goods that give the same level of utility
If you get the same utility you must be indifferent.
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8. Indifference Curve
Let’s say you are indifferent between A, B, C and D.
Hamburgers
per week
Draw a curve through those points.
Every point gives the same level of utility. A 6 B 4 C 3 D 2 U1
Soft drinks
per week 2 3 4 5 6
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9. Indifference Curve What can we say about combination E? What about F?
Hamburgers
per week
What about F? A 6 B 4 E C 3 D 2 U1 F
Soft drinks
per week 2 3 4 5 6
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

10. Indifference Curve
Why does the indifference curve have a negative slope?
Hamburgers
per week
If you give up hamburgers, you need to get more soft drinks to still get the same level of utility. A 6 B 4 E C 3 D 2 U1 F
Soft drinks
per week 2 3 4 5 6
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11. Indifference Curves and the Marginal Rate of Substitution
The marginal rate of substitution (MRS) measures the rate at which you are willing to reduce the consumption of one good to get one more unit of another good and still remain indifferent.
The absolute value of the slope of the indifference curve measures the MRS.
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12. Indifference Curves and the MRS
From A to B: the person is willing to give up 2 burgers to get 1 more soda.
From B to C: the person is willing to give up 1 burger to get 1 more soda.
Hamburgers
per week
From C to D: the person is willing to give up ½ burger to get 1 more soda. A 6 B 4 E C 3 D 2 U1 F
Soft drinks
per week 2 3 4 5 6
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13. Indifference Curves and the MRS
Do you notice a pattern?
As you consume more and more soda, the number of burgers you are willing to give up to get one more soda gets smaller and smaller.
This is known as diminishing marginal rate of substitution.
People prefer balanced consumption to extremes.
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14. Indifference Curves and the MRS
Suppose we create a basket that is ½ of A and ½ of B: point G.
Hamburgers
per week
You would prefer 4 burgers and 4 sodas to 6 of one good and 2 of the other good. A 6 G 4 D 2 U1
Soft drinks
per week 2 3 4 6
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

15. Indifference Curve Maps
An indifference curve map shows the utility a person gets from all possible combinations of two goods.
Hamburgers
per week
As you move to the northwest, utility increases: U3 > U2 > U1 U3 U2 U1
Soft drinks
per week
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16. Four Particular Preferences
A useless good.
More of a useless good neither increases nor decreases utility.
Smoke grinders
per week U1 U2 U3
For a given amount of food, additional grinders do not increase utility.
Food per week
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

17. Four Particular Preferences
An economic bad.
More of an economic bad decreases your utility.
Holding the amount of food constant, additional flies reduces utility.
Houseflies
per week U1 U2 U3
Food per week
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18. Four Particular Preferences
Perfect Substitutes
Two goods are perfect substitutes if the MRS is constant.
In this case the MRS = -1 everywhere
Gallons of Exxon per week
Does it always have to be -1?
What if it was quarts of Exxon? U1 U2 U3
Gallons of Mobil per week
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19. Four Particular Preferences
Perfect Complements:
Goods are perfect complements if they are consumed together in fixed proportions.
Right shoes
What if you had three feet: two left and one right? 3 U3 2 U2 1 U1
Left shoes 1 2 3
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20. Utility Maximization
Faced with a choice from among a number of goods, how do you choose the one that gives you the highest utility.
Your decision is constrained by your income and the prices of the goods you can buy.
Assume you have $100 per week to spend on burgers and soda.
How do you allocate the $100 in order to maximize your utility?
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21. Utility Maximization
To maximize your utility two conditions must be met:
You spend all your income.
MRS is equal to the price ratio.
Why does the second condition have to hold?
Suppose that right now the MRS = 1. To remain indifferent, you would be willing to give up 1 burger to get 1 soda.
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22. Utility Maximization Conditions
Why does the second condition have to hold?
Suppose that right now the MRS = 1. To remain indifferent, you would be willing to give up 1 burger to get 1 soda.
If the price of soda is $1 and the price of a burger is $ MRS = 1 > PS/PB = ½
If you give up one burger, you can get one more soda to keep you indifferent plus you get one more additional soda.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

23. Utility Maximization Conditions
So when MRS > PS/PB you can increase your utility by buying less burgers and more soda.
What if the MRS < PS/PB?
Therefore, only when MRS = price ratio are you maximizing utility.
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24. Utility Maximization: A Graphical View
Start by showing the budget constraint: this shows the limit that income places on the combinations of goods that can be bought.
Ymax – spend all income on good Y
Quantity of Y
per week
Xmax – spend all income on good X
Ymax
Buy some mix of X and Y and spend all income.
Points inside the budget constraint are affordable, but you have money left over.
Quantity of X
per week
Xmax
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25. Budget Constraint Algebra
Assume you have I dollars of income to spend on goods X and Y.
Px and PY are the prices of goods X and Y.
Since all income must be spent:
Total amount spent on X and Y = Total Income
Px X + Py Y = I
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26. Budget Constraint Algebra
Rewrite the last equation so that:
If all income spent on Y, you buy I/PY units.
If all income is spent on X, you buy I/PX units.
The slope of budget line (-PX/PY) represents the opportunity cost of X in terms of foregone Y.
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27. Budget Constraint Algebra
Suppose you have $100 to spend on burgers and soda: PB = $4 and PS = $2.
Write out the budget constraint:
4B + 2S = 100 or S = B
If you only buy soda (B = 0), you can buy 50 units.
The opportunity cost of one burger is two sodas.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

28. Utility Maximization: A Graphical View
Given the budget constraint, we now want to add an indifference curve.
Quantity of burgers
per week
Are you maximizing utility at point A?
No. You are not spending all your income. A
Quantity of sodas
per week
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

29. Utility Maximization: A Graphical View
Are you maximizing utility at point B?
Quantity of burgers
per week
No. The MRS (the slope of the indifference curve) > price ratio (the slope of the budget constraint)
You could buy less burgers and more soda and end up on a higher indifference curve at point C. B C A
Quantity of sodas
per week
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

30. Utility Maximization: A Graphical View
So at point C, you are maximizing utility
Quantity of burgers
per week
1. You are on the budget constraint: all income is spent.
2. The indifference curve is tangent to the budget constraint: MRS = price ratio. B C A
Quantity of sodas
per week
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

31. Using The Model of Choice: Differences in Preferences
Hamburgers per week
Hungry Joe has a relatively strong preference for burgers
Extra thirsty Ed is super thirsty
Thirsty Theresa has a relatively strong preference for soda.
Soft drinks
per week
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32. Using The Model of Choice: Differences in Preferences
What indicates each persons’ preference for one good over the other?
Hamburgers per week
The flatter (steeper) the indifference curve the stronger the preference for the good on the Y-axis (X-axis).
Soft drinks
per week
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

33. Using The Model of Choice: Different Types of Goods
A useless good.
Smoke grinders
per week U1 U2
The person buys only food and does not buy the useless good
Food per week
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34. Using The Model of Choice: Different Types of Goods
An economic bad.
Houseflies
per week U1 U2
The person buys only food and does not buy the economic bad
Food per week
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35. Using The Model of Choice: Different Types of Goods
Perfect Substitutes
Gallons of Exxon per week
The person buys only Exxon gas since it costs less per gallon (steep budget constraint) U1 U2
Gallons of Mobil per week
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36. Using The Model of Choice: Different Types of Goods
Perfect Complements
Right shoes
The person buys shoes only in pairs. 2 U2 1 U1
Left shoes 1 2
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37. Numerical Example: Perfect Substitutes
Example 1: You have to decide whether to buy Exxon gas or Mobil gas. You have $30. The price of Exxon gas is $3 and the price of Mobil gas is $3.25.
Since the goods are identical you will only buy gas at the lowest price. Therefore, you will buy 10 gallons of Exxon gas.
Note that if the goods are perfect substitutes you do not necessarily buy the good with the lowest price.
If you get enough extra utility from the more expensive good, you may end up buying that good.
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38. Numerical Example: Perfect Complements
Example 1: You have to buy pairs of shoes. Left and right shoes each cost $10, and you have $60 to spend.
What are your possible options?
What would you do?
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39. Numerical Example: Perfect Complements
Example 2: Each time you go to the movies you buy 2 bags of popcorn. The price of popcorn is $2.50 and the price of a movie ticket is $10. You have $30.
Utility function: U(M,C) = Min (2M,C)
Consumption ratio: C = 2M
Budget constraint: 10M C = 30
Plug C = 2M into the budget constraint: 10M + 5M = 30
M = 2
C = 4
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40. Willie’s Utility and His Uncle’s Promises
Other Goods
Willie prefers point A if no promise is made
Uncle offers point B: no sin, but higher utility due to more consumption of other goods and services
Uncle promised to give the money to Willie once he was “capable of using it wisely”, but he died before paying
Budget constraint B C
Willie ends up at C with a lower utility compared to A A
Willie got paid in the end U3 U2 U1
Sin

41. Rationing of Tickets Leads to Scalping
Other
goods
Since Super Bowl tickets are rationed at one per consumer, the individual maximizes utility at point B, but would be happier if he or she could be at point A purchasing 4 tickets.
Buying two tickets to move to point C is preferable in terms of utility
CD is the amount of other goods this consumer is willing to sacrifice for the ability to move to C. B C
Income D A U2 U1
Super Bowl
tickets 1 2 3 4 5

42. Some Generalizations
So far we have considered fairly simple choice problems.
More than two goods.
Complicated budget constraints: volume discounts, tie-in sales, rationing.
Composite goods: food and housing, X and “all other goods”.
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43. Summary
People make choices in order to maximize their utility or happiness.
An indifference curve shows the different combinations of two goods that a person views as equally attractive: gets the same utility.
The slope of the indifference curve – the MRS – measures the rate at which a person is willing to substitute one good for another.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

44. Summary
Peoples’ choices are constrained in what they can purchase by their income and the prices of the goods.
A person will maximize their utility by: 1) spending all their income, and 2) choose the mix of goods for which the MRS is equal to the price ratio.
©2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.