Intermediate Microeconomics

Budget Sets 1

Consumer Theory

 First part of class we want to understand “demand”.

 We want to do so from “first principles”.



Consumer Theory

- a model to describe how individuals behave.

 How do individuals choose what to consume?

 How do these decisions respond to changes in the environment?

 How can we use this model to describe market demand for goods?

 How should we start?

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Budget Set



Consumption Bundle

– A list of numbers indicating how much of each good an individual is consuming: {q 1 , q 2 , …., q n }  Ex: Suppose there are two goods, peanuts and beer.

 {5,12} is a consumption bundle containing 5 oz. of peanuts and 12 oz of beer.

 {20,6} is a consumption bundle containing 20 oz of peanuts and 6 oz of beer.



Budget Set

– the set of consumption bundles of goods a person can afford.

 What does an individual’s Budget Set depend on?

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Budget Set

  Suppose you are

endowed

with $10 (i.e. m = 10) and only goods you consume are peanuts and beer.

  Peanuts cost $0.10/oz (i.e. p p = 0.10) Beer costs $0.20/oz (i.e. p b = 0.20) How can we fully describe your budget set?

 Analytically?

 Graphically?

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Budget Set

 Interpreting prices   As we will see, prices will play a big role in our analysis of consumer behavior.

How would we describe the price of an ounce of beer intuitively?

 So what would slope of budget set look like if you lived in London, were endowed with 5 pounds, and where:   Peanuts cost 0.5 pence/oz Beer costs 0.10 pence/oz 5

Graphing Budget Sets

q 2 m/p 2 1 -p 1 /p 2 m/p 1 q 1  Slope of budget constraint is rise/run or simply negative of price ratio (-p 1 /p 2 ).

 So how do we interpret this slope?

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Graphing Budget Sets

 What happens when relative prices change?

 (original) m = 10, p p = 0.10 and p b = 0.20

 m = 10, p p = 0.20, and p b = 0.20

 m = 10, p p = 0.10 and p b = 0.10

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Graphing Budget Sets

 What happens when endowment changes but relative prices don’t?

 (original) m = 10, p p = 0.10 and p b = 0.20

 m = 20, p p = 0.10, and p b = 0.20

 m = 4, p p = 0.10 and p b = 0.20

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Budget Sets and Taxes

 Suppose m = $10, p p = 0.10, and p b = 0.20

 How would budget set change if a 25% sales tax were imposed on beer?

 How about if a 25% sales tax were imposed on all goods?

 How about if a 25% tax were imposed on each person’s endowment?

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Is two-good framework sufficient?

 With two goods, we could write a budget set as : p 1 q 1 + p 2 q 2 ≤ m  Suppose we are interested in analyzing good 1, but there are two other goods that a consumer can also spend money on.

  Analyze good 1 compared to a just the amount of money spent on all other goods (i.e. goods 2 and 3).

composite good

which is Denoting “dollars” of composite good as q c budget set as: 1.

2.

q p c 2 q + p 2 1 q + p 1 3 q ≤ m 3 ≤ q c we can write   If we are only interested in analyzing good 1, we can ignore equation 2, and we are back in two-good framework.

How would we draw this? What is slope?

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More Complicated Budget Constraints

 Budget constraints seem pretty simple, why do we make them so complicated?

 Consider more complicated pricing schemes.

 Bulk Pricing  Hamburger is $2/lb for first 3lbs, but only $1/lb for each additional amount past 3lbs.

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More Complicated Budget Constraints

 Government policy can also often make budget constraints more complicated  Food Stamps  pre-1979 – qualifying “poor” households could “buy” up to $200 worth of food stamps/month at a rate of $1 worth of food stamps for $0.50.

 post-1979 - qualifying “poor” households given $100 in food stamps.

 How do budget sets differ across two programs for a person earning $300/mo.?

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More Complicated Budget Constraints

 Public housing    Suppose a person is given a take-it-or-leave it offer of a free apartment Further suppose this apartment would rent for $300/month in the marketplace.

If person had $500/mo. in income, what would budget constraint look like?

 What if instead of this “in-kind” benefit, person was given $300 in cash.  What would budget constraint look like?

 So why don’t we always give cash benefits?

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Budget Constraints more broadly

 Suppose you worked for

Doctors without Borders.

 Your funds are enough to have twenty “beds” in your clinic.

  Each malaria patient you treat needs one week in your clinic for full treatment.

Each tuberculosis patient you treat needs two weeks in your clinic for full treatment.

 What is monthly budget constraint? What is the “cost/price” of treating a tuberculosis patient?

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