1 Intermediate Microeconomics Budget Sets

2 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?

3 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?

4 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?

5 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

6 Graphing Budget Sets Slope of budget constraint is rise/run or simply negative of price ratio (-p 1 /p 2 ). So how do we interpret this slope? q1q1 q2q2 m/p 2 m/p 1 -p 1 /p 2 1

7 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

8 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

9 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?

10 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 composite good which is just the amount of money spent on all other goods (i.e. goods 2 and 3). Denoting “dollars” of composite good as q c we can write budget set as: 1. q c + p 1 q 1 ≤ m 2. p 2 q 2 + p 3 q 3 ≤ q c 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?

11 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.

12 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 qualifying “poor” households given $100 in food stamps. How do budget sets differ across two programs for a person earning $300/mo.?

13 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?

14 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?