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 How do you know what goods you can choose to consume at any one time?

4 Budget Set Suppose you are endowed with $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 what combinations of peanuts and beer you can consume? Graphically? Analytically?

5 Budget Set Consumption Bundle – A list of numbers indicating how much of each good an individual is consuming: {q 1, q 2, …., q n } Budget Set – the set of consumption bundles of goods a person can afford to consume. Generally can be expressed by equation of form: p 1 q 1 + p 2 q 2 + … + p 3 q 3 ≤ m

6 Budget Set Ex: Suppose there are two goods, peanuts and beer. {50, 20} is a consumption bundle containing 50 oz. of peanuts and 20 oz of beer, {0,50} is a consumption bundle containing 0 oz. of peanuts and 50 oz of beer, {10,50} is a consumption bundle containing 10 oz. of peanuts and 50 oz of beer. If p p = 0.10, p b = 0.20, and m = 10, the budget set is 0.10q p q b ≤ 10 Is the bundle {50, 20} in your budget set? How about {0,50}? How about {10,50} ? What does it mean when the budget equation holds with inequality as opposed to equality?

7 Budget Set Interpreting prices As we will see, prices will play a big role in our analysis of consumer behavior. In our previous example, peanuts cost $0.10/oz, beer cost $0.20oz, and you had $10. Suppose you lived in London and were endowed with 5 pounds, Peanuts cost 5 pence/oz and Beer costs 10 pence/oz. How does this change your budget set? So what was the price of beer? How do you interpret the slope of budget set?

8 Graphing Budget Sets So slope of budget constraint is rise/run or simply negative of price ratio (-p 1 /p 2 ). Interpretation of slope: relative cost of good 1 in terms of good 2. q1q1 q2q2 m/p 2 m/p 1 p 1 /p 2

9 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

10 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

11 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?

12 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 two equation: 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?

13 More Complicated Budget Constraints Government policy can make budget constraints more complicated Food Stamps pre-1979 – qualifying poor households could get “50% off coupons” for up to $200 worth of food per month. post qualifying poor households given $100 in food vouchers. How do budget sets differ across two programs for a person earning $300/mo.?

14 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?

15 Budget Constraints more broadly Suppose you work 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?