# 1 Intermediate Microeconomics Budget Sets. 2 Consumer Theory Consumer Theory - a model to describe how individuals behave. How do individuals choose what.

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1 Intermediate Microeconomics Budget Sets

2 Consumer Theory 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 should we proceed?

3 Budget Sets What is the cost of purchasing another CD?

4 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, pizza a beer. {5,3} is a consumption bundle containing 5 slices of pizza and 3 beers. {20,1} is a consumption bundle containing 20 slices of pizza and 1 beer. Budget Set – the set of consumption bundles of goods a person can afford. What does an individual’s Budget Set depend on?

5 Budget Set Suppose you are endowed with \$24 (i.e. m = 24) and only goods you consume are pizza and beer. Pizza costs \$2/slice (i.e. p p = 2) Beers cost \$4/each (i.e. p b = 4) How can we fully describe your budget set? Analytically? Graphically? What if you lived in London and had £12 and Pizza cost £1/slice and Beers cost £2 each?

6 Graphing Budget Sets Slope of budget constraint is simply negative of price ratio (-p 1 /p 2 ) at that point. How do we interpret this? q1q1 q2q2 m/p 2 m/p 1 -p 1 /p 2 1

7 Graphing Budget Sets What happens when prices change? m = 24, p p = 4 and p b = 8 m = 24, p p = 4, and p b = 4 m = 24, p p = 2 and p b = 6

8 Graphing Budget Sets What happens when endowment changes but prices don’t? m = 40, p p = 2, and p b = 4 m = 16, p p = 2 and p b = 4

9 Budget Sets and Taxes Suppose m = \$24, p p = 2, and p b = 4 How would budget set change if a 50% sales tax were imposed on beer? How about if a 50% sales tax were imposed on all goods? How about if pizza was subsidized (i.e. CMC paid half the price of each slice)?

10 Is two-good framework sufficient? 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. Quotas. Bulk Pricing

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-1979 - 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 \$300/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 Goods and endowments can be thought of more broadly. Ex. Suppose you work for the Doctors Without Borders. Budget: \$10,000/mo. Each AIDS patient you treat costs \$1000/mo. Each Tuberculosis patient costs \$500/mo. What is your budget set? What does slope tell us? What happens if the drug company who makes the AIDS drugs drops their price to \$500/mo. for each treatment you buy in excess of 5?

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