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1 Intermediate Microeconomics Budget Sets

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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?

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

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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?

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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?

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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

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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

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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

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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)?

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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?

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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

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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.?

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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?

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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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Chapter 5 Constraints, Choices, and Demand McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Chapter 5 Constraints, Choices, and Demand McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

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