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Ch 2: Budget Constraint

Ch 2: Budget Constraint. Part I. 1. Consumers will always choose the best bundle of goods they can afford. What we mean by “ afford ”?. 2. Assumptions. 2 goods: X, Y Consumption Bundle (X,Y): The amount consumed of both goods 2 prices: Px, Py

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Ch 2: Budget Constraint

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  1. Ch 2: Budget Constraint Part I 1

  2. Consumers will always choose the best bundle of goods they can afford. • What we mean by “afford”? 2

  3. Assumptions • 2 goods: X, Y • Consumption Bundle (X,Y): The amount consumed of both goods • 2 prices: Px, Py • The amount of money to spend on 2 goods: m • The budget constraint: m ≥ Px X + Py Y 3

  4. (Px X) is the amount of money spent on good X • (Py Y) is the amount of money spent on good Y • Affordable consumption bundle: consumption bundle that cost less than, or equal to m, or Px X + Py Y ≤ m 4

  5. Assume now that (Y) is all other goods the consumer might want to consume: “Composite Good” Think of good (Y) as the amount of $ that the consumer is spending on other goods • Therefore, (Py =1), and the budget constraint: m ≥ Px X + Y 5

  6. The amount of money spent on good X, plus the amount spent on all other goods, (Y), must be NO more than m. 6

  7. Properties of the Budget Set • The budget line is the set of bundles that cost exactly m: Px X + Py Y = m These are the bundles of goods that just exhaust the consumer’s income 7

  8. The Budget Set m/Py m/Px 8

  9. Properties of the Budget Set • The budget line is the set of bundles that cost exactly m: Px X + Py Y = m Py Y = m – Px X Y = (m/Py) – (Px/Py) X Intercept: (m/Py) Slope: - (Px/Py) 9

  10. If x=0, then spend m on y m/Py m/Px 10

  11. If x=0, then spend m on y m/Py m/Px 11

  12. The Budget Set Budget line: Slope = -(Px/Py) m/Py m/Px 12

  13. Properties of the Budget Set • The budget line is the set of bundles that cost exactly m: Px X + Py Y = m Py Y = m – Px X Y = (m/Py) – (Px/Py) X Intercept: (m/Py) Slope: - (Px/Py) 13

  14. The slope of the BL measures the rate at which the consumer is Willing to substitute good X for Y m/Py m/Px 14

  15. If the consumer is going to increase consumption of good X by (∆X), m/Py m/Px ∆X 15

  16. How much of good Y have to change (∆Y) in order to satisfy the budget constraint? m/Py ∆Y m/Px ∆X 16

  17. PxX + PyY = m --- (1) Since consumption is changing by ∆X and ∆Y PxX+ Px∆X + PyY + Py ∆Y = m, or Px(X+ ∆X) + Py(Y+ ∆Y) = m --- (2) Subtracting (1) from (2) Px(X+ ∆X) + Py(Y+ ∆Y) - PxX + PyY = m –m Px ∆X + Py ∆Y = 0 The total value of the change in consumption must be zero 17

  18. Which is the slop of the budget line! ∆Y = - (Px /Py) ∆X ∆Y / ∆X = - Px/Py, 18

  19. The slop is negative since consumingmore of X means less of Y “Opportunity cost” ∆Y = - (Px /Py) ∆X ∆Y / ∆X = - Px/Py, 19

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