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Chapter Two Budgetary and Other Constraints on Choice.

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Presentation on theme: "Chapter Two Budgetary and Other Constraints on Choice."— Presentation transcript:

1 Chapter Two Budgetary and Other Constraints on Choice

2 Consumption Choice Sets u A consumption choice set is the collection of all consumption choices available to the consumer. u What constrains consumption choice? –Budgetary, time and other resource limitations.

3 Budget Constraints u A consumption bundle containing x 1 units of commodity 1, x 2 units of commodity 2 and so on up to x n units of commodity n is denoted by the vector (x 1, x 2, …, x n ). u Commodity prices are p 1, p 2, …, p n.

4 Budget Constraints u Q: When is a consumption bundle (x 1, …, x n ) affordable at given prices p 1, …, p n ?

5 Budget Constraints u Q: When is a bundle (x 1, …, x n ) affordable at prices p 1, …, p n ? A: When p 1 x 1 + … + p n x n m where m is the consumers (disposable) income.

6 Budget Constraints The bundles that are only just affordable form the consumers budget constraint. This is the set { (x 1,…,x n ) | x 1 0, …, x n and p 1 x 1 + … + p n x n m }.

7 Budget Constraints The consumers budget set is the set of all affordable bundles; B(p 1, …, p n, m) = { (x 1, …, x n ) | x 1 0, …, x n 0 and p 1 x 1 + … + p n x n m } u The budget constraint is the upper boundary of the budget set.

8 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 m /p 2

9 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 2 m /p 1

10 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Just affordable m /p 2

11 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Just affordable Not affordable m /p 2

12 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Affordable Just affordable Not affordable m /p 2

13 Budget Set and Constraint for Two Commodities x2x2 x1x1 Budget constraint is p 1 x 1 + p 2 x 2 = m. m /p 1 Budget Set the collection of all affordable bundles. m /p 2

14 Budget Set and Constraint for Two Commodities x2x2 x1x1 p 1 x 1 + p 2 x 2 = m is x 2 = -(p 1 /p 2 )x 1 + m/p 2 so slope is -p 1 /p 2. m /p 1 Budget Set m /p 2

15 Budget Constraints u For n = 2 and x 1 on the horizontal axis, the constraints slope is -p 1 /p 2. What does it mean?

16 Budget Constraints u For n = 2 and x 1 on the horizontal axis, the constraints slope is -p 1 /p 2. What does it mean? u Increasing x 1 by 1 must reduce x 2 by p 1 /p 2.

17 Budget Constraints x2x2 x1x1 Slope is -p 1 /p p 1 /p 2

18 Budget Constraints x2x2 x1x1 +1 -p 1 /p 2 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2.

19 Budget Constraints x2x2 x1x1 Opp. cost of an extra unit of commodity 1 is p 1 /p 2 units foregone of commodity 2. And the opp. cost of an extra unit of commodity 2 is p 2 /p 1 units foregone of commodity 1. -p 2 /p 1 +1

20 Budget Sets & Constraints; Income and Price Changes u The budget constraint and budget set depend upon prices and income. What happens as prices or income change?

21 How do the budget set and budget constraint change as income m increases? Original budget set x2x2 x1x1

22 Higher income gives more choice Original budget set New affordable consumption choices x2x2 x1x1 Original and new budget constraints are parallel (same slope).

23 How do the budget set and budget constraint change as income m decreases? Original budget set x2x2 x1x1

24 How do the budget set and budget constraint change as income m decreases? x2x2 x1x1 New, smaller budget set Consumption bundles that are no longer affordable. Old and new constraints are parallel.

25 Budget Constraints - Income Changes u Increases in income m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice.

26 Budget Constraints - Income Changes u Increases in income m shift the constraint outward in a parallel manner, thereby enlarging the budget set and improving choice. u Decreases in income m shift the constraint inward in a parallel manner, thereby shrinking the budget set and reducing choice.

27 Budget Constraints - Income Changes u No original choice is lost and new choices are added when income increases, so higher income cannot make a consumer worse off. u An income decrease may (typically will) make the consumer worse off.

28 Budget Constraints - Price Changes u What happens if just one price decreases? u Suppose p 1 decreases.

29 How do the budget set and budget constraint change as p 1 decreases from p 1 to p 1? Original budget set x2x2 x1x1 m/p 2 m/p 1 -p 1 /p 2

30 How do the budget set and budget constraint change as p 1 decreases from p 1 to p 1? Original budget set x2x2 x1x1 m/p 2 m/p 1 New affordable choices -p 1 /p 2

31 How do the budget set and budget constraint change as p 1 decreases from p 1 to p 1? Original budget set x2x2 x1x1 m/p 2 m/p 1 New affordable choices Budget constraint pivots; slope flattens from -p 1 /p 2 to -p 1 /p 2

32 Budget Constraints - Price Changes u Reducing the price of one commodity pivots the constraint outward. No old choice is lost and new choices are added, so reducing one price cannot make the consumer worse off.

33 Budget Constraints - Price Changes u Similarly, increasing one price pivots the constraint inwards, reduces choice and may (typically will) make the consumer worse off.

34 Shapes of Budget Constraints u Q: What makes a budget constraint a straight line? u A: A straight line has a constant slope and the constraint is p 1 x 1 + … + p n x n = m so if prices are constants then a constraint is a straight line.


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