1. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constraints We said that our understanding of Consumer Choice rests on the analysis of Preferences and Constraints. Let’s now turn to consider Constraints. X Y X max 0 Y max 1

2. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constraints We can represent a budget set and a budget frontier (or constraint) X Y X max 0 Y max 2 What equation can we give this constraint?

3. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constraints The equation tells us that if we spend all our money income, M, on X and Y, our spending be equal to: 3

4. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constraints Re-arranging, the equation for the budget constraint is: How do you interpret this equation? And Graphically? 4

5. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constraints The equation of the budget constraint: X Y X max 0 Y max 5

6. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constraints Given the position of the budget constraint, what will be the consumer’s choice of X and Y? This will depend on their preferences: X Y X max 0 Y max 6

7. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constrained choice Given the position of the budget constraint, what will be the consumer’s choice of X and Y? This will depend on their preferences: X Y X max 0 Y max IC 1 IC 2 IC 3 7

8. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constrained choice Given the position of the budget constraint, what will be the consumer’s choice of X and Y? This will depend on their preferences: X Y X max 0 Y max IC max 8

9. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Constrained choice So, by bringing together preferences and constraints, we have a model which predicts/explains the consumer’s choices (demands) for X and Y... given...? X Y X max 0 Y max X* Y* a 9

10. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Comparative Statics What will happen to the optimal choices of X and Y if there are changes to the parameters of the model? X Y X max 0 Y max X* Y* a What are the ‘parameters’? 10

11. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Comparative Statics What will happen to the optimal choices of X and Y if there are relevant changes to the parameters of the model? X Y X max 0 Y max X* Y* a Consider a change in money income. How do we show this? 11

12. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Change in money income X Y X max 0 Y max X* Y* a 12

13. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Change in money income X Y X max 0 Y max X* Y* a â What can you say about the demand for X as M↑? And the demand for Y? 13

14. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Change in money income X Y X max 0 Y max X* Y* a â What can you say about the demand for X as M↑? And the demand for Y? 14

15. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Change in money income X Y X max 0 Y max X* Y* a â What can you say about the demand for X as M↑? And the demand for Y? 15

16. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Change in money income X Y X max 0 Y max X* Y* a â What can you say about the demand for X as M↑? And the demand for Y? 16

17. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 Demand Analysis: Change in money income X Y X max 0 Y max X* Y* a â What can you say about the demand for X as M↑? And the demand for Y? 17

18. Robin Naylor, Department of Economics, Warwick Topic 1: Lecture 5 18 Now read B&B 4 th Ed., pp. 103-138 (but don’t worry about issues which go beyond what you have seen in lecture notes or seminar exercise sheets)