Chapter 6 Demand

1. Chapter 6 Demand Course: Microeconomics Text: Varian’s Intermediate Microeconomics

2. Introduction • In Chapter 5, we talk about the optimal choice under the budget constraint. • Here, we consider how the changes of exogenous variables affect decisions. • Recallendogenous variables: quantities of goods x1, x2exogenous variables: prices and income.

3. Own-Price Changes • Consider the two-good case. • Denote the ordinary demand functions as x1*(p1,p2,m), x2*(p1,p2,m). • How does x1*(p1,p2,m) change as p1 changes, holding p2 and m constant? • Suppose only p1 increases, from p1’ to p1’’ and then to p1’’’.

4. Own-Price Changes Fixed p2 and m. x2 p1x1 + p2x2 = m p1 = p1’ x1

5. Own-Price Changes Fixed p2 and m. x2 p1x1 + p2x2 = m p1 = p1’ p1= p1’’ x1

6. Own-Price Changes Fixed p2 and y. x2 p1x1 + p2x2 = m p1 = p1’ p1=p1’’’ p1= p1’’ x1

7. Own-Price Changes Fixed p2 and y. p1 = p1’ x1*(p1’)

8. p1 Own-Price Changes Fixed p2 and m. p1 = p1’ p1’ x1* x1*(p1’) x1*(p1’)

9. p1 Own-Price Changes Fixed p2 and m. p1’’ p1’ x1* x1*(p1’) x1*(p1’’) x1*(p1’) x1*(p1’’)

10. p1 Own-Price Changes Fixed p2 and m. p1’’’ p1’’ p1’ x1* x1*(p1’) x1*(p1’’’) x1*(p1’’) x1*(p1’’’) x1*(p1’) x1*(p1’’)

11. p1 Own-Price Changes Ordinarydemand curvefor commodity 1 Fixed p2 and m. p1’’’ p1’’ p1’ x1* x1*(p1’) x1*(p1’’’) x1*(p1’’) x1*(p1’’’) x1*(p1’) x1*(p1’’)

12. p1 Own-Price Changes Ordinarydemand curvefor commodity 1 Fixed p2 and m. p1’’’ p1’’ p1 price offer curve p1’ x1* x1*(p1’) x1*(p1’’’) x1*(p1’’) x1*(p1’’’) x1*(p1’) x1*(p1’’)

13. Own-Price Changes • The curve containing all the utility-maximizing bundles traced out as p1 changes, with p2 and y constant, is the p1- price offer curve. • The plot of the x1-coordinate of the p1- price offer curve against p1 is the ordinary demand curve for commodity 1.

14. Ordinary Goods • A good is called an ordinary good if the quantity demanded of it always increases as its own price decreases and vice versa (negatively related), holding all other factors, such as prices, income and preference constant.

15. Ordinary Goods Fixed p2 and y. Downward-sloping demand curve x2 p1 p1 price offer curve Û Good 1 isordinary x1* x1

16. Giffen Goods • If the quantity demanded of a good decreases as its own-price decreases and vice versa (i.e. positively related) holding all other factors constant, then the good is called a Giffen Good. • Note: we need to hold other factors constant. Thus, if the price change is also associated with change in income or preference, then even if there’s a positive relation between price and quantity, it is not characterized as Giffen good.

17. GiffenGoods Demand curve has a positively sloped part Fixed p2 and y. x2 p1 p1 price offer curve Û Good 1 isGiffen x1* x1

18. Own–Price Changes– Perfect Complements • What does a p1 price-offer curve look like for a perfect-complements utility function?

19. Own-Price Changes– Perfect Complements

20. Own-Price Changes – Perfect Complements With p2 and y fixed, higher p1 causessmaller x1* and x2*. As As

21. Own-Price Change—Perfect Complements x2 Fixed p2 and y. x1

22. p1 Perfect Complement Fixed p2 and y. x2 p1 = p1’ y/p2 p1’ x1* ’ x1 ’

23. p1 Perfect Complement Fixed p2 and y. x2 p1 = p1’’ p1’’ y/p2 p1’ x1* x1

24. p1 Perfect Complement Fixed p2 and y. p1’’’ x2 p1 = p1’’’ p1’’ y/p2 p1’ x1* ’’’ x1

25. p1 Perfect Complement Ordinarydemand curvefor commodity 1 is Fixed p2 and y. p1’’’ x2 p1’’ y/p2 p1’ x1* x1

26. Own Price Changes – Perfect Substitutes • What does a p1 price-offer curve look like for a perfect-substitutes utility function?

27. Own-Price Changes – Perfect Substitutes and

28. p1 Perfect Substitutes Fixed p2 and y. Fixed p2 and y. x2 p1 = p1’ < p2 p1’ x1* x1

29. p1 Perfect Substitutes Fixed p2 and y. Fixed p2 and y. x2 p1 = p1’’ = p2 p1’ x1* x1

30. p1 Perfect Substitutes Fixed p2 and y. Fixed p2 and y. x2 p1 = p1’’ = p2 p1’ x1* x1

31. p1 Perfect Substitutes Fixed p2 and y. Fixed p2 and y. x2 p1 = p1’’ = p2 p2 = p1’’ p1’ x1* x1

32. p1 Perfect Substitutes Fixed p2 and y. Fixed p2 and y. p1’’’ x2 p2 = p1’’ p1’ x1* x1

33. p1 Perfect Substitutes Ordinarydemand curvefor commodity 1 Fixed p2 and y. Fixed p2 and y. p1’’’ x2 p2 = p1’’ p1 price offer curve p1’ x1* x1

34. Inverse Demand Function • Usually we ask “Given the price for commodity 1 what is the quantity demanded of commodity 1?” • But we could also ask the inverse question “At what price for commodity 1 would a given quantity of commodity 1 be demanded?” • Taking quantity demanded as given and then asking what must be price describes the inverse demand function of a commodity.

35. Inverse Demand Function p1 Given p1’, what quantity isdemanded of commodity 1?Answer: x1’ units. p1’ x1* x1’

36. Inverse Demand Function p1 Given p1’, what quantity isdemanded of commodity 1?Answer: x1’ units. The inverse question is:Given x1’ units are demanded, what is the price of commodity 1? Answer: p1’ p1’ x1* x1’

37. Cross-Price Effects • If an increase in p2, holding p1 constant, • increases demand for commodity 1 then commodity 1 is a gross substitute for commodity 2. • reduces demand for commodity 1 then commodity 1 is a gross complement for commodity 2.

38. Gross Substitutes and Complements • Substitutes: if the price is higher for one good, you turn to buy other goods to give you satisfaction. E.g. drinks: bubble tea vs fruit juice; entertainment: movie vs magazine. • Complements: things tend to be used together so when one of the prices increases, the demand for the other will decrease.E.g.: camera and memory cards

39. Cross-Price Effects A perfect-complements example: so Therefore commodity 2 is a gross complement for commodity 1.

40. Cross-Price Effects p1 Increase the price ofgood 2 from p2’ to p2’’and p1’’’ p1’’ p1’ x1*

41. Cross-Price Effects p1 Increase the price ofgood 2 from p2’ to p2’’and the demand curve for good 1 shifts inwards-- good 1 is acomplement for good 2. p1’’’ p1’’ p1’ x1*

42. Cross Price Effect • For perfect substitutes, how will the quantity demanded x1 change when p2 increases? • Note: it only changes the point where x1 starts to be positive.

43. Cross-Price Effects p1 Generally, an increase the price of good 2 from p2’ to p2’’ and the demand curve for good 1 shifts outwards-- good 1 is asubstitute for good 2. p1’’’ p1’’ p1’ x1*

44. Income Changes • How does the value of x1*(p1,p2,m) change as m changes, holding both p1 and p2 constant?

45. Income Changes Fixed p1 and p2. m’ < m’’ < m’’’

46. Income Changes Fixed p1 and p2. m’ < m’’ < m’’’ x2’’’ x2’’ x2’ x1’ x1’’’ x1’’

47. Income Changes Fixed p1 and p2. m’ < m’’ < m’’’ Incomeoffer curve x2’’’ x2’’ x2’ x1’ x1’’’ x1’’

48. Income Changes • A plot of income against quantity demanded is called an Engel curve.

49. Income Changes Engelcurve; good 2 y Fixed p1 and p2. m’’’ m’’ m’ < m’’ < m’’’ m’ Incomeoffer curve x2’’’ x2’ x2* y x2’’ x2’’’ m’’’ Engelcurve; good 1 x2’’ m’’ x2’ m’ x1’ x1’’’ x1’ x1’’’ x1* x1’’ x1’’

50. Income Changes p1 When income increases, the curve shifts outward for each give price, if the good is a normal good. p1’’’ p1’’ p1’ x1*