Part 4 The Theory of Demand

1. Part 4The Theory of Demand • We have drawn all our demand curves downward sloping • Why do economists think demand curves normally slope downward? • Market demand curves are aggregations of individual (or household) demand curves • What factors will affect a household’s demand for a good?

2. Household Consumption Choices • Households buy a variety of goods (a “bundle” of goods) • Different households buy different bundles of goods • Household choice will depend on: - income - relative prices of goods - preferences • Income and prices can be shown in a budget constraint • What shapes preferences? • How can a given set of preferences be represented?

3. Budget Constraint Qy Unaffordable Affordable Qx Budget constraint with given income = I and given prices Px and Py: I = PxQx + PyQy

4. Preferences and Utility • Which of the affordable combinations will a household choose to purchase? • The intuitive answer is that the household will choose the bundle of goods that it “likes the best” or provides the most satisfaction of all the affordable bundles • More formally, if the degree of satisfaction of all wants and desires can be measured on a single “utility” scale, the household will choose the bundle of goods that maximizes utility

5. Cardinal Utility Theory • When the idea of a utility measure was first proposed in economics it was sometimes assumed that one could think of units of utility in the same way as units of weight or temperature • Such a measure has a defined unit that can be added, multiplied, & etc • Many possible units of measure but they are all linear transformations of each other (eg: deg F = 32 + 9/5 C)

6. Total and Marginal Utility • More goods give more total utility • More of any particular good will tend to give less additional total utility with each increment • Diminishing marginal utility • Diminishing marginal utility and the “paradox of value” • What is the rule for maximizing total utility out of a given budget when each good has diminishing marginal utility?

7. Maximizing Utility Example of two goods x and y Utility maximizing bundle with an income Of $6 and Px and Py= $1? Utility maximizing bundle with an income $16 and Px=$3 and Py=$2

8. Maximizing Utility • The total utility gained from a given budget will be maximized where the budget is all spent and marginal utility per dollar spent is equalized across all goods • Rules for a utility maximum: I=PxQx+PyQy and MUx/Px = MUy/Py or MUx/MUy = Px/Py

9. Implications • Maximization is where I=PxQx+PyQy and MUx/Px = MUy/Py • Fall in Px will increase ability to purchase X and Y. If X is normal Qx increases. • Fall in Px leads to a substitution of X for Y • Increase in Qx decreases MUx • Decrease in Qy increases MUy

10. Individual and Market Demand • Market demand curves are the horizontal summation of the demand curves of all individuals or households

11. Ordinal Utility Theory • The idea of utility as measurable in a cardinal way was subject to much criticism • The idea of a utility measure as a rank ordering replaced the idea of cardinal measurement • An “ordinal” measure is a ranking only. • No unit of measurement • Higher numbers imply only more preferred

12. Preferences If both X and Y provide utility Qy Definitely Preferred to A: U>5 Y’ Definitely Less preferred to A: U<5 Bundle A: X’,Y’ U=5 Qx X’

13. Indifference Curves A locus of all bundles with the same utility ranking. The consumer is indifferent between them Qy Indifferent between any point on U=5 U>5 (preferred to Any point on U=5) U<5 (any point on U=5 preferred) U=5 Qx

14. A Preference Map Qy d c a U=6 b U=5 Qx

15. Preference Maps • In order to draw a preference map at all we are assuming: • goods are infinitely divisible (indifference curves are continuous) • Every combination of goods can be ranked (preferences are complete) • Preferences are consistent (indifference curve cannot intersect or touch)

16. The Shape of Indifference curves • Negative slope (more is preferred to less) • Marginal rate of substitution (MRS) • Convex to the origin (diminishing marginal rate of substitution) • MRS=ΔQy/ΔQx keeping utility constant—slope of the indifference curve

17. Maximizing Utility Once Again • In the ordinal utility context maximizing utility means choosing that bundle of goods that is on the highest indifference curve achievable with given income and prices • Budget line: I = PyQy+PxQx PyQy = I- PxQx Qy = I/Py – (Px/Py)Qx I/Py is the Y intercept Px/Py is the slope of the budget line

18. Budget line Qy I/Py I = PyQy+PxQx I/Px Qx Px/Py is the slope of the budget line

19. Utility Maximization:Indifference Curves Qy Highest indifference curve achievable Qy* U=6 U=5 U=4 Qx* Qx Budget line and indifference curve are tangent. On budget line and highest indifference curve where MRS=Px/Py

20. Changes in Income • Changes in income with constant prices will shift the budget line outwards in a parallel fashion • Normal goods will show increased consumption with higher income • Inferior goods will show decreased consumption with higher income • Consumer preferences determine if a good is normal or inferior (shape of indifference curves)

21. Income Effect Qy I” X and Y normal I’ Income consumption line U” U’ Qx Qx’ Qx” Qy X inferior, Y normal U” I” I’ U’ Qx Qx” Qx’

22. Changes in Price • Change in the price of X changes the slope of the budget line by changing the X intercept Qy Px’>Px” I/Py Qx I/Px” I/Px’

23. Price Effect and Demand Curves Qy Budget line with Px’ Budget line with Px” U” U’ Qx Qx’ Qx” Px Px’ Px” Demand curve for X Qx Qx’ Qx”

24. Income and Substitution Effects of a Price Change • The effect of a price change on the demand for a good can be decomposed into two effects • The substitution effect is the effect of the change in relative prices keeping real income (utility) constant • The income effect is the effect on real purchasing power of the price change

25. Income and Substitution Effects of a Price Change Qy Overall effect (a to b) can be broken down into a substitution and income effect a b s Qx’ Qx” Qxs Qx Sub Inc

26. Income and Substitution Effects of a Price Change • Income effects of a price change are usually small--unless the good accounts for a high proportion of expenditure • For normal goods the income effect works to reinforce substitution effect and a price decline must increase quantity demanded • For inferior goods the income effect works against the substitution effect, but the substitution effect is usually larger

27. Income and Substitution Effects of a Price Change • What does it take to get an upward sloping demand curve? The “Giffen” good case • Giffen goods must be both inferior and important in the budget • Very unlikely to come across a Giffen good • Policy uses of income and substitution effects--carbon taxes and income tax rebates