3. Demand and Behavior in Markets

1. 3. Demand and Behavior in Markets assume for now that perfectly competitive markets are given. How they arose will be discussed in part 4. properties of perf. comp. markets: • any agent can exchange as much of any good as desired at a fixed given price • anonymity: the identity of the agent does not matter • uniform pricing: no quantity discounts 3.1 Individual Maximization and Impersonal Markets • in markets with few agents, strategic bargaining is important • large, competitive markets are impersonal markets where consumers can be assumed to maximize utility taking prices as given

2. 3.2 The Problem of Consumer Choice • assume that a consumer has a fixed income, this determines the economically feasible set, the slope of the budget line is given by the relative prices of the goods • his preferences are represented by the shape of the indifferences curves • optimal consumption bundle where indifference curve is tangent to budget line, i.e. MRS = price ratio • quantity demanded of a good: the quantity he wishes to buy at a certain price questions: • how does the quantity demanded change with changes in relative prices and income? • How can we measure gains and losses of a consumer due to price changes?

3. 3.3 Income Expansion Paths • let the income increase, but prices remain constant  parallel shift of the budget line outward  this leads to a new optimal consumption bundle Income expansion path connects these optimal consumption bundles (Fig 3.2) 3.4 Inferior and Superior Goods Superior good:consumer demands more of this good if his income increases Inferior good: consumer demands less of this good if his income increases Note: whether a good is inferior or superior depends on his preferences, i.e. the shape of his IC’s (Fig 3.4) why is income expansion path not always a straight line? If consumption of two goods is increased proportionally, their MRS can change If there are only two goods, can both be inferior?

4. 3.5 Homothetic Preferences • A consumer has homothetic preferences if he increases his consumption of all goods proportionally as his income increases • consumes goods in fixed proportions independent of income, all goods are superior 3.6. Price-Consumption Paths • change the price of one good, but let the income and all other prices be constant • rotates budget line Price consumption path connect the optimal consumption bundles as this price is changes (Fig 3.6)

5. 3.7 Demand Curves Demand Curve represents the relationship between the quantity of a good demanded and its price (holding income and prices of other goods fixed) (Fig 3.7) 3.8 Demand and Utility Functions • nonconvex preferences imply that the consumer spends all his income on one good (Fig 3.8) this implies jumps in the demand curve • nonstrictly convex preferences, i.e. indifference curves with flat portions (MRS is constant) can lead to demand curves with flat portions  assuming strictly convex preferences makes analysis substantially easier in the following we study demand curves based on preferences that are strictly convex, nonsatiable, and selfish

6. How to derive the demand curve? (Appendix A) Consumer wants to maximize his utility u(x1,x2) given his budget constraint W=p1x1+ p2x2. We note that for the optimal consumption bundle MRS = price ratio, i.e. MRS = (U / x1) / (U / x2) = p1/p2 E.g. let u(x1,x2) = x1x2 then U / x1 = x2 and U / x2 = x1, hence MRS = x2 /x1 = p1/p2 Substitute x2 = x1 p1/p2 into the budget constraint W = p1x1+ p2 x1 p1/p2 = 2 p1x1 which yields the demand functions x1* = W/(2p1) and x2* = W/(2p2)

7. 3.9 Income and Substitution Effects Do demand curves necessarily slope downward, i.e. does consumption of a good always increase when its price decreases? If the price decreases, 2 things happen: (Fig 3.10) • the real income increases Income Effect this implies higher consumption if the good is superior • the relative prices change Substitution Effect if we eliminate the income effect after the price of good 1 decreases, i.e. we reduce income so that the consumer is on the same IC as before, then since good 1 has become cheaper relative to good 2, she will want to substitute good 1 for good 2 Substitution effect is always opposite to price change

8. 3.10 Normal Goods and Downward-Sloping Demand Curves • the income effect can be positive (superior good) or negative (inferior good) • if it is positive or negative but does not completely offset the substitution effect, the demand function is downward sloping (Fig 3.12) • Normal good: demand increases if price decreases 3.11 Giffen Goods and Upward-Sloping Demand Curves • if income effect overpowers substitution effect, the demand function is upward-sloping (Fig 3.13) • Giffen good: demand decreases as price decreases • example: basic cheap food components that take large share of income • Note: all Giffen goods are inferior, all superior goods are normal • A good can only “locally” be a Giffen good

9. 3.12 Compensated and Uncompensated Demand Curves Uncompensated demand curve: as above, substitution and income effect Compensated demand curve: theoretical demand curve where the income effect is removed by adjusting income so that utility stays constant (Figs 3.14, 3.15) 3.13 An Application of Consumer Analysis: work and leisure assume labor market is given, hours worked are exchanged for money (Fig 3.18) worker consumes two goods: leisure and money each hour of leisure has opportunity costs in the amount of money that could have been earned in that time consider effect of wage increase: substitution effect implies more work, but income effect implies less work, total effect is unclear (the same holds e.g. for tax cuts) Experimental Evidence: Taxi Drivers appear to follow this on a day-by-day basis, but do not optimize over more days

10. 3.14 Measuring Price Sensitivity of Demand elasticity of demand measures the percentage change in demand given a 1% change in price || > 1: demand is elastic || < 1: demand is inelastic || = 1: demand has unitary elasticity for linear demand (q=a-bp) hence for p large the demand is elastic and for p small the demand is inelastic perfectly inelastic demand: demand is independent of price, vertical line perfectly elastic demand: demand is 0 for all prices above some p and infinite for all prices below p, horizontal line

11. 3.15 The Slutsky Equation Slutsky Equation summarizes impact of price change on demand change let x1 be the change in quantity demanded of good 1 p1 change in price of good 1 B be change in income, then in terms of elasticities, divide by x1 / p1 first term: price elasticity of compensated demand, second term share of income spent on good 1, last term income elasticity of demand

12. 3.16 Properties of Demand Functions • If income and all prices are multiplied by the same constant, demand will be the same (no money illusion) • If preferences are represented by an ordinal utility function, the level of utility assigned to indiff curves is irrelevant (only order matters) • Budget exhaustion: nonsatiation implies that consumer will always spent whole income in terms of elasticities: let k1 and k2 be the shares of the incomes spent on goods 1 and 2, and 1 and 2 be the income elasticities of goods 1 and 2, then k1 1 + k2 2 = 1

13. 3.17 From Individual Demand to Market Demand In markets many buyers and sellers interact How to derive market demand from individual demand? Group all goods other than the one in focus into one composite good and consider its price as constant We can study demand for the good in two-dimensional graph Market demand curve is derived by adding up individual demand curves horizontally (Fig 3.26) Theoretical construction, because individual demand functions are not known Example: 3 consumers, demand functions D1 = 10 - p, D2 = 6 - 2p, D3 = 24 - 3p, i.e. they start consuming at p = 10, p = 3, and p = 8, respectively Hence market demand is DA = 0for p > 10, DA = D1 = 10 - p for 8 < p ≤ 10, DA = D1 + D3 = 34 - 4p for 3 < p ≤ 8, DA = D1 + D2 + D3 = 40 - 6p for p ≤ 3

14. 3.18 Expenditure Functions An expenditure functionE(p1,p2,u) identifies the minimal income necessary to provide a consumer with a utility u given prices p1,p2. This corresponds to finding the lowest budget line that meets the indiff. curve for utility level u. Obviously, the cost minimizing bundle is again one where the indiff. curve is tangent to a budget line

15. 3.19 Consumer Surplus provides a monetary measure of net gain of consuming a good at a certain price, and e.g. loss due to taxes consider composite good income that combines the amount of money spent on all other goods the MRS measures willingness to pay for an additional unit net gain is difference of WtP and price Consumer surplus corresponds to area between demand curve and price (Fig 3.28) Experimental Evidence: Disparity between Willingness to Pay and Willingness to Accept: • numerous experiments show an endowment effect, i.e. subjects request more money to give an object away than they are willing to pay for it exact CS should be measured with compensated demand curve, but CDC is impossible to measure and difference between measures is small

16. 3.20 Measures of Consumer Gain Effects of Price Changes on the Well-being of consumers can be measured in terms of changes in consumer surplus Price change causes consumer surplus to decrease in two ways: • the net gain on units still bought decreases • fewer units are bought (for downward sloping demand) Alternative measure: price-compensating variation: additional income needed to keep consumer at the same level of utility as before price change (Fig 3.33) 3.21 Price Compensation Variations and Expenditure Functions EF can be used to measure PCV: let price change from p1 to p1 +  than PCV = E(p1+ , p2,u) - E(p1, p2,u)