Chapter 4: Individual and Market Demand • Extends individual theory of consumer demand • Start with individual’s budget constraint/indifference curve analysis to show how quantity of good changes as price changes. • Steps: • 1. Start at single U-max. • 2. Show es in PF es in QF • 3. Price-Consumption Curve • 4. Individual Demand Curve • 5. See Figure 4.1.
Individual’s Demand Curve: 2 Properties • 1. As move down D curve, level of attainable utility increases because a P implies an in purchasing power. • *Utility es as move down D Curve. • 2. As move down D curve and PF is , MRS is falling too. • Why? Each pt on D curve comes from U max, where MRS=-PF/PC; so when PF falls, MRS falls too. • Explain using MRS = MUF/MUC.
Effect of Income on Quantity of Food • Goal: Link es in income to shifts in the Demand Curve. • Steps: • 1. Start at single U-max. • 2. Show es in I es in QF • 3. Income-Consumption Curve • 4. Shifts in Individual D Curve • 5. See Figure 4.2.
Review Link Between Income and QF • Key: Income-Consumption Curve shows points on different demand curves. • If have : I associated with D curve shifting to right for the two goods on both axes Income-Consumption Curve slopes upward AND the goods are normal goods and income elasticity of demand is positive.
More on Income and Consumption • Inferior Good: Income consumption . In this case, if this inferior good on vertical axis: Income-Consumption curve slopes downward. • Income-Consumption curve can be backward-bending (See Figure 4.3.) • Engel Curve: shows relationship between income and consumption for a specific good. (See Figure 4.4.) This curve can also be backward-bending.
Substitutes versus Complements • If PA DB, then the two goods are substitutes. • Review: PA QD of good A (Law of Demand), DB ) • If PA DB, then the two goods are complements. • Relate to price-consumption curve: • If slopes up: complements. • If slopes down: substitutes.
Exercise • Considering two goods C and F, with C on the vertical axis. Sketch indifference curves and budget constraints, showing two different levels of income. 1. Is the slope of the income-consumption curve positive or negative if both F and C are normal goods? Show. 2. Is the slope positive or negative if F is normal and C is inferior? Show. 3. With only two goods, can both goods be inferior in the same income range? Why or why not?
Decomposing Full Effect of PA on QA • Consider a Price: • 1) relative prices: now one good relatively less expensive so individual will substitute away from other goods to this good. Substitution Effect • 2) This P is an in real purchasing power: Like an Income so buy more of all normal goods. Income Effect
Show Decomposition Graphically • Start with Substitution effect: show the substituting by allowing price line to change slope but keeping utility fixed (so stay on original indifference curve). This new b.c. is just temporary one to show this effect. • Then Income effect: Allow pure change I as a shift of this new temporary budget line up to higher indifference curve. Shows the increased utility from the increased income.
Further Details • From this Price Food: • Substitution Effect ALWAYS leads to Food due to convexity of indifference curves. Pure relative prices with no Income. • Income Effect: If good is normal, income causes consumption. For normal good: income effect is positive. (This positive means the P like a I, which causes QF)
More Details • Total Effect = Subst Effect + Income Effect. • Subst Effect usually large. • Could have negative income effect if good is inferior (means increase income causes decrease demand). But still get downward sloped Demand Curve. • Giffen good: Theoretical case of negative income effect dominating the substitution effect. This violates the Law of Demand.
Exercise • Consider two normal goods X and Y with good X on the horizontal axis. • 1. Sketch and label a graph showing an initial U-max bundle of X and Y. • 2. Now a 10% sales tax is imposed on good X so there is an increase in the price of X. • A. Graph the income and substitution effects. • B. Label completely.
Example: Gas Tax w/Rebate • Why tax gasoline? • 1) taxes raise revenues for govt. • 2) gas tax consumption of gas by altering relative prices. • Concern about gas tax: any tax on such a necessity tends to be regressive (low-income individuals pay higher % of income on the tax). • See Figure 4.9: first impose tax; then add in the rebate.
Market Demand Curve • Derive market demand curve from set of individual demand curves. • Horizontal Summation: At each price, add together the quantity demanded by each individual. • This market demand curve can be for an entire market or some sort of sub-market. • Example: market for home computers can be divided into sub-markets, such as households with young children, etc. • See Table 4.2 and Figure 4.10
EP and Total Revenue • Review price elasticity of demand: • EP = % QD resulting from a 1% P • = P/Q * Q/P • Issue: When price changes by 1%, what happens to the total expenditures on the good? (same as TR = total revenue = P * Q) • Starting Point: Law of Demand: Whenever P goes up, Q goes down. • Issue is BY HOW MUCH does Q go down?
More on EP and TR • Inelastic Demand: EP 1 • Q relatively unresponsive to P • When P by 1%, Q 1% • So when P, Q no fall very much, so TR = P*Q too. • See example. • Elastic Demand: EP 1 • Q very responsive to P • So P leads to TR. • See Example.
Example • Family buys 1,000 gallons of gas per year at P = $1/gallon. • EP = -0.5. • Interpret EP = 1% P causes a 0.5% Q. • Total Revenue = TR = P * Q • TR = $1 * 1,000 = $1,000. • Now P to $1.10, a 10% . • SO: Causes a 5% Q, down to 950 gallons. • New TR = $1.10 * 950 = $1045. • See that TR has .
Exercise • Family buys 100 lbs chicken/yr • P = $2/lb and EP = -1.5. • What is total expenditures? • Now P to $2.20/lb. • What % is this? • What is new Q? • What is new total expenditures?
Isoelastic Demand • ‘Iso’ means same. • Isoelastic: when EP is the same along the entire Demand curve (so this curve is not straight). • Special case is Unitary Isoelastic demand curve, where EP = -1 along entire curve. • With unit elastic D curve: TR is the same at each P,Q combination • See Figure 4.11
More on EP • Point elasticity: defined as EP at a specific point. We use this. • EP = P/Q * 1/slope • So if the demand curve is straight line, 1/slope is same number. Can calculate EP for specific value of P,Q (like at equilibrium values) • But usually think of measuring EP over a specific portion of D curve. This leads to uncertainty: which P,Q combination to use? • Arc Elasticity is alternative measure • = AvgP/AvgQ * 1/slope.
Consumer Surplus • Important concept that will re-occur repeatedly throughout this course! • Definition: the difference between what a consumer is willing to pay and what she actually pays. • Two basic components: • Demand Curve reveals willingness to pay for each Q. • We assume single market P
Aggregate Consumer Surplus • The triangle formed by the demand curve and the price line: the area under the demand curve but above the price line. • To measure the area of a triangle: • AREA = ½ * base * height.
Exercise • Two individual consumers for one firm’s long-distance services; each indiv. with own D curve: • Indiv. A: Q = 40 – 0.5P • Indiv. B: Q = 120 – P • Q = # minutes long distance calls; • P = cents/minute = 20 cents; (P=20). • 1. Draw each Demand curve and its corresponding equilibrium price line. • 2. Calculate CS for both; calculate firm’s total revenue. • 3. If firm adds $10/month flat fee plus per/minute, what is new TR?