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Individual Choice Principles of Microeconomics Professor Dalton ECON 202 – Fall 2013 1 Models of Consumer Behavior Marginal Utility approaches • Ordinal analysis • Cardinal analysis • problem of handling complements and substitutes Indifference Curve approach • Ordinal utility • Handles complements and substitutes well 2 Terminology Warning! Economists use the terms value, utility and benefit interchangeably when speaking of individual choice. Marginal utility = Marginal value = Marginal benefit 3 Ordinal Analysis: Marginal Utility Alternative Uses for horses (in order of declining value) 1st 2nd 3rd 4th Pull plow Pull wagon Ride for farmer Ride for farmer’s wife Most valuable use of a horse Least valuable use of a horse 5th Ride for farmer’s children 4 Law of Diminishing Marginal Utility For all human actions, as the quantity of a good increases, the utility from each additional unit diminishes. 5 Ordinal Analysis: Marginal Utility Suppose the farmer owns three horses 1st 2nd 3rd 4th Farmer will use one Pull plow horse to pull plow, one Pull wagon horse to pull wagon, and Ride for farmer one to ride himself Ride for farmer’s wife 5th Ride for farmer’s children 6 Ordinal Analysis: Marginal Utility The farmer rides the “third” horse because the marginal benefit from riding the horse himself is greater than the marginal benefit from having his wife ride a horse. The marginal cost of his riding the horse is the foregone marginal benefit from his wife riding the horse. The marginal benefit from riding the horse himself is greater than the marginal cost of his riding the horse. 7 Cardinal Analysis: Marginal Utility Uses cardinal measure of utility Makes distinction between Total and Marginal utility “law of diminishing Marginal Utility” still holds Produces the Equimarginal rule and allows for utility maximization 8 Total utility [TU] is defined as the amount of utility an individual derives from consuming a given quantity of a good during a specific period of time. TU = f (Q, preferences, . . .) Utility TU Q TU 120 100 2 30 55 75 60 1 3 4 5 6 90 7 100 105 105 8 100 80 40 20 . 1 . 2 . 3 . . . . . TU 4 5 6 7 Q/t 9 Marginal Utility Marginal utility [MU] is the change in total utility associated with a 1 unit change in consumption. As total utility increases at a decreasing rate, MU declines. As total utility declines, MU is negative. When TU is a maximum, MU is 0. • “Satiation point” 10 Marginal Utility [MU] is the change in total utility [ΔTU] caused by a one unit change in quantity [ΔQ] ; MU = ΔTU ΔQ Utility DQ=1 DQ=1 DQ=1 Q TU 1 2 3 4 5 6 7 8 30 55 DTU=25 75 20 90 100 105 105 100 MU DTU=30 30 25 DTU=20 15 10 5 0 -5 The first unit consumed increases TU by 30. MU The 2nd unit increases TU by 25. 30 25 20 .. 10 .. 1DQ2 3 4 .. . MU 5 6 7 . Q/t The marginal utility is associated with the midpoint between the units as each additional unit is added. 11 Individual Choice If there are no costs associated with choice, the individual consumes until MU = 0, thereby maximizing TU. Typically, individuals are constrained by a budget [or income] and the prices they pay for the goods they consume. Net benefits are maximized where MU = MC; as long as the MU of the next unit of good purchased exceeds the MC, it will increase net benefits. 12 Individual Choice The individual purchases more of a good so long as their expected MU exceeds the price they must pay for the good: Buy so long as MU (MB) > MC; Don’t buy if MU (MB) < MC. The maximum net utility (consumer surplus) occurs where MU (MB) = MC. 13 Constrained Optimization Individual choices become a function of the price of the good, income, prices of related goods and preferences. QX = f (PX , I, PY, Preferences, . . . ) • • • • Where: PX = price of good X I = income PY = prices of related goods • “preferences” is the individual’s utility function 14 Consider an individual’s utility preference for 2 goods, X & Y; Utility X Qx 1 2 3 4 5 6 TUx MUx 30 55 30 25 75 20 90 7 100 105 105 8 100 15 10 5 0 -5 If the two goods were “free,” [ or no budget constraint], the individual would consume each good until the MU of that good was 0, 7 units of good X and 6 of Y. Once the goods have a price and there is a budget constraint, the individual will try to maximize the utility from each additional dollar spent. Utility Y Qy 1 2 3 4 TUy MUy 60 90 60 30 110 20 120 10 5 6 128 7 120 8 100 - 20 128 8 0 -8 15 Given the budget constraint, individuals will attempt to gain the maximum utility for each additional dollar spent, “the marginal dollar.” Utility X Qx 1 2 3 4 5 6 TUx MUx 30 55 30 25 75 20 90 7 100 105 105 8 100 15 10 5 0 -5 MUX PX 10. 8.33 6.67 5.00 3.33 1.67 0 For PX = $3, the MUX per dollar spent on good X is… For PY = $5, the MUY per dollar spent on good Y is… MUY PY Utility Y Qy 12 1 6 2 4 3 4 2 1.6 0 5 6 TUy MUy 60 90 60 30 110 20 120 10 7 128 128 120 8 0 -8 8 100 - 20 16 Given the budget constraint, individuals will attempt to gain the maximum utility for each additional dollar spent, “the marginal dollar.” Utility X Qx 1 2 3 4 5 6 TUx MUx 30 55 30 25 75 20 90 7 100 105 105 8 100 15 10 5 0 -5 MUX PX 10. 8.33 6.67 5.00 3.33 1.67 0 If the objective is PX = $3,utility the toFor maximize MUX prices, per dollar given spent on good preferences, and X is… spend each budget, additional $ on the For PY = $5, the good that yields MUY per dollar the greater utility spent on good for that Y is… expenditure. MUY PY Utility Y Qy 12 1 6 2 4 3 4 2 1.6 0 5 6 TUy MUy 60 90 60 30 110 20 120 10 7 128 128 120 8 0 -8 8 100 - 20 17 Constrained Optimization Budget = $30 MUX PX 10. 8.33 $3 $3 6.67 $3 $3 5.00 3.33 1.67 0 $3 if if MUX PX MUX PX >MU P Y Y , BUY X ! <P MUY , BUY Y ! Y Continue to maximize the MU per $ spent until the budget of $30 has been spent. MUY PY $5 $5 $5 12 6 4 2 1.6 0 18 Constrained Optimization If MUx/Px > MUy/Py then an additional dollar spent on good X increases TU by more than an additional dollar spent on good Y. If MUx/Px < MUy/Py then an additional dollar spent on good X increases TU by less than an additional dollar spent on good Y. 19 Constrained Optimization When the entire budget is spent, if MUx/Px > MUy/Py, then one should buy more X and less Y. When the entire budget is spent, if MUx/Px < MUy/Py, then one should buy less X and more Y. When the entire budget is spent, if MUx/Px = MUy/Py, then one has “maximized utility subject to the budget constraint”. 20 Constrained Optimization MUx/Px = MUy/Py is an equilibrium condition for individual choice. 21 MUX MUY subject to the constraint: = PX PY PX X + PY Y = I insures the individual has maximized their total utility and has not spent more on the two goods than their budget. This model can be expanded to include as many goods as necessary: MUX MUY MUZ = = = . . . . . . . = MUN PX PZ PY PN subject to PX X + PY Y + Pz Z + . . . + PN N = I 22 Constructing a Demand Curve From the information of utility maximization, given prices and income, one can construct a demand curve for a good by varying the price of that good, with other information held constant (ceteris paribus). 23 Given preferences, prices [PX = $3, PY = $5] and budget [$30], the individual’s choices were: MUX PX Five units of X and 3 units of Y were purchased 10. 8.33 $3 $3 6.67 $3 $3 5.00 3.33 1.67 0 $3 Graphically… PX . 5 4 PX = 3 MUY PY $5 12 $5 6 $5 4 This point lies on the demand curve for good X. 2 1 1 2 3 4 55 6 7 2 1.6 0 QX/t 24 MU MUXX Now, suppose the price of X [PX ] increases to $5. The MUx/Px falls, and now at the combination of 5 X and 3 Y, the MUx/Px < MUy/Py. There is now an incentive to buy less X and more Y. PPXX Choices about spending the $30 are now: [$3] [$5] 10. 6 8.33 5 $5 $5 6.67 4 5.00 3 $5 3.33 2 1.671 0 0 MUY PY PX 4 3 2 MUX PX = MUY PY . 5 1 Demand That portion of demand between $3 and $5 is mapped! 1 2 3 . 4 5 $5 12 $5 6 $5 4 At PX = $5, ceteris paribus, 3 units of X are purchased. 6 7 2 1.6 0 QX/ut 25 Demand By continuing to change the price of good X (and holding all other variables constant) the rest of the demand for good X can be mapped. All price and quantity combinations on the demand curve for X are equilibrium points, or points of maximized utility for the consumer. 26 By changing the price of the good and holding all Other variables constant, the demand for the good can be mapped. The demand function is a schedule of the PX quantities that individuals are willing 5 and able to buy at a 4 schedule of prices 3 during a specific 2 period of time, ceteris paribus. 1 1 2 3 4 5 6 7 QX/t 27 The demand function has a negative slope because of the income and substitution effects. Income effect: As the price of a good that you buy increases and money income is held constant, your real income decreases and you can not afford to buy as much as you PX could before. Substitution effect: As the price of one good rises relative to the prices of other goods, you will substitute the good that is relatively cheaper for the good that is relatively more expensive. 5 4 3 2 1 1 2 3 4 5 6 7 QX/t 28 Elasticity Elasticity - measure of responsiveness Measures how much a dependent variable changes due to a change in an independent variable Elasticity = %Δ X / %Δ Y • Elasticity can be computed for any two related variables 29 Price Elasticity of Demand Can be computed at a point on a demand function or as an average [arc] between two points on a demand function ep, h, e are common symbols used to represent price elasticity of demand Price elasticity of demand, ε, is related to revenue • “How will a change in price effect the total revenue?” is an important question. 30 Price Elasticity of Demand The “law of demand” tells us that as the price of a good increases the quantity that will be bought decreases but does not tell us by how much. The price elasticity of demand, ε, is a measure of that information “If you change price by 5%, by what percent will the quantity purchased change? 31 Price Elasticity of Demand ε ε= At a point on a demand function this can be calculated by: %DQ %DP QQ 2 2--Q Q1 1= D Q Q1 PP22-- PP11 = D P P1 = DQ Q1 DP P1 =(ΔQ/ΔP) x (P1/Q1) 32 using our formula, For a simple demand function: Q = 10 - 1P price quantity $0 10 $1 9 $2 8 $3 7 $4 6 $5 5 $6 4 $7 3 $8 2 $9 1 $10 0 ep 0 -.11 -.25 -.43 -.67 -1. -1.5 -2.3 -4. -9 undefined Total Revenue ε = DQ P1 D P * Q1 the slope is -1, price is 7 P71 DQ ε = (-1) * Q1 = -2.3 3 DP at a price of $7, Q = 3 Calculate Q=1 ε at P = $9 ε = (-1) 9 1 = -9 Calculate ε for all other price and quantity combinations. 33 For a simple demand function: Q = 10 - 1P price quantity $0 10 $1 9 $2 8 $3 7 $4 6 $5 5 $6 4 $7 3 $8 2 $9 1 $10 0 ep 0 -.11 -.25 -.43 -.67 -1. -1.5 -2.3 -4. -9 undefined Total Revenue 0 Notice that at higher prices the absolute value of the price elasticity of demand, ε, is greater. Total revenue is price times quantity; TR = PQ. Where the total revenue [TR] is a maximum, ε is equal to 1 9 16 21 24 25 24 In the range where ε< 1, [less than 1 or “inelastic”], TR increases as price increases, TR decreases as P decreases. 21 16 9 0 In the range where ε> 1, [greater than 1 or “elastic”], TR decreases as price increases, TR increases as P decreases. 34 Graphing Q = 10 - P, TR is a maximum where ep is -1 or TR’s slope = 0 Price When ε is -1 TR is a maximum. When | ε | > 1 [elastic], TR and P move in opposite directions. (P has a negative slope, TR a positive slope.) 10 The top “half” of the demand function is elastic. | ε | > 1 [elastic] ε = -1 When | ε | < 1 [inelastic], TR and P move in the same direction. (P and TR 5 both have a negative slope.) Arc or average ε is the average elasticity between two point [or prices] point ε is the elasticity at a point or price. TR |ε|<1 inelastic 5 10 Q/t The bottom “half” of the demand Price elasticity of demand describes function is inelastic. how responsive buyers are to change in the price of the good. The more “elastic,” the more responsive to DP. 35 Use of Price Elasticity Ruffin and Gregory [Principles of Economics, Addison-Wesley, 1997, p 101] report that: |ε| of gasoline is = .15 (inelastic) long run |ε| of gasoline is = .78 (inelastic) short run |ε| of electricity is = . 13 (inelastic) long run |ε| of electricity is = 1.89 (elastic) • short run • • • Why is the long run elasticity greater than short run? What are the determinants of elasticity? 36 Determinants of Price Elasticity Availability of substitutes • greater availability of substitutes makes a good more elastic Proportion of budget expended on good • higher proportion – more elastic Time to adjust to the price changes • longer time period means more adjustments possible and increases elasticity Price elasticity for “brands” tends to be more elastic than for the category 37