1 Individual Choice Principles of Microeconomics Professor Dalton ECON 202 – Fall 2013

2  Marginal Utility approaches Ordinal analysis Cardinal analysis problem of handling complements and substitutes  Indifference Curve approach Ordinal utility Handles complements and substitutes well Models of Consumer Behavior

3  Economists use the terms value, utility and benefit interchangeably when speaking of individual choice. Marginal utility = Marginal value = Marginal benefit Terminology Warning!

4 Ordinal Analysis: Marginal Utility Alternative Uses for horses (in order of declining value) 1stPull plow 2ndPull wagon 3rdRide for farmer 4th Ride for farmer’s wife 5thRide for farmer’s children Most valuable use of a horse Least valuable use of a horse

5 Law of Diminishing Marginal Utility For all human actions, as the quantity of a good increases, the utility from each additional unit diminishes.

6 Ordinal Analysis: Marginal Utility Suppose the farmer owns three horses 1stPull plow 2ndPull wagon 3rdRide for farmer 4th Ride for farmer’s wife 5thRide for farmer’s children Farmer will use one horse to pull plow, one horse to pull wagon, and one to ride himself

7 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.

8  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 Cardinal Analysis: Marginal Utility

9 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,...) Q/t Utility Q TU TU TU

10  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” Marginal Utility

11 Marginal Utility [MU] is the change in total utility [ΔTU] caused by a one unit change in quantity [ΔQ] ; MU = Δ TU ΔQΔQ Utility Q TU MU  Q=1  TU=30 The first unit consumed increases TU by 30.. The marginal utility is associated with the midpoint between the units as each additional unit is added. 30  Q=1  TU= QQ The 2nd unit increases TU by  Q=1  TU= Q/t MU... MU

12  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. Individual Choice

13  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. Individual Choice

14  Individual choices become a function of the price of the good, income, prices of related goods and preferences.  Q X = f (P X, I, P Y, Preferences,... ) Where: P X = price of good X I = income P Y = prices of related goods “preferences” is the individual’s utility function Constrained Optimization

15 Utility X QxQx TU x MU x Utility Y QyQy TU y MU y Consider an individual’s utility preference for 2 goods, X & Y; 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.

16 Utility X QxQx TU x MU x For P X = $3, the MU X per dollar spent on good X is… Given the budget constraint, individuals will attempt to gain the maximum utility for each additional dollar spent, “the marginal dollar.” MU X PXPX For P Y = $5, the MU Y per dollar spent on good Y is… Utility Y QyQy TU y MU y MU Y PYPY

17 Utility X QxQx TU x MU x For P X = $3, the MU X per dollar spent on good X is… Given the budget constraint, individuals will attempt to gain the maximum utility for each additional dollar spent, “the marginal dollar.” MU X PXPX For P Y = $5, the MU Y per dollar spent on good Y is… Utility Y QyQy TU y MU y MU Y PYPY If the objective is to maximize utility given prices, preferences, and budget, spend each additional $ on the good that yields the greater utility for that expenditure.

18 MU X PXPX MU Y PYPY  $5  $3  $3  $3  $5 Continue to maximize the MU per $ spent until the budget of $30 has been spent.  $3  $5  $3 MU X PXPX < MU Y PYPY, BUY Y ! Constrained Optimization, BUY X ! MU X PXPX > MU Y PYPY if Budget = $30

19 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.

20 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”.

21 Constrained Optimization MUx/Px = MUy/Py is an equilibrium condition for individual choice.

22 P X X + P Y Y = I = MU X PXPX MU Y PYPY subject to the constraint: 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: = MU X PXPX MU Y PYPY = = = MU Z PZPZ MU N PNPN subject to P X X + P Y Y + P z Z P N N = I

23 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).

24 MU X PXPX MU Y PYPY Given preferences, prices [P X = $3, P Y = $5] and budget [$30], the individual’s choices were:  $5  $3    $5  $3  $5  $3 Five units of X and 3 units of Y were purchased Graphically… Q X /t PXPX P X = 5 This point lies on the demand curve for good X..

25 MU Y PYPY Q X /ut PXPX MU X PXPX [$3] Now, suppose the price of X [P X ] increases to $5. The MU x /P x falls, and now at the combination of 5 X and 3 Y, the MU x /P x < MU y /P y. There is now an incentive to buy less X and more Y. MU X PXPX [$5] Choices about spending the $30 are now:  $5      = MU X PXPX MU Y PYPY At P X = $5, ceteris paribus, 3 units of X are purchased.. Demand That portion of demand between $3 and $5 is mapped!

26  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. Demand

Q X /t PXPX By changing the price of the good and holding all Other variables constant, the demand for the good can be mapped. Demand The demand function is a schedule of the quantities that individuals are willing and able to buy at a schedule of prices during a specific period of time, ceteris paribus.

Q X /t PXPX Demand 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 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.

29 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

30 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,  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.

31 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?

32 ε  %  Q %  P At a point on a demand function this can be calculated by: ε = Q 2 - Q 1 Q1Q1 P 2 - P 1 P1P1 Q 2 - Q 1 =  Q P 2 - P 1 =  P =  Q Q1Q1  P P1P1 Price Elasticity of Demand =(ΔQ/ΔP) x (P1/Q1)

33 For a simple demand function: Q = P pricequantityepTotal Revenue $010 $19 $28 $37 $46 $55 $64 $73 $82 $91 $100 using our formula, ε =  Q P 1 Q1Q1 *  P ε =  Q P1P1 Q1Q1  P * the slope is -1, (-1) price is 7 7 at a price of $7, Q = 3 3 = Calculate ε at P = $9 Q = 1 ε = (-1) 9 1 = -9 Calculate ε for all other price and quantity combinations undefined

34 For a simple demand function: Q = P pricequantityepTotal Revenue $010 $19 $28 $37 $46 $55 $64 $73 $82 $91 $ undefined 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 In the range where  ε  < 1, [less than 1 or “inelastic”], TR increases as price increases, TR decreases as P decreases. In the range where  ε  > 1, [greater than 1 or “elastic”], TR decreases as price increases, TR increases as P decreases.

35 Q/t Price 10 ε = |  ε | > 1 [elastic] The top “half” of the demand function is elastic. |  ε | < 1 inelastic The bottom “half” of the demand function is inelastic. Graphing Q = 10 - P, TR TR is a maximum where e p is -1 or TR’s slope = 0 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.) When |  ε | < 1 [inelastic], TR and P move in the same direction. (P and TR 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. Price elasticity of demand describes how responsive buyers are to change in the price of the good. The more “elastic,” the more responsive to  P.

36 Use of Price Elasticity  Ruffin and Gregory [Principles of Economics, Addison-Wesley, 1997, p 101] report that: short run  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)  Why is the long run elasticity greater than short run?  What are the determinants of elasticity?

37 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