Handout+6a (2)

1 ECO101: Handout 6a Lecture Video 6.1 – Utility Maximization  When we combine the individual consumer’s preferences (represented by _______) and their constraints (represented by the _____), we can observe their optimal consumption bundle  To maximize utility, the optimal bundle must satisfy two conditions: o 1 st : it must be ____________ ; it must be _____________ to represent the entire income is spent. o 2 nd : it must achieve the highest level of _____________________________________________.  Graphically: we can plot ICs and the BL onto the same axis to see where both conditions are satisfied. Some things to remember:  Bundles A and B satisfy the _____ condition, but not the ______.  Bundles D and E satisfy the _____ condition, but not the ______.  Only Bundle C satisfies __________ conditions. q C q F Y/P C Y/P F BL 1 (Y, P C , P F ) IC 1 IC 2 IC 3 A B C D E slope of the IC _____ MRS _____ ࠵?࠵? ࠵? ࠵?࠵? ࠵? slope of the BL ___ | −࠵? ࠵? ࠵? ࠵? | ___ ࠵? ࠵? ࠵? ࠵? utility of IC 1 ____ utility of IC 2 ____ utility of IC 3 IC BL affordable on the BL slope Ice stop ofRL affodobe utiity forgery Carrion margin in a sun a arm p prices c c 1st 2 at U a UB C U 2 I go off odour L money ref aw both

2 Lecture Video 6.2 – Equal Margin Principle  Note that there is a ______________ between the IC and BL at Bundle C, which implies:  Called the __________________________ – another way to think about the tangency condition  Interpretation: the marginal utility derived from the last dollar spent on C _______________ the marginal utility derived from the last dollar spent on F  If ࠵?࠵? ࠵? ࠵? ࠵? = ࠵?࠵? ࠵? ࠵? ࠵? , you have _______________________. Why? There is no other way to reallocate your income that will increase your total utility Numerical example: P F = $1.50, P C = $2.25  1 st counter-example: suppose that at Point A, MU F = 5, MU C = 5 o Slope IC > Slope of BL o MRS > ࠵? ࠵? ࠵? ࠵? , or ࠵?࠵? ࠵? ࠵?࠵? ࠵? > ࠵? ࠵? ࠵? ࠵? , or ࠵?࠵? ࠵? ࠵? ࠵? > ࠵?࠵? ࠵? ࠵? ࠵? o Substituting in the numbers: ࠵?࠵? ࠵? ࠵? ࠵? ࠵?࠵? ࠵? ࠵? ࠵? o Current allocation of income at Point A: get more utility from the last dollar spent on F o Conclusion: too much _____ consumed, not enough ____. o Solution: give up _____ (MU C will ___________) and buy more _____ (MU F will __________). Recall diminishing MU:  As units consumed increases, the MU of additional units _________________.  As units consumed decreases, the MU of the last unit _________________. forgery scope of Ic cave Mrs mtg II Ppf atgtgat.in gsiopofBl Pg Mp p smart forgery Comoros egnormargin principle is equn to Mae invited unity g 3.33 25 2.22 c in one f f jeered TCF.IT Dt derren inverses

4 Lecture Video 6.3 – Deriving Individual Demand Individual demand curves (d) respond the same way as market demand curves (D): o The consumer ________________________ the curve when the price changes. o The demand curve ___________ when a third-variable (such as Y) changes. o Consider the following income values: Y 3 < Y 1 < Y 2 . q F P F P F1 P F3 P F2 F D F A F C q F Y 1 /P C1 q C Deriving the individual demand curve for F, where P F3 < P F1 < P F2 IC 2 IC 1 IC 3 Y 1 /P F2 Y 1 /P F1 Y 1 /P F3 F D F A F C C A C C C D When prices for goods change, individuals have to re-optimize, or pick alternate bundles that meet the two utility-max conditions. Consider the following price changes: P F3 < P F1 < P F2 Bundles A, D and C are ____________________________. When prices change, the line that connects all utility maximizing bundles is called a _____________________________________ because it reflects price changes.  Bundles A, D , and C are also part of the individual’s _____________________ curve, which tells you that all points on the individual demand curve are ___________________________.  However, not all points on the demand curve provide the same level of utility! Utility levels ___________________ as you move down along the demand curve.  Consider the units of food contained in each of the bundles: _________________, so it follows that _____________________. D A C 00 Prie consumption Con Pcc gym O demand unity not 236 Fpl FACE UD CUA LU must D O

5 Decomposing the Response to a Price Change Lecture Video 6.4 – Substitution Effect In the earlier graph, we demonstrated how the individual responded to the _____________ in the price of F (from Bundle A to Bundle C). Although we show this response as a one-step change, in reality, there are two separate forces as work. They occur simultaneously, but we will discuss them sequentially to understand how each force impacts the individual’s consumption bundle. To decomposing the total change from Bundle A to Bundle C into two separate effects, we introduce Point B as the decomposition bundle. It enables us to identify which part of the total change is attributed to the SE and which part of the total change is attributed to the IE. Substitution effect addresses the how the consumer responds to a change in the ___________ ____________ of the two goods, measured as: Bundle B – Bundle A = SE  What does it capture: how the individual shifts ___________ from consuming the relatively more expensive good (C), and substitutes ____________ the relatively cheaper good (F).  Requires: Bundles A and B to stay on the same IC to show the individual is enjoying the ___________ level of utility.  How this is represented graphically: stay on the same IC, but allow the individual to select another bundle which contains ________________ to account for the new P F .  Specifically: Point B should share the same slope as the new budget line ࠵? ࠵?2 ࠵? ࠵? , where ࠵? ࠵?2 ࠵? ࠵? < ࠵? ࠵?1 ࠵? ࠵? .  This ensures the 2 nd condition of utility maximization is satisfied since Bundle B will be at the point of ________________ between IC 1 and the _______________ BL, or CBL (slope of CBP = slope as BL 3 = ࠵? ࠵?2 ࠵? ࠵? ). q F Y 1 /P C1 q C IC 1 IC 3 BL 3 BL 1 C Y 1 /P F3 Y 1 /P F1 A F C F A Jeroen Ipr Pi footie prices off by any towarrs Some more F tongan composes IE Fp CBL

7 Lecture Video 6.6 - Slope of Demand Curves From the individual demand curves drawn, you can see that the shape of the curve depends on the type of good.  Demand curves for normal goods are negatively-sloped and relatively __________. o _________ the SE and IE cause the individual to ↑ q d when P F ↓. o A small decrease in price leads to _________ increases to q d .  Demand curves for inferior goods are negatively-sloped and relatively __________. o The SE causes the individual to buy more of the good when P F ↓, but th e IE causes the individual to ↓q d , _________________ some of the SE. o A small decrease in price leads to a relatively ____________ increases in q d .  Demand curves for Giffen goods are positively-sloped. o The SE causes the individual to buy more of the good when P F ↓, but th e IE causes the individual to ↓q d , more than _________________ the SE. o A small decrease in price leads to a _______________ decrease in q d . o Notice P and q d are positively correlated, resulting in an upward-sloping demand curve. Lecture Video 6.7 – From Individual to Market Demand  To derive the market demand curve (D), simply sum up the individual demand curves (d) for all consumers in a market.  Start with a simple market where only 3 consumers participate: you, Mickey and Minnie. o Sum up q d for all consumers at a single price point → enables you to create a demand __________________, from which you can plot a market demand curve.  As additional consumers enter the market, the number of goods demanded at every price point increase, which _________ the mkt D curve to the right. flat loom large Step off setting snow off selling Praga loop Secetan Shift

8 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 30 Price Q demanded Market demand curve From Individual Demand to Market Demand 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 8 9 10 Price q demanded Your demand curve 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 8 9 10 Price q demanded Mickey's demand curve 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 8 9 10 Price q demanded Minnie's demand curve Price You Mickey Minnie Market $2.50 2 4 1 7 $2.00 3 5 3 11 $1.50 4 6 5 $1.00 5 7 7 19 $0.50 6 8 9 23 d d d D Is

Substitution and Income Effects Charlie only consumes donuts and coffee and has the utility function U(C, D) = CD and an income of $24. The marginal utility derived from donuts is MU D = C and the marginal utility derived from coffee is MU C = D. Initially, the price of coffee (P C ) is $1 and the price of donuts (P D ) is $2. Then the price of donuts increases to $3 while the price of coffee remained at $1. What is Charlie’s initial utility maximizing bundle? Final utility maximizing bundle? D C First conditor is it or tie BL P P D Y DC DD 24 0 2nd conation tangency between IC BL slope of Ic mens Ttt 53mg casino E E 95 Slope of BL 13 7 cross maripy 212 1 Sore for 10712 12 C Sore for c by subsinig into Sore for C 1 21 etc I can let I 2 29 6 12 Sortor D by page into 12 217 24 uniting Mae Buon A 125617 5 s

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Are donuts and coffee normal, inferior or Giffen goods? SE IE for CoD SE Buon 13 Burne A Cofe SE CB la 4 12 2 IE C 27 TE 1 pours SE 9 a 6 I I m look ar te income even Ppr y parang pone h Fees 12s wearer for c IE 2.7 Jars buying is for D I n e a eco for by tho hero Y d by use of C D are drongos

ECO101: Solutions to Crowdmark Problem (Module 6) Suppose you are given the following information: ࠵?(࠵?, ࠵?) = ࠵? 1 2 ࠵? 1 2 ࠵?࠵? ࠵? = ࠵? 1 2 2࠵? 1 2 ࠵?࠵? ࠵? = ࠵? 1 2 2࠵? 1 2 We derived the MRS together before you worked on the Crowdmark problem: ࠵?࠵?࠵? = ࠵?࠵? ࠵? ࠵?࠵? ࠵? = ࠵?࠵? ࠵? × 1 ࠵?࠵? ࠵? = ࠵? 1 2 2࠵? 1 2 × 2࠵? 1 2 ࠵? 1 2 = 2࠵? 1 2 ࠵? 1 2 2࠵? 1 2 ࠵? 1 2 = ࠵? ࠵? Using the MRS derived for you: ࠵?࠵?࠵? = ࠵?࠵? ࠵? ࠵?࠵? ࠵? = ࠵? ࠵? a. Determine the initial utility-maximizing bundle when ࠵? ࠵? = $2, ࠵? ࠵? = $4, ࠵? = $120 Tangency condition: ࠵?࠵? ࠵? ࠵?࠵? ࠵? = ࠵? ࠵? ࠵? ࠵? → ࠵? ࠵? = 2 4 . Cross multiplying: 2࠵? = 4࠵? ࠵? = 2࠵? ࠵? = 1 2 ࠵? ࠵? ࠵? ࠵? + ࠵? ࠵? ࠵? = ࠵? ࠵? ࠵? ࠵? + ࠵? ࠵? ࠵? = ࠵? 2࠵? + 4࠵? = 120 2࠵? + 4࠵? = 120 2(2࠵?) + 4࠵? = 120 2࠵? + 4 ( 1 2 ࠵?) = 120 8࠵? = 120 4࠵? = 120 ࠵? = 15 ࠵? = 30 b. Determine the new utility-maximizing bundle when the Price of B falls to ࠵? ࠵? = $3 Note: ࠵? ࠵? and ࠵? have not changed. Tangency condition: ࠵?࠵? ࠵? ࠵?࠵? ࠵? = ࠵? ࠵? ࠵? ࠵? → ࠵? ࠵? = 2 3 . Cross multiplying: 2࠵? = 3࠵? ࠵? = 3 2 ࠵? ࠵? = 2 3 ࠵? ࠵? ࠵? ࠵? + ࠵? ࠵? ࠵? = ࠵? ࠵? ࠵? ࠵? + ࠵? ࠵? ࠵? = ࠵? 2࠵? + 4࠵? = 120 2࠵? + 3࠵? = 120 2 ( 3 2 ࠵?) + 3࠵? = 120 2࠵? + 3 ( 2 3 ࠵?) = 120 6࠵? = 120 4࠵? = 120 ࠵? = 20 ࠵? = 30 Note: Usually, it is not important how you assign the goods to the axis (vertical vs horizontal), as long as you remain consistent about which good variable appears in the numerator and which appears in the denominator. where I assigned Good A on the horizontal axis and Good B on the vertical axis. **See note at the bottom about this.** First conairon 2A 27 12 PaAtPaB Y I 2A 413 120 0 Second contion A 3 I Gota 12 Au B 5 1 8 up g 1513,30A 13 13 1 21 313 120 13 3 2 331 12 24 3 A B 41 120 A2 313 30 1 604313 12 i 307,2 R III

ECO101: Handout 6c Suppose an individual with the utility function ࠵?(࠵?, ࠵?) = ࠵?࠵? must decide how to allocate their income of $72 across Good X and Good Y when the initial price of Good X is $9 and Good Y costs $1. Later, the price of Good X falls to $4, while the price of Good Y does not change (remains at $1). • First, find the initial (Bundle A) and final (Bundle C) utility-max combination of X, Y. • Then calculate income effect (IE) and substitution effect (SE) when the price of Good X falls to $4 by solving for the decomposition bundle (Bundle B) Step 1: Calculate the Initial Consumption Basket (Point A) Utility-max must satisfy two conditions Step 2: Calculate the Final Consumption Basket (Point C) Is condition BL 9 14 72 2h2 Contino Max may Parp 4 91 9114 2 9143 4 2 184 72 36 4 72 4 36 Bunter 11 4 4 36 1st confirms 4 11 22 2nd Corrao D 7 22 4 4 Ulta ez 8 72 36 7 22 7 31 Bunter X 9,4 32

Step 3: Calculate the Decomposition Bundle (Point B) Step 4: breakdown the total effect = SE + IE UA UB 4 36 Up 144 413 X BAY Mu Glyn ran X ut 144 413 29 4712 144 Bunker 72 31 11 6 4 24 43 6 SE A toB Subsiture towns he rewriting Cheaper good goes from D 701 8 consumer 2 orisons units of k when led fion 9 t 154 IE BI C Refreasinisce in purchasing power Joes from 22 6 to 1 9 can Supion inner by 3 urns of x i concrate that good X is a norm good bereece consumption Minot Lion Gto a ants or Dc when considering IF Jpa y Borsa Moran good bears it indeed from 2n unis in Buse B to 36 hors in Burren c

ECO101: Practice Problem Set 6 1. The rule of equal marginal utility per dollar spent suggests that consumers maximize utility by a. equalizing marginal utility across goods and services. b. equalizing the marginal utility per dollar spent across goods and services. c. maximizing the marginal rate of substitution. d. minimizing the marginal utility per dollar spent across goods and services e. consuming goods and services until marginal utility is zero. Refer to the graph below for Questions 15 – 16. Debra travels to Mexico and enjoys burritos and Coronas. The diagram below shows her utility-maximizing choices. 2. If the budget line is line 1, describe why point A is Debra's utility-maximizing choice. (Select all that apply.) a. At point A, ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? = ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? . b. At point A, marginal rate of substitution is equal to the relative prices of the two goods. c. At point A, ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? = ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? . d. At point A, ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵? = ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? .

3. Using the graph below (where X, Y and Z represent utility maximizing consumption bundles), determine the cause of the consumer’s move from point Z to point X. a. An increase in the price of milk. b. A decrease in the price of bread. c. A change in the consumer’ preferences towards milk. d. An increase in the price of bread. e. A decrease in nominal income. 4. (continuation of Practice Problem Set 5, Questions 26-29; you may need to refer to your answers there to answer this question) Given Katie ’s monthly budget constraint, she would choose bundle ____ to maximize her utility. a. H b. B c. C d. G e. I Bundle Ice Cream Cones Magazines A 9 0 B 7 2 C 6 2 D 6 3 E 4 4 F 4 3 G 3 4 H 1 7 I 0 6 a 4 6 36 3 0 12 36 in 18 2 3 6 in 36 36