Section 01: customer Behavior

Utility

In this section, we space going to take it a closer look in ~ what is behind the need curve and the habits of consumers. Exactly how does a customer decide to spend his/her revenue on the plenty of different points that he/she wants, i.e., food, clothing, housing, entertainment? we assume the the score of the consumer is come maximize his/her level of satisfaction or joy, constrained through his/her income.

Economists usage the term utility as a measure up of satisfaction, joy, or happiness. Just how much satisfaction go a person gain from eating a pizza or city hall a movie? Measuring energy is based specifically on the preferences of the individual and also has nothing to do with the price the the good. Let’s do an experiment in utility.

Step 01: obtain some of her favorite candy, pastries, or cookies.

Step 02: take it a bite and also evaluate, on a scale from 0 come 100 (with 100 being the greatest utility), the level of utility from that bite. Document the marginal utility of that bite (i.e., just how much you gain from that one additional bite).

Step 03: Repeat step 02. That is important to be constant with every unit consumed, i.e., the exact same size and no drinking milk or water part means though. Once you operation out of liquid or your marginal utility goes to zero you have the right to stop.

You are watching: A consumer is maximizing her utility with a particular money income when:

Law the Diminishing Marginal Utility

The law of diminishing marginal utility says that as more of the an excellent is consumed, the extr satisfaction from one more bite will at some point decline. The marginal energy is the satisfaction acquired from each added bite. As more of the good is consumed, we obtain less added satisfaction indigenous consuming an additional unit. Thus also if a good were totally free and you could consume as lot as you wanted, there would certainly be a border to the lot you would certainly consume due to the regulation of diminishing marginal utility.

Summing the marginal utilities gives us the total utility. For example, let’s say the an initial chocolate to be an 85 and also the 2nd chocolate had actually a marginal energy of 79, then the full utility native consuming 2 chocolates is 164. The complete utility native consuming 3 chocolates is 85+79+73 = 237. As lengthy as ours marginal energy is positive our total utility increases although with diminishing marginal energy it boosts at a to decrease rate.

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Can marginal utility be negative? Yes. In ~ a vacation dinner, you might overeat and suffer native indigestion later on to a point where you regret having consumed too much, but at the time of the dinner, girlfriend expected better utility from eat the last of the meal. We would not willingly consume an object that provided us an unfavorable marginal utility. Climate why would certainly an individual stuff themselves during a warm dog eating dispute where clearly the last warm dogs consumed room making castle worse off? return the marginal utility from the last hot dog itself renders the human being worse off, the utility from to win the dispute is greater making the marginal utility positive.

The marginal utility of an item can change. For example, throughout a dryness water gives a high optimistic marginal utility, and with more rain the marginal utility declines. At part point, there is too lot rain, it turns from being a good utility come a poor one and the marginal energy of much more rain, as soon as it is currently flooding, is negative.

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Maximizing Utility

Utility values deserve to be figured out by an individual ranking his/her preferences from least wanted to most preferred. The result ranking or utility values are subjective or individual. Castle are likewise ordinal fairly than cardinal. Ordinal means that the energy values simply specify a ranking of preferences rather than an yes, really cardinal measurement.

Imagine a course has 10 college student in the class and also the teacher lined the college student up follow to height. He climate numbered them turn off according to height, assigning the shortest student a 1 and also the tallest college student a 10. Is it true that student number 4 is twice tall together student number 2? Of course not. Every we understand from the ranking is that student number 4 is taller 보다 student number 2. Now, imagine that in another class an additional teacher has additionally ranked 10 students according to height. Is that true that student number 10 from the 2nd classroom is taller 보다 student 1 native the first classroom? us cannot say due to the fact that the ranking is only valid in ~ a details course. In order to say a student is twice as high as an additional student or to have the ability to compare students between classes, we would need a cardinal measure up of height like inch or centimeters.

Since utility is ordinal and also not cardinal us cannot do interpersonal to compare of utility. Walk a rich person value a dollar much more or much less than a negative person? when some would certainly say the a negative person likely has much more unmet needs and also thus the would value the dissension more. The price is the it all relies on the preferences of the individuals. A poor person may prefer come live a an ext simplistic life and also place a reduced value on having actually an extra dollar 보다 a rich person who has actually a “love that money” (1 Timothy 6:10). We just cannot do such one interpersonal to compare of utility.

So how does the consumer decide what to purchase? Unfortunately every little thing has a price and also consumers only have actually so lot money come spend. Subsequently consumers try to spend the limited money they have on what will offer them the best amount that satisfaction. The decision dominance for energy maximization is to acquisition those items that provide the best marginal utility per dollar and are affordable or within the budget. Numerous grocery stores administer a tags that indicates the price per pound for the good. This allows consumers to compare the expense per lb for various brands or various sizes. The same concept is supplied for maximizing utility however we division the marginal energy by the price to get the marginal energy per dollar.

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Let’s speak that we eat only two goods: milk shakes and pizza whereby the price of each slice of pizza is $2 and also the price of every shake is $1 and we only have actually $11 come spend. Since the price the each great is various we need to divide the marginal energy by the price to allow for a common comparison. We then to compare the marginal energy per dollar because that pizzas verses shakes. Because that the very first unit the marginal energy per dissension of a shake is 50 contrasted to only 45 because that the pizza, so we would purchase the first shake. Us then to compare the marginal energy per dissension of the very first pizza (45) come the marginal utility per dollar of the 2nd shake (40) and purchase the an initial slice that pizza. If the marginal utility per dissension is the very same for the two goods and also we have income to purchase both then us would perform so, as watched in the second slice that pizza and the 2nd shake.

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We proceed to clues on budget on those goods that yield the highest possible marginal energy per dollar. In this example, we would purchase 4 slices or pizza and three milkshakes and spend our entire budget plan of $11. The total utility indigenous this acquisition would it is in the amount of the marginal utilities: 50 + 90 + 80 + 40 + 70 + 60 + 30 = 420. At the last items purchase the marginal utility per dollar invested on the two goods is the same, no other mix of pizzas and milk shakes will provide us higher utility provided our budget.

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Practice

Here is your opportunity to practice. Holly has $20 to invest on one of two people movies or bowling and wants to maximize her utility. Finish the table and determine how countless movies and rounds of bowling will certainly maximize she utility.

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Our first step is to divide the marginal energy of each item through the price. Through an earnings of $20 she is minimal in what she can purchase. Since the marginal utility per dollar because that bowling (15) is higher than the marginal utility of the very first movie (12.5) she would originally go bowling, spending $4. Compare the an initial movie (12.5) come the second round that bowling (10) she would go come the movie spending an additional $8 and a full of $12. The decision is a little harder. Holly has eight dollars still come spend and the marginal utility per dissension is the same for each good. If she choose the movie she will invest all eight dollars, however if she goes bowling she will spend 4 dollars and also still have four to spend. We have assumed the she desires to spend all she money and also gains no energy from stop the cash. Because she can not afford come buy one more movie however would instead by a third round the bowling, i beg your pardon only has actually a marginal utility per dissension of 7.5. Thus we view that come maximize her utility, she would acquisition one round of bowling and two movies giving her a total utility the (60 + 100 + 80) = 240. Recall ours decision preeminence is to have actually the marginal utility per dollar spent on the critical items it is in the exact same for every goods. In this case, we space unable to have that exactly however we shot to get as close together possible. Over there is no other combination that would provide us higher utility provided our income.

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Deriving Demand

Knowing exactly how the customer behaves allows us to derive a need curve. Stop say the Suzette eats either an apple or one orange as a snack. She has $12 to spend. Offered that every fruit costs two dollars, she will certainly maximize her utility by purchase 3 apples and 3 oranges. If we space looking in ~ the demand for oranges, this will offer us one point on the need curve. In ~ a price the $2.00, the amount demanded that oranges is 3.

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Recall that together we relocate along the need curve, the just thing that changes is the price of the an excellent (ceteris paribus or holding every else constant). If the price the oranges decreases come $1, the quantity of oranges demanded increases to 6.

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We can plot the 2 points and also create a demand curve because that oranges. At a price that $2 the quantity demanded is 3 and also at a price of $1 the quantity demanded is 6. Recall that the need curve reflects the marginal advantage or the willingness to salary of the consumer.

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The demand curve have the right to be seen in the diamond-water paradox. Why go water that is vital to sustain life expense so much less than diamonds that room atheistically pleasing, however are relatively unnecessary? Recall the price reflects the scarcity the a good. Overall, the it is provided of water is fairly abundant when the it is provided of diamonds is fairly limited. Thus the price we pay because that water is low contrasted to the price that diamonds.

Is the logical for someone who is maximizing his utility to purchase both water and diamonds? when deciding what to acquisition we compare the marginal utility split by the price. With several water consumption, the complete utility the water is very big but the marginal energy of the last gallon consumed is fairly low. Few diamonds space purchased therefore while the marginal utility is really large, say the diamond ring you just purchased for her future spouse, the complete utility is short since couple of diamonds room purchased.

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How companies React

Knowing that people experience diminishing marginal utility, exactly how do businesses react? recall that consumer surplus is the area listed below the need curve but above the price. Think of some instances of how businesses react given the law of diminishing marginal utility.

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One instance is the price every unit based upon package size. An ice cream cream store has three various serving size - a 6, 10, and 12 ounce cup. The price that the the smallest size, "Like It," is $4.29 or 71.5 cent per ounce. For just 32 cents more, one deserve to have four more ounces, "Love It," do the marginal expense per ounce 8 cents and the average expense per oz 46 cents. Upgrading come the "Gotta have actually It" size adds second two ounces with just 15.5 cent per ounce more and an average price per oz of just 41 cents. Absolutely the big size is cheaper per ounce, yet not everyone wants to eat that huge of a serving. Because that those only wanting a little serving, the store takes advantage of their greater willingness come pay for that part size. Even if it is its ice cream cream, eggs, milk, popcorn, or cereal, the is common practice to charge a greater price per unit for a smaller sized package size. Yet it payment for consumers to execute the math because businesses will certainly at times fee a higher price on the larger packages size. If customers believe that enlarge is constantly cheaper and also fail to do the math, they might get captured paying a higher price per unit.

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Services often follow a comparable pricing system with reduced average price for more frequent attendance. For example, below are the prices because that the “hopper pass” in ~ Disneyland. Ticket to sporting occasions follow a similar pricing approach with the per game price being lower if multiple games are purchased, such as the season pass.

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Consider this example. You room on a long airplane ride, seated beside an eccentric looking woman and a businessman. Halfway right into the flight, the woman claims to you and also the businessman, the she is an extremely rich and bored the flying. To break up the monotony, she offers you and also the businessman a chance to separation $5,000. The rules room as follows: the businessman makes an offer of exactly how to break-up the money and also you either expropriate or reject. If you accept, you get the agreed ~ above split. If girlfriend don’t, friend both obtain nothing. This is a one time offer. The businessman thinks and also offers the following break-up $4,995 for him and also $5 for you. Perform you expropriate or reject the offer? Why?

The answer come these concerns will vary among individuals. Some will accept stating castle have five dollars an ext than they did before. Others will reject the offer, saying the it is worth at least five dollars to them to refuse they businessman the $4,995. Remember that as soon as we talk around utility, it includes not only monetary items but likewise the nonmonetary.

In The concept of ethical Sentiments, Adam smith wrote: "How selfish soever male may it is in supposed, there are evidently some values in his nature which attention him in the luck of others and render their happiness crucial to him despite he derives nothing native it except the satisfied of seeing it.” mental that utility is acquired from plenty of different locations including service and also philanthropic acts.

Reference: http://www.econlib.org/Library/Enc/bios/Smith.html

Section 02: Indifference Curves and Budget Constraints

Indifference Curves

Indifference curves and also budget constraints allow for a an ext in-depth evaluation of demand. For modeling purposes we will certainly look at the two goods. An indifference curve shows the various combinations that the two goods that productivity the same level of utility, elevation of the price of the goods. Because of the legislation of diminishing marginal utility, the indifference curve in between the two products is convex come the origin. All combinations that the two products (pizza and shakes) that room on the indifference curve (A, B, and C) yield the exact same level the utility, say utility = 100. Having much more of good, returns a higher level of utility (combination D) and also having much less of the items yields a lower level of energy (combination E).

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An indifference curve map shows the household of indifference curves. There might be one infinite number of indifference curve that would reflect the level of utility at various combinations the the two goods. Just as a line on a topographical map suggests the various points that are at the exact same elevation, the various points follow me an indifference curve, show that same level that utility.

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Source: U.S. Geology Survey

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Marginal rate of Substitution

The marginal rate of substitution is the steep of the curve and measures the rate at i m sorry the consumer would be ready to give up one an excellent for the other while keeping the exact same level of utility. For this reason the marginal rate of substitution shows the ratio of marginal utilities between the two goods.

For example, at point A, the consumer would be willing to profession one shake for one additional slice that pizza. At point B, the consumer currently has a lot of pizza but couple of shakes so the marginal utility from secondary pizza is reasonably lower and also the marginal utility from the shake that would have to give up would certainly be relatively large, hence to maintain the very same level of energy he would have to get 3 pizzas to willingly offer up one fifty percent a shake.

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Since any mix of the two goods will only yield one level of utility at a particular point in time, indifference curves will never ever cross each other.

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Budget Constraint

The spending plan constraint shows the combine of the two goods that deserve to be purchased provided the consumer’s income and prices that the two goods. The intercept clues of the budget plan constraint are computer by dividing the revenue by the price the the good. For example, if the consumer had $8 come spend and also the price the pizza was $2 and also shakes to be $1, climate the consumer could buy 4 pizzas ($8/$2) or eight shakes ($8/$1). Any combination of the two products that are on or in ~ the budget plan constraint are affordable, while those come the external (farther from the origin) are unaffordable.

A higher income will cause a parallel shift rightward that the budget plan constraint if a diminish in revenue will reason a parallel change leftward.

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Changing the prices of the goods transforms the slope of the spending plan constraint. If the consumer’s earnings is $8 and the price of pizza is $2 and the price that shakes is $1, climate the spending plan constraint would be BC1. If the price that pizza drops come $1, climate the spending plan constraint would rotate out top top the x-axis to BC2. Alternatively, if the price of shakes increased to two dollars climate the spending plan constraint would come to be BC3.

The steep of the spending plan constraint is the an adverse ratio of the prices (-Px/Py). Because that example, provided the price that pizza (on the x-axis) is $2 and the price that shakes (on the y-axis) is $1, climate the steep of the budget plan constraint would be -2.

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Utlity Maximization

Given the goal of consumer is to maximize utility provided their budget constraints, they look for that combination of items that enables them to with the highest indifference curve given their budget plan constraint. This occurs whereby the indifference curve is tangent come the spending plan constraint (combination A). Note that combine B and also C cost the same amount as A; however, A is top top a greater indifference curve. Mix D returns that very same utility together C and also B but doesn’t use all of the income, therefore the customer can increase utility by spend more. Mix E is desired to mix A, however is unattainable provided the budget plan constraint.

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We aforementioned that utility is maximized whereby the marginal energy per dollar invested is the very same for each of the goods. At the suggest where the indifference curve is tangent to the spending plan constraint, the slope of the indifference curve i m sorry is the proportion of marginal utilities (-MUx/Muy) is same to the slope of the budget constraint (- Price x / Price y). This equation deserve to be rewritten to show that the marginal energy per dollar invested will it is in the exact same for both goods.

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The demand curve have the right to be acquired from the indifference curves and budget border by transforming the price of the good. For example, if the price the pizza is $4, the amount demanded that pizza is two. If the price the pizza decreases, the budget plan constraint i do not care flatter and the customer can purchase much more pizza, say the price the pizza drops come $2 and consumer to buy 4 units. If the price drops to $1.33, the quantity demanded boosts to 5. Plotting every of the price and also quantity inquiry points creates the need curve because that pizza.

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Income and Substitution Effects

When stating why the demand curve is downward sloping, us outlined the substitution effect and also income effect. We have the right to observe the alters in quantity demanded follow me the need curve due to the readjust in price; however, the indifference curves and also budget border can help us analyze the size of the income and also substitution effects.

For example, to speak the consumers revenue is $15 and the price of to apologize is $1 and also the price the oranges is $3. At this prices the consumer purchases six apples and three oranges. When the price the oranges falls to $1, the consumer purchases eight apples and seven oranges. For this reason on the need curve because that oranges, the consumer purchases 3 oranges once the price is 3 dollars and also seven oranges when the price is one dollar.

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Bringing the new budget constraint back to the initial indifference curve allows us to breakdown the income and also substitution effects. Because the steep of the budget constraint shows the proportion of prices, the substitution result is the rise in the variety of oranges that would be purchased provided the brand-new prices, while staying on the initial indifference curve the is relocating from point A to suggest B. The activity from allude B to point C is the revenue effect, the additional consumption of oranges due to the increased purchasing power. Through a diminish in the price that oranges, the family member price of apples has actually increased and also fewer apples would certainly be consumed because of the substitution effect; however, as result of increased to buy power, more apples space purchased as well as much more oranges.

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Recall from our elasticity conversation that the earnings elasticity for an inferior an excellent is negative. Because that example, as income rises the need for used garments decreases. Looking at second-hand garments on the x-axis, as the price decreases the substitution will be hopeful (movement from allude A to allude B); however, the income impact (movement native B to C) will certainly be negative.

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Extreme Cases

When evaluating indifference curves and also budget constraints, we have the right to look at a couple of extremes. One extreme instance would it is in if the two products are perfect complements. For example, you perform not get added satisfaction from having another right shoe, uneven you have a left shoes to go through it. In the situation of perfect complements, you constantly consume in ~ the minimum mix of the 2 goods.

Another too much is perfect substitutes. Girlfriend purchase file in one of two people the 100 or 200 sheet packs and only worth the variety of sheets. You space indifferent between having two one-hundred sheet packages or one two-hundred sheet package. In the situation of perfect substitutes, there are three different outcomes that will maximize utility. If the price of one package, returns a lower per sheet cost, the consumer will buy only that good, so consumption will take ar at one of the two intercepts. The third outcome is once the spending plan constraint has the very same slope together the indifference curve. In this case, any mix along the budget plan constraint will yield the exact same level of utility.

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Government Food Stamps Example

Why walk the government offer welfare recipients food stamps instead of cash? Why are food stamps marketed on the black industry for a discount? stop assume a person has actually $75 of income and also receives $75 the food stamps from the government. Because that simplicity, we will assume the the price of every unit that food and also the price of garments are each one dollar. The spending plan constraint permits the customer to purchase up come 150 devices of food, but because food stamps can only be offered to purchase food, the customer is minimal to only being able to acquisition 75 systems of various other items.

The quantity of food and other goods, the separation, personal, instance will acquisition depends top top the form of his indifference curve. Provided that the human being spends at the very least 75 dollars top top food, the is not constrained through receiving food stamps instead of cash.

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Unfortunately, because that those individuals with solid addictions, such as cigarettes or alcohol, your indifference curve reflect the greater value got from the addict substance. Because food stamps only use to to buy food, the customer is not able to obtain as much utility and also is minimal to allude A. If the food stamps had been in the kind of cash, the customer would have purchased 40 systems of food and 110 systems of alcohol, allude B, which would yield a greater level the utility.

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If the customer could convert a portion of the food stamps come cash, even at a discount, he would have the ability to reach a greater indifference curve. Assume the he can trade food stamps on the black market for 50 cents on the dollar i beg your pardon extends his budget plan constraint increasing the lot of alcohol that can be purchased. Selling food stamps in ~ a discount enables the customer to relocate to allude C, which yields a higher utility than suggest A.

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We can likewise model why people purchase items today and carry the debt on their credit transaction cards payment a high interest rate. Because that example, let’s say the price of each an excellent is $1. I think Will has actually $100 of revenue which he could spend this day or invest the money and also receive $150 in the future. By waiting, will would have actually a better purchasing power, yet his intake bundle will rely on his preferences. If he has a strong preference for having usage today, he would be ready to pay a greater price because that those goods today. The very same is true for those that buy items on credit. They space willing to salary the acquisition price plus every the interest, so the they deserve to have it this day (so the indifference curve touch the spending plan constraint in ~ a allude closer to the x-axis as viewed in the figure).

Similarly, some individuals are ready to pay to walk to the expensive theater to check out a movie once it is very first released. Others will wait till it pertains to the cheap theaters or even until that comes the end on DVD/Blu-ray. Although individuals are paying because that the “movie experience” and also not just the film itself, we deserve to see the time preferences of individuals and the price differentials in time (as represented by different placements that the indifference curves).