<7.1 UTILITY>

--7.1.1 TOTAL & MARGINAL UTILITY--

--INTRODUCTION--

Economists have long been interested in the way that consumers behave. Aspects of demand theory were introduced earlier in Chapter 2. For the demand curve, it was assumed that it could be derived from data collected for the demand schedule. Here we shall look behind the demand curve and explore why it really is the case that consumers buy more of a good when its price falls. A relevant starting point is the notion of utility. This idea dates back to the nineteenth century and is a term used to record the level of happiness or satisfaction that someone receives from the consumption of a good. Th e concept assumes that this satisfaction can be measured, in the same way that the actual units consumed can be calculated. Two important measures are:

--TOTAL UTILITY--

TOTAL UTILITY refers to the overall satisfaction that is derived from the consumption of all units of a good over a given time period.

--MARGINAL UTILITY--

MARGINAL UTILITY refers to the additional utility derived from the consumption of one more unit of a particular good. So, if someone gets ten units of satisfaction from consuming one bar of chocolate and 15 units aft er consuming two bars, then the marginal utility is five units.

--7.1.2 DIMINISHING MARGINAL UTILITY--

The marginal utility gained from the consumption of a product tends to fall as consumption increases. For example, if you buy an ice cream you will get a lot of satisfaction from consuming it, especially in hot weather. If you consume a second one, you will still get some satisfaction, but this is likely to be less than from the fi rst ice cream. A third ice cream will yield even less satisfaction.
This aspect of consumer behaviour is referred to as the law of diminishing marginal utility. As consumption increases, there may actually come a point where marginal utility is negative, indicating dissatisfaction or disutility.

--TASK--

1 Table 7.1 below shows the total utility gained from the consumption of lemonade in a week.

Quantity consumed (bottles) Total utility

0 0

1 20

2 35

3 45

4 53

5 58

6 54

7 48

Table 7.1

a Calculate the marginal utility as the quantity consumed increases.

b Sketch the total utility and marginal utility curves (put utility on the vertical axis, quantity consumed on the horizontal axis).

2 If the price of lemonade increases from $1 to $2 per bottle, how might it affect consumption? Explain your answer using the data above.

3 Comment on how confident you are on the answer you have provided to question 2.

--7.1.3 EQUI-MARGINAL PRINCIPLE--

--HOW TO MAXIMISE UTILITY? [SINGLE GOOD]--

If a consumer is only interested in a single good then total utility is maximised when MU = 0, however it is unlikely that you will ever consume up to this quantity as the good will likely have a price and the consumer will likely have a budget, as such they will consume the goods in descending marginal utility rates until their budget doesn't allow anymore.
- - - E.g I have $20, and a pizza slice costs $10 each, my utility for the first slice is worth $18, so I buy the 1st slice, leaving me with $15, my utility for a second slice is now $15 so I buy another slice leaving me with $0, even though my utility for a 3rd slice is $12 and greater than the price I am restrained by my budget.

--UTILITY MAXIMISATION [TWO GOODS + SAME PRICE]--

In reality a consumer does not just deal with a single good (with a single set of diminishing marginal utilities) nor a single price but a multitude. As such they will need to look at MU per $, rather than simply MU, to decide which goods to buy.
TWO GOODS, SAME PRICE:
- - - In this case, the consumer will simply rank the items in descending order of MU and choose accordingly until our budget constraint is reached
TWO GOODS, DIFFERENT PRICES:
- - - In this case, consumers can't simply rank them in descending order of MU as now we have different prices, as such it could be the case that a unit of a good derives double the MU than another good, but it is three times more expensive, meaning that they would gain more utility from buying three of these goods. Hence to incorporate different prices we need to use MU per $ spent.
    - Once we have ranked the units by this metric we an again start choosing the items in descending order until our budget constraint is reached.
    - Now this leads to an important principle related to demand, if the price rises the MU per $ obviously falls, making alternative goods more attractive in terms of MU per $ and this leading to the consumer 'switching away' and Qd falling (Law of demand).

So how do they maximise their utility?
When we go to supermarket to buy goods, ideally we want to maximise our total utility given our financial budget right? In other words we need to consider both the marginal utility along with the price of the good right? But how do we know when this occurs?
Well we can use the 'EQUI-MARGINAL PRINCIPLE', which states that TOTAL UTILITY WILL BE MAXIMISED WHEN THE MARGINAL UTILITY PER DOLLAR of EACH GOOD is EQUAL
WHY IS THIS THE CASE? Well, if all goods share the same MU then the next dollar you spend
Hower once we intriduce a budget then it is not always possible to maximise utility only maximise up to the budget.

The law of diminishing marginal utility that is applied only in the case of a single commodity, states that as more and more commodities are consumed, the marginal utility derived from each successive unit goes on diminishing. But in real-life situations, a consumer normally consumes more than one type of commodity. Therefore, in the case of two commodities, the law of equi-marginal utility is applied which helps consumers to optimally allocate their income. The law of equi-marginal utility states that a consumer will attain equilibrium when the ratio of marginal utility of one commodity to its price is equal to the ratio of the marginal utility of another commodity to its price.

basically says we should rank each item by its marginal utility per $, and then purchase as many goods as possible within our budget choosing the item with the highest MU per $ first and so on.
This will ultimately end with the
once the MU$ for good A is equal to the MU$ for good B, then the consumer will be indifferent and the TU can increase no more
, to lowest until the budget is reached.
Why MU PER $ and NOT MU?
Clearly
when will a consumer maximise their utility? How do we maximise our utility when there are so many goods at different prices to choose from?
Firstly its important to acknowledge that
Given a choice between two goods both priced equally at $10, with the first unit of Good A yielding MU of 100, and the first good of Good B yielding MU of 50, if you had a budget of $10, which would you choose to maximise your utility? Good A of course as this would get 10 utils per $ as opposed to only 5 utils per dollar.
Given a choice between two goods both priced equally at $5, with the first unit of Good A yielding MU of 100 and the 2nd unit yielding 75, and the first good of Good B yielding MU of 50, and the 2nd unit if you had a budget of $10, which would you choose to maximise your utility? Cleary you would buy the first two units of Good A as they yield the most utility and stays within your budget.

Would you buy one good that yields 100 utils or 2 goods that each yield 75 utils? clearly tou would

We DO NOT CHOOSE TO CONSUME THE GOOD WITH THE HIGHEST MU, WE CHOOSE TO CONSUMER THE GOOD WITH THE HIGHEST MU PER $, WHY?

Let's look at this example:

- - - Imagine we have a budget of $10 what combination of goods will maximise your total utility?
      - Good A, $4, 60, 50, 40, 30
        Good B, $2, 55, 52, 49, 46, 43
        Now at first glance you may choose ABBB, yielding 60+55+52+49 = 216 utils, however this doesn't make sense as you could get more utils from consuming BBBBB which yields 245 utils, so it is important to work out MU PER DOLLAR, then make our selections
        Good A 15, 12.5, 10, 7.5
        Good B 27.5, 26, 24.5, 23, 21.5
        Clearly BBBBB is the best choice for a rational utility maximising consumer.

This example shows how a consumer chooses each item in turn until the utility is maximised and it is IMPOSSIBLE TO SWITCH TO OTHER GOODS in order to get any additional utility.
This conculsion is called the equimarginal principle and can be summarised using this equation:

We can see above that the MU per $ of good A was 60/4 = 15

In order to maximize utility (for a given fixed income) a consumer needs to consider each subsequent dollar that they spend, as they want to CHOOSE THE UNIT OF THE GOOD THAT GIVES THEM THE HIGHEST LEVEL OF MARGINAL UTILITY PER DOLLAR
In other words they need to to rank the level of satisfaction derived per dollar, from each additional unit of good they consume, so that they can compare and switch expenditure accordingly, choosing the unit of the good that yields the highest utils per dollar first and so on, until the total spend reaches the fixed income (budget).
Clearly as the goods are ranked the level of MU/$ of each good should eventually be the same (or close), meaning the following is true at maximum utility levels:
M
Only then can you see how many of each item will be purchased in order to maximise utility.
This will occu when
If we consider a consumer who only ever wants one good and the budget is $10, then
Obviously In other words when it is not possible to switch any expenditure from, say, product A to product B to increase total utility. This is referred to as the equimarginal principle and can be represented as:
In other words when the marginal utility per dollar per dollar of each good is the same then it isn't possible to switch between them to derive any more utils, and thus you are at maximum utility.

Once we work out the MU per $ for each unit we can start our selections up to our budget.

Selection 1: We choose our fisrt unit of Coke

Go to the sites below and read about the equimarginal principle, then use it to explain why

--UTILITY MAXIMISATION [TWO GOODS + TWO PRICES]--

TWO GOODS, DIFFERENT PRICES:
- - - - In this case, consumers can't simply rank them in descending order of MU as now we have different prices, as such it could be the case that a unit of a good derives double the MU than another good, but it is three times more expensive, meaning that they would gain more utility from buying three of these goods. Hence to incorporate different prices we need to use MU per $ spent.
        Once we have ranked the units by this metric we an again start choosing the items in descending order until our budget constraint is reached.
        Now this leads to an important principle related to demand, if the price rises the MU per $ obviously falls, making alternative goods more attractive in terms of MU per $ and this leading to the consumer 'switching away' and Qd falling (Law of demand).
    - wHEN THE MU/$ is equal the consumer

So how do they maximise their utility?
When we go to supermarket to buy goods, ideally we want to maximise our total utility given our financial budget right? In other words we need to consider both the marginal utility along with the price of the good right? But how do we know when this occurs?
Well we can use the 'EQUI-MARGINAL PRINCIPLE', which states that TOTAL UTILITY WILL BE MAXIMISED WHEN THE MARGINAL UTILITY PER DOLLAR of EACH GOOD is EQUAL
WHY IS THIS THE CASE? Well, if all goods share the same MU then the next dollar you spend
Hower once we intriduce a budget then it is not always possible to maximise utility only maximise up to the budget.

basically says we should rank each item by its marginal utility per $, and then purchase as many goods as possible within our budget choosing the item with the highest MU per $ first and so on.
This will ultimately end with the
once the MU$ for good A is equal to the MU$ for good B, then the consumer will be indifferent and the TU can increase no more
, to lowest until the budget is reached.
Why MU PER $ and NOT MU?
Clearly
when will a consumer maximise their utility? How do we maximise our utility when there are so many goods at different prices to choose from?
Firstly its important to acknowledge that
Given a choice between two goods both priced equally at $10, with the first unit of Good A yielding MU of 100, and the first good of Good B yielding MU of 50, if you had a budget of $10, which would you choose to maximise your utility? Good A of course as this would get 10 utils per $ as opposed to only 5 utils per dollar.
Given a choice between two goods both priced equally at $5, with the first unit of Good A yielding MU of 100 and the 2nd unit yielding 75, and the first good of Good B yielding MU of 50, and the 2nd unit if you had a budget of $10, which would you choose to maximise your utility? Cleary you would buy the first two units of Good A as they yield the most utility and stays within your budget.

Would you buy one good that yields 100 utils or 2 goods that each yield 75 utils? clearly tou would

We DO NOT CHOOSE TO CONSUME THE GOOD WITH THE HIGHEST MU, WE CHOOSE TO CONSUMER THE GOOD WITH THE HIGHEST MU PER $, WHY?

Let's look at this example:

- - - Imagine we have a budget of $10 what combination of goods will maximise your total utility?
      - Good A, $4, 60, 50, 40, 30
        Good B, $2, 55, 52, 49, 46, 43
        Now at first glance you may choose ABBB, yielding 60+55+52+49 = 216 utils, however this doesn't make sense as you could get more utils from consuming BBBBB which yields 245 utils, so it is important to work out MU PER DOLLAR, then make our selections
        Good A 15, 12.5, 10, 7.5
        Good B 27.5, 26, 24.5, 23, 21.5
        Clearly BBBBB is the best choice for a rational utility maximising consumer.

This example shows how a consumer chooses each item in turn until the utility is maximised and it is IMPOSSIBLE TO SWITCH TO OTHER GOODS in order to get any additional utility.
This conculsion is called the equimarginal principle and can be summarised using this equation:

We can see above that the MU per $ of good A was 60/4 = 15

In order to maximize utility (for a given fixed income) a consumer needs to consider each subsequent dollar that they spend, as they want to CHOOSE THE UNIT OF THE GOOD THAT GIVES THEM THE HIGHEST LEVEL OF MARGINAL UTILITY PER DOLLAR
In other words they need to to rank the level of satisfaction derived per dollar, from each additional unit of good they consume, so that they can compare and switch expenditure accordingly, choosing the unit of the good that yields the highest utils per dollar first and so on, until the total spend reaches the fixed income (budget).
Clearly as the goods are ranked the level of MU/$ of each good should eventually be the same (or close), meaning the following is true at maximum utility levels:
M
Only then can you see how many of each item will be purchased in order to maximise utility.
This will occu when
If we consider a consumer who only ever wants one good and the budget is $10, then
Obviously In other words when it is not possible to switch any expenditure from, say, product A to product B to increase total utility. This is referred to as the equimarginal principle and can be represented as:
In other words when the marginal utility per dollar per dollar of each good is the same then it isn't possible to switch between them to derive any more utils, and thus you are at maximum utility.

Once we work out the MU per $ for each unit we can start our selections up to our budget.

Selection 1: We choose our fisrt unit of Coke

Go to the sites below and read about the equimarginal principle, then use it to explain why

--HOW TO MAXIMISE UTILITY? [MULTIPLE GOODS]--

In reality a consumer does not just deal with a single good (with a single set of diminishing marginal utilities) nor a single price but a multitude. As such they will need to look at MU per $, rather than simply MU, to decide which goods to buy.
TWO GOODS, SAME PRICE:
- - - In this case, the consumer will simply rank the items in descending order of MU and choose accordingly until our budget constraint is reached
TWO GOODS, DIFFERENT PRICES:
- - - In this case, consumers can't simply rank them in descending order of MU as now we have different prices, as such it could be the case that a unit of a good derives double the MU than another good, but it is three times more expensive, meaning that they would gain more utility from buying three of these goods. Hence to incorporate different prices we need to use MU per $ spent.
    - Once we have ranked the units by this metric we an again start choosing the items in descending order until our budget constraint is reached.
    - Now this leads to an important principle related to demand, if the price rises the MU per $ obviously falls, making alternative goods more attractive in terms of MU per $ and this leading to the consumer 'switching away' and Qd falling (Law of demand).

So how do they maximise their utility?
When we go to supermarket to buy goods, ideally we want to maximise our total utility given our financial budget right? In other words we need to consider both the marginal utility along with the price of the good right? But how do we know when this occurs?
Well we can use the 'EQUI-MARGINAL PRINCIPLE', which states that TOTAL UTILITY WILL BE MAXIMISED WHEN THE MARGINAL UTILITY PER DOLLAR of EACH GOOD is EQUAL
WHY IS THIS THE CASE? Well, if all goods share the same MU then the next dollar you spend
Hower once we intriduce a budget then it is not always possible to maximise utility only maximise up to the budget.

basically says we should rank each item by its marginal utility per $, and then purchase as many goods as possible within our budget choosing the item with the highest MU per $ first and so on.
This will ultimately end with the
once the MU$ for good A is equal to the MU$ for good B, then the consumer will be indifferent and the TU can increase no more
, to lowest until the budget is reached.
Why MU PER $ and NOT MU?
Clearly
when will a consumer maximise their utility? How do we maximise our utility when there are so many goods at different prices to choose from?
Firstly its important to acknowledge that
Given a choice between two goods both priced equally at $10, with the first unit of Good A yielding MU of 100, and the first good of Good B yielding MU of 50, if you had a budget of $10, which would you choose to maximise your utility? Good A of course as this would get 10 utils per $ as opposed to only 5 utils per dollar.
Given a choice between two goods both priced equally at $5, with the first unit of Good A yielding MU of 100 and the 2nd unit yielding 75, and the first good of Good B yielding MU of 50, and the 2nd unit if you had a budget of $10, which would you choose to maximise your utility? Cleary you would buy the first two units of Good A as they yield the most utility and stays within your budget.

Would you buy one good that yields 100 utils or 2 goods that each yield 75 utils? clearly tou would

We DO NOT CHOOSE TO CONSUME THE GOOD WITH THE HIGHEST MU, WE CHOOSE TO CONSUMER THE GOOD WITH THE HIGHEST MU PER $, WHY?

Let's look at this example:

- - - Imagine we have a budget of $10 what combination of goods will maximise your total utility?
      - Good A, $4, 60, 50, 40, 30
        Good B, $2, 55, 52, 49, 46, 43
        Now at first glance you may choose ABBB, yielding 60+55+52+49 = 216 utils, however this doesn't make sense as you could get more utils from consuming BBBBB which yields 245 utils, so it is important to work out MU PER DOLLAR, then make our selections
        Good A 15, 12.5, 10, 7.5
        Good B 27.5, 26, 24.5, 23, 21.5
        Clearly BBBBB is the best choice for a rational utility maximising consumer.

This example shows how a consumer chooses each item in turn until the utility is maximised and it is IMPOSSIBLE TO SWITCH TO OTHER GOODS in order to get any additional utility.
This conculsion is called the equimarginal principle and can be summarised using this equation:

We can see above that the MU per $ of good A was 60/4 = 15

In order to maximize utility (for a given fixed income) a consumer needs to consider each subsequent dollar that they spend, as they want to CHOOSE THE UNIT OF THE GOOD THAT GIVES THEM THE HIGHEST LEVEL OF MARGINAL UTILITY PER DOLLAR
In other words they need to to rank the level of satisfaction derived per dollar, from each additional unit of good they consume, so that they can compare and switch expenditure accordingly, choosing the unit of the good that yields the highest utils per dollar first and so on, until the total spend reaches the fixed income (budget).
Clearly as the goods are ranked the level of MU/$ of each good should eventually be the same (or close), meaning the following is true at maximum utility levels:
M
Only then can you see how many of each item will be purchased in order to maximise utility.
This will occu when
If we consider a consumer who only ever wants one good and the budget is $10, then
Obviously In other words when it is not possible to switch any expenditure from, say, product A to product B to increase total utility. This is referred to as the equimarginal principle and can be represented as:
In other words when the marginal utility per dollar per dollar of each good is the same then it isn't possible to switch between them to derive any more utils, and thus you are at maximum utility.

Once we work out the MU per $ for each unit we can start our selections up to our budget.

Selection 1: We choose our fisrt unit of Coke

Go to the sites below and read about the equimarginal principle, then use it to explain why

--7.1.4 INDIVIDUAL DEMAND CURVE--

--7.1.4 DERIVATION OF AN INDIVIDUAL DEMAND CURVE--

It is possible to use marginal utility to derive an individual demand curve. Th e fundamental principle of demand is that an increase in the price of a good leads to a reduction in its demand. Using the above principle, this can now be proved. Th e value of the expression
As the price of A RISES, the marginal utility of A per dollar spent will now be LESS than on any other goods. The consumer will therefore increase total utility by spending less on good A and more on all other goods. Tis will in turn reduce the value of their marginal utility.
In other words, the consumer only maximises total utility by buying less of good A. Th e conclusion is that the demand curve for a good is downward sloping.

--7.1.5 LIMITS OF UTILITY THEORY--

--7.1.5 LIMITATIONS OF MARGINAL UTILITY THEORY AND ITS ASSUMPTIONS OF RATIONAL BEHAVIOUR--

Are consumers rational?

Th e law of diminishing marginal utility assumes that

consumers act and behave in a rational way in their

purchasing decisions. Th is is a big assumption to make.

Empirical evidence consistently shows that there are other

factors apart from just utility that determine what we

purchase. To understand the behavioural factors involved

requires ‘getting inside people’s heads’ to determine and

then model such psychological infl uences.

A few examples will show why consumers oft en act in

an irrational way.

■ In the case of special off ers such as ‘buy one get one free’.

Consumers may have no intention of buying the product

until they enter the shop. Seeing the off er produces an

impulsive cognitive response to buy.

■ Where payment can be deferred. This allows consumers to

purchase beyond their ability to pay outright at the time of

sale – they may use a credit card to obtain what they want.

■ Where a consumer is emotionally attached to a brand or

where there is a prejudice against a brand, so influencing

consumption.

Th is type of behaviour cannot be represented in a rational

economic model. Interestingly, if consumers were rational,

fi rms would have little need for marketing. Advertising that

is designed to infl uence consumer choice would appear to

be irrelevant. Behavioural economic models explore why

consumers make irrational decisions, against what might

have been predicted by conventional economic theory.

It is therefore useful to bear these points in mind when

evaluating the eff ectiveness of conventional economic

models like that of utility.

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