Utility maximisation

Question 1

What can economists explain about what we want?

Answer 1

Economists can explain not just what you demand, but also the quantities you demand, which is where the demand curve comes in.

Question 2

Why must people make choices?

Answer 2

People must make choices because their means of satisfying their wants are limited.

You never have enough money or time to do everything you desire.

Consequently, you need to choose wisely to get the most happiness of the limited resources that you do have.

Question 3

What are constrained optimisation problems?

Answer 3

When people are trying to optimise their happiness given the fact that they’re constrained by their limited resources.

Question 4

Describe utility.

Answer 4

Economists imagine that people assign a common measure of happiness to each possible thing they buy and use.

Economists imagine that if they were able to get inside your head and measure utility, they’d do so using a unit called a util.

Question 5

Some people very naturally object to assgning specific numbers of utils to a different thing. What philosopher came up with this scheme and what is this called?

Answer 5

(Although the philosopher Jeremy Bentham came up with a scheme for doing just this) Making such specific assignments is called cardinal utility (like the cardinal numbers: 1, 2, 3..)

Question 6

Why do people object to cardinal utility?

Answer 6

The objections to cardinal utility centre on doubts about whether people even make such assessments - after all, how many utils do you think you receive from a sunny day or a baby’s smile?

Question 7

What is a much less objectionable verson of cardinal utility?

Answer 7

Ordinal utility is a system in which you simply rank things.

Ex. rather than saying a sunset (75 utils) is better than a brownie (25 utils) you simply say that sunsets are prefferred to brownies.

Question 8

What are the benefits of ordinal utility?

Answer 8

This system has a much more intuitive feeling for most people and eliminates the need to try to measure things using the imaginary unit called the util.

Also, it’s been mathematically proven that you can describe the same human choice behaviour using ordinal utility that you can using cardinal utility (so economists don’t have to use cardinal utility).

Question 9

So why then, do some economists use Cardinal utility?

Answer 9

Because its a much easier way to explain the concept of diminishing marginal utility.

You can also explain diminishing marginal utility using the ordinal sytem, but the maths is much more complex.

Question 10

What happens to total utility as you eat more and more pizza?

Answer 10

First slice - total utility increases by 20 utils, from 0 to 20.

Second slice - the increase is only 16 utils; total utility increases from 20 utils to 36 utils.

Third slice - total utility increases only 14 utils, from 36 to 50.

Question 11

Graphically depict the marginal utility derived from each slice of pizza?

Answer 11

The downward slope of the points shows that the marginal utility diminishes as one eats mare and more slices of pizza.

Question 12

From the graph, why does the diminishing marginal utility for all slices of pizza start with the second slice?

Answer 12

Because each successive slice has a smaller utility tha the previous one.

But the marginal utilities are still positive up until the 7th slice, abd become negative for slices 9 and 10.

Question 13

How can marginal utility be diminishing but still positive?

Answer 13

You enjoy eating every slice up until and including the 7th because doing so brings you an increase in utility (happiness).

So don’ think that just because marginal utility is diminishing for a particular slice, you don’t want to eat it. Marginal utility be diminishing but still positive.

Question 14

Why is your preference for chocolate or vanilla icecream depending on what you’ve already eaten?

Answer 14

If you haven’t had any icecream in months and you’re asked whether you’d like choc or vanilla, you may choose choc. But if you’re asked whether you’d like choc or van after you’ve just eaten a tub of choc you’re probably going to say vanilla because you’ve satisfied your choc craving.

Question 15

Describe the marginal utility example in a student bar.

Answer 15

• You have a tenner to spend, and in the student bar there are only two things money can buy: pizza slices and beer.
• The intelligent way to best spend your tenner is to think in terms of buying uop as much utility as you can with your limited budget.
• Both beer and pizza make you happy, but your goal isn’t just to be happy; you wan to be as happy as possible given your likited budget.
• So you wanrt to make sure that every pound buys you the max possible amount of utility.

Question 16

What is the key concept of the marginal utility example from the student bar?

Answer 16

Keep in mind that you don’t care where utility comes from. One util from beer makes you just as happy as one util from pizza.

The key concept turns out to be the price of utility.

Question 17

What is the price of a util?

Answer 17

It depends.

The last two columns calculates how much it costs to get some additional happiness (marginal utility) if buying slices of pizza is the way you’re getting it.

Question 18

If pizza costs £2 per slice, why does each pound spent bring you less marginal utility than when the pizza cost only £1 per slice?

Answer 18

Ex. because pizza now costs £2 per slice, when you buy the first slice and it brings you 20 utils, you’re getting only 10 utils per pound spent.

Question 19

Why should you not spend all your tenner on just beer or just pizza?

Answer 19

If you spent it all on pizza = 60 utils

If you spent it just on beer = 80 utils (so you should clearly spend all of it on beer, right?0

Wrong, you can get even more utiltiy if you wisely mix up your consumption a bit and spend some of your money on beer and some on pizza.

Question 20

How should you spend pound 1?

Answer 20

Pound 1: pizza = 20 utils

Pound 1: beer (along with a second pound because pints cost £2) = only 10 utils

So the obvius thing to do is spend the first pound on pizza rather then beer.

Question 21

How should you spend pound 2?

Answer 21

Pound 2: Pizza = 16 utils

Pound 2: Beer (along with a THIRD £ because beer costs £2 per pint)= only 10 utils.

So once again, the obvious thing to do is spend the second pound on pizza. This is the same for Pound 3.

Question 22

How should you spend pound 4 and 5?

Answer 22

At pound 4 everything changes.

Pound 4: Pizza = 8 utils

or

Pound 4: Beer (along with a fifth pound) you get a MU per pound of 10 utils.

So you should spend pound 4 and 5 on beer.

This is the same for pounds 6 and 7.

Question 23

How shoud you spend pounds 8, 9 and 10?

Answer 23

For pound 8 the MU’s per pound are tied.

If you use this to buy a fourth slice of pizza you get 8 utils which is the same you get for buying a third pint.

So, what you should do is spend your last three pounds on buying a 4th slice of pizza and a 3rd pint of beer.

In the end, the total utility that you can purchase with your tenner is now 112 utils (way more than 60 for just pizza or 80 for just pints).

Question 24

If you only have two goods or services to choose from, what is the formula that is used to help you decide how to best spend your budget?

Answer 24

MUx / P_x = MU_y / P_y

P_x is pounds for each unit of X and vice versa.

Question 25

What does this formula, MUx / Px = MUy / Py, mean?

Answer 25

It means that if a person has allocated their limited budget optimally between the two goods, the MU per pounds of X and Y are equal at the optimal quantities of X and Y.

Question 26

Why must marginal utilities per pound have to be equal if you want to maximise your utiltity when spending a limited budget?

Answer 26

If marginal utilities per pound aren’t equal, you want to keep rearranging your purchases until they are.

Question 27

Give an example of MU per pound being UNEQUAL.

Answer 27

Imagine you choose some other q of each good, so that for the final unit of X and the final unit of Y you purchase:

MU_x / P_x > MU_y / P_y.

Say Pizza = X and beer = Y.

If you purchase 4 pints and 2 slices of pizza, the MU per pound for the 4th pint is 7 utils, while the NU per pound of pizza is much bigger than the MU per pound of beer if you spend your limited budget in this way.

Question 28

Why is this kind of spending not optimal?

Answer 28

because the money you’re spending on what is currently the final unit of X (pizza) buys more marginal utility than the money you’re currently spending on the final unit of Y (beer).

If you can get more utility by spending a pound on X than you can on Y, take money away from spending on Y in order to spend it on X.

Question 29

Give a real world example of how we never see perfect inflation in which the prices of all goods and services go up by exactly the same amount at exactly the same time?

Answer 29

• Instead, prices of different goods and services go up at different rates, so the fractions in our MU equations are thrown completely out of whack because their denominators change at different rates.
• When this happens, people start drastically changing their quantities demanded in an attempt to re-establish equality between all their marginal utilities per pound
• as they do this, chaos results, some firms find demand suddenly falling for their products, others find it suddenly rising.
• So don’t all MU equations trick you into thinking that inflation doesn’t matter in the real world. It does.

Question 30

How can our MU equation be generalised to apply to many goods?

Answer 30

Ex. In the case of three goods you arrange your buying so that for the last unit of each of the 3 goods X, Y and Z:

MU_X / P_X = MU_Y / P_Y = MU_Z/P_Z

Once again, if any of the three goods has a higher MU per pound than the others, you rearrange your purchases to buy less of the others and more of that good. You keep rearranging until the above equation holds true.

Question 31

Why can’t you look at each good in isolation?

Answer 31

How much of it you want to buy depends not only on its price, but also on the prices of everything else and how their marginal utilities vary as you buy more or less of them.

Question 32

If pizza increases to £2 per slice rather than £1, how might this price change affect the quantity demanded of both pizza and beer?

Answer 32

Doubling the price of pizza means that the MU per pound spent on each slice of pizza is exactly half of what it was before - naturally this affects where you spend your limited budget of £10.

Higher price of pizza = you eat less pizza and drink more beer.

You can now only afford 2 slices of pizza and 3 pints.

Question 33

What would happen if the price of pizza rose even further?

Answer 33

You’d reallocate so that you’d only buy one slice of pizza and four pints of beer.

At £3 per slice, you’d be completely out of the pizza market altogether, as the utility gained from spending all £10 on 5 pints of beer would be higher than the utility gained from consuming any pizza.

Question 34

Describe the substitution effect.

Answer 34

When you substitute towards the cheaper good to get yourself as much utility as possible.

i.e. as the price of one goes up and you get less utility per pound from buying it, you’ll substitute towards the good that gives you more utility per pound spent.

Question 35

Using an example, describe the income effect.

Answer 35

The increase in the price of pizza has also made you poorer in the only sense that really matters: you’re less happy.

Due to the price increase, the total no. of utils that you can buy with your tenner has fallen from 112 utils to only 90.

Despite rearranging your quantities consumed of beer and pizza to make the most of the new situation, the price increase still hurts you overall. This is what’s called the income effect.

Question 36

What is the difference between croos-price effects and own-price effects?

Answer 36

Cross price effects: where changes in thee price of one good affect the qunatity demanded of another good.

Own price effects: where changes in a good’s own price affects its quantity demanded.

Note - whereas cross price effects cause the d curve to shift, own price effects cause movements along the d curves.

Question 37

What are complementary goods?

Answer 37

Goods which complement eachother.

I.e. Fish and chips, sausages and ketchup, shoes and shoelaces.

In each of these pairs, the goods in question are more useful or more pleasing when consumed with the other member of the pair.

Question 38

What is interesting about complementary goods?

Answer 38

Changes in th price of one complement affect the other complement.

Ex. the price of petrol you put in your car affects the demand for cars; if the p of petrol increases, fewer cars are sold.

Question 39

What are substitue goods?

Answer 39

These are goods that serve similar functions so that if the p of one goes up, people switch to the other one.

Ex. If the price of train travel goes up, more people drive cars. If the cost of mail increases, more people use email.

Question 40

Why is it important to think of the economy as one great big organic whole?

Answer 40

Because things don’t happen in isolation. When the price of one good changes, it doesn’t affect just that good, but also many other goods.

And if the prices of the substitutes or complements change too, as a result of the initial price change, all their substitues and complements are also affected, like a gigantic ripple effect.