Economic explanation - Theory

Clauric

Hi,

I am trying to work out Utility Maximization. This is what our lecturer gave us, but gave little explanation. I am looking for a reasonably simplistic explanation of the following:

•Preferences:- We shall represent preferences using the utility function

U = U f(x,y) where x and y are two goods.

•Indifference Curves:- Represents a series of points which all have the same utility.

U = U f(x1,y1)
[IMG]file:///C:/DOCUME%7E1/Mark_J/LOCALS%7E1/Temp/moz-screenshot.png[/IMG]

•Properties of Indifference Curves include

- they slope downwards

- smooth

- continuous

- convex (e.g. curves towards the origin)

•Budget Constraint

•Can only afford to buy limited amounts of goods

- represents affordable combinations using budget constraint

- position depends upon ratio of good prices and income

•Utility maximisation .

•Maximise utility subject to budget constraint.

•Most north-easterly indifference curve possible.

•This is the point of tangency between the indifference curve and the budget constraint.

•Efficient Budget Allocation

•Marginal utility

- MUx

- increase in utility from one more unit of good x

•The slope of the indifference curve

= - MUx /MUy

•Efficient Budget Allocation II

•The slope of the budget constraint equals

- (minus) Px /Py

•Efficient allocation of resources occurs where

- (minus) MUx /Px = MUy /Py

•Equalise marginal utility per Euro spent.

Anonymous1987

What exactly are you having trouble with? If all of it, then start by asking one question at a time. It also might be useful if say what level is your course i.e. first, second... etc

In a nutshell you are trying to maximise your satisfaction (i.e. utility) with a basket of goods (e.g. apples and oranges) subject to your preferences (how much do like apples and oranges) and a budget constraint (how much money you have in your wallet to spend on apples and oranges). The point where you get the most utility will be the point where the curve which represents you preferences (i.e the indifference curve) touches the budget constraint. At this point you will have maximised your utility subject to your preferences and the budget constraint, it not beneficial for you to substitute one good for another as there is no marginal benefit from doing so subject to your both budget and preferences constraints.



The straight line above is the budget constraint.
The curves are called indifference curves and represent your preferences for different combinations or baskets of the two goods. You would be happy with any of these (hence indifferent curves) although the budget constraint means only one will maximise your utility. The curve below the budget constraint does not spend all your money and the one above it spends more than you have in your wallet hence the optimal one is where the indifference curve touches the budget constraint.

gerry87

Clauric wrote: »

Hi,

I am trying to work out Utility Maximization. This is what our lecturer gave us, but gave little explanation. I am looking for a reasonably simplistic explanation of the following:

•Preferences:- We shall represent preferences using the utility function

U = U f(x,y) where x and y are two goods.

•Indifference Curves:- Represents a series of points which all have the same utility.

U = U f(x1,y1)
[IMG]file:///C:/DOCUME%7E1/Mark_J/LOCALS%7E1/Temp/moz-screenshot.png[/IMG]

•Properties of Indifference Curves include

- they slope downwards

- smooth

- continuous

- convex (e.g. curves towards the origin)

•Budget Constraint

•Can only afford to buy limited amounts of goods

- represents affordable combinations using budget constraint

- position depends upon ratio of good prices and income

•Utility maximisation .

•Maximise utility subject to budget constraint.

•Most north-easterly indifference curve possible.

•This is the point of tangency between the indifference curve and the budget constraint.

•Efficient Budget Allocation

•Marginal utility

- MUx

- increase in utility from one more unit of good x

•The slope of the indifference curve

= - MUx /MUy

•Efficient Budget Allocation II

•The slope of the budget constraint equals

- (minus) Px /Py

•Efficient allocation of resources occurs where

- (minus) MUx /Px = MUy /Py

•Equalise marginal utility per Euro spent.

To save someone typing out an entire chunk of your course, what specific bits are you having trouble understanding?
- Do you get how the budget line works?
- Do you understand what the indifference curves are and how they function?
- Do you know how the budget and indifference curve relate to each other to give an answer?

Budget

The basics are you have a given amount of money and two goods you can buy with this money. You can spend all of your money on good x good y or a mix of the two, but you will spend all your money.

The prices of good x and y are px and py respectively. The amount of good x and y you buy is just denoted x and y respectively. So you could buy 10 units of good x, then x=10.

Say you have an amount of money M. You are going to pick an amount of x and y to make the following equation true: (px and py are given, you only choose x and y)

px*x + py*y = M

Thats your budget constraint.

Indifference Curves

I didn't really 'get' indifference curves until they were explained to me like this, but if i'm just confusing things then ignore. The curve shows you the amount of one good you would give up to get one more unit of the other good.

Indifference curves are actually full circles, in this case you're just taking the bottom left quadrant of the circle because both goods are desirable. Say you took the top left quadrant, then because of the shape of the curve you would as you increase the amount of one good, you increase the amount of the 2nd, so that would be the case if one good was desirable and one was undesirable.

Now imagine a smaller circle inside the previous circle, at every point on this circle you're at a better situation than on the bigger circle. When both goods are desirable you have more of each, when both are undesirable you have less of each and so on. So these circles get smaller and smaller until there's a point in the middle - this is called the Bliss Point where everything is perfect.

In your questions you only need the bottom left quadrant, so to move to a better indifference curve, you want to be on the bottom left quadrant of a smaller circle inside the current circle.

See and too see what i'm talking about .

Your indifference curves are given by a function U = f(x,y)

Combined

Now plot your indifference curves as above using U=f(x,y) and your budget constraint using px*x + py*y = M


Wherever the budget line touches any of the indifference curves only once, (i.e. is a tangent) then that's your best indifference curve. And the point that it touches is your best mix of good x and good y.

I won't go through the maths of it as I assume you'll be going through that in your course at some stage, but you do it using the lagrangian method, see here for a worked example.

Clauric

Thank you for the explanations. They make far more sense than what we were given.

Much appreciated.