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### Course: Microeconomics>Unit 5

Lesson 3: Utility maximization with indifference curves

# Indifference curves and marginal rate of substitution

We can graph how we value tradeoffs between two goods. Created by Sal Khan.

## Want to join the conversation?

• Are Opportunity cost and Rate of substitution same ?
• Opportunity cost is the cost of the next best alternative given up or sacrificed.
The Marginal Rate of Substitution is the amount of of a good that has to be given up to obtain an additional unit of another good while keeping the satisfaction the same. As some amount of a good has to be sacrificed for an additional unit of another good it is the Opportunity Cost.
The MRS is basically a way of mathematically representing the opportunity cost of getting an additional unit of some good.
The MRS only gives the opportunity cost of getting a additional unit of a good.
Opportunity cost itself is a wider concept like if a person has a choice of either being a farmer or a shopkeeper and the person becomes a farmer then the opportunity cost is the chance of being a shopkeeper.
• what is difference between marginal rate of exchange and marginal rate of substitution?
• MRS describes a substitution between two goods. MRS changes from person to person, as it depends on an individual's subjective preferences.

Marginal Rate of Exchange, on the other hand, describes the price ratio of two goods relative to each other. It does not depend on an individual preference, but is determined by the market, hence the same MRE applies to everyone.
• Why two Indifference curves cannot intersect each other?
• Each curve represents a set of combinations of goods that give a specific level of utility. Different curves, different levels of utility. If two curves intersected, the intersection point would represent a combination of goods with two different levels of utility --> impossible.
• Don't the theories of diminishing marginal utility and monotonic preferences go against each other, in a sense? I mean, if a consumer keeps on consuming more and more of a particular good, then by law of DMU, he'll stop after a while, but according to monotonic preferences, he'll keep on and on consuming.
• No - diminishing marginal utility only means that the utility from the good decreases, not that it hits zero (which would be required for an unconstrained consumer to stop consuming that good).

Consumption will only stop if marginal utility falls to (or below) zero, but that would violate monotonicity.

If the utility function u(x) is monotonic, then u'(x) is always positive even though u''(x) is negative - that's the 'non-satiety axiom'. So u(x) is increasing in x, but at a decreasing rate.
• What is an example of a third axis that could be used for a graph like this?
• Imagine that you could buy not only fruit and chocolate, but also bread. In that case you have 3 variables to choose from
• Can a indifference curve intersect the x or y axis ?
• Yes, it can. There is actually an indifference curve in every single point in this coordinate system. This is just not so important, we are interested in the indifference curve which gives the highest utility.
• Can indifference be area not curve?
• No. It has to be a line (consisting of points), otherwise it violates the principle of monotonicity (more is better), since you'd be saying you are indifferent between two bundles even though one bundle has more of both goods.
• Does it matter where you put f or c. Do you have to put the fruit on the x axis. Thanks.