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Demand Theory – Consumer Choice Problem

Normal, Inferior, Neutral, Luxury, Necessary Goods

There are three fundamental questions about a consumer’s consumption response:

1. How will demand change for a good i change in response to a increase or decrease in the price of i?
2. How will demand for good i change in response to an increase or decrease in M (fixed income)?
3. How will demand for good i change in response to increase or decrease in the price of good j?

By altering the value of the exogenous variables of the demand function we can compare the solutions to the utility maximizing problem before and after the change.

With the formula for max. utility in mind, let’s look at some changes in consumer behaviour graphically.

1. Consumption responses to a chance in M (fixed income).

The assumed goal for consumers is to reach the highest attainable indifference curve (or the highest utility) subject to their budget constraint. In an formulaic expression:

maxquad Uleft( { x }_{ 1 },...{ x }_{ n } right) quad subjectquad toquad sum _{ i=1 }^{ n }{  } { P }_{ i }{ x }_{ i }quad le quad M

Keep in mind these assumptions: non-satiation still holds true (that more is better); to reach maximum utility the individual spends all their money (a point on the budget line).

consumer choice graph

In this graph the desired is point B (IC that reside on the budget line).

Note: Consumers choose a particular X (endogenous); prices and income are exogenous.

The solution to the consumer choice problem is to find the optimal utility maximizing set of quantities in a bundle.

consumer choice graph

The variables are determined by: 1) preferences (utility function), 2) prices, 3) income

Therefore endogenous variable, xi is some function of exogenous variable. We know can create a demand function….

demand function

Which will lead us to the next instalment, a discussion on the Cobb Douglas demand function.

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