Theory of Consumer Behavior - Topics of Importance

Elasticity

Price elasticity of demand is a measure of the responsiveness of demand to changes in price. If price goes up, for example, we know that quantity demanded will normally go down. The issue here is, by how much. In order to measure the responsiveness of demand to price changes, we need to use a method which can be applied to all products, and which will allow a comparison of responsiveness among products. The method chosen compares percentage changes in quantity demanded for a given percentage change in price. Elasticity, then, is the percentage change in quantity demanded divided by the percentage change in price. In algebraic terms, this is:

%D Q/%D P

Where
% = percent
D = Change in
Q = quantity demanded
P = price

If the change in percentage change in quantity exceeds the percentage change in price, the product is said to be elastic. If the percent change in quantity is less than the percent change in price, the product is inelastic. If the ration equals 1, then the product is unit elastic.

In other words:

If elasticity > 1, the product is elastic

If elasticity = 1, the product is unit elastic

If elasticity < 1, the product is inelastic.

Elastic goods are those that we're willing to significantly vary our consumption of with changes in price -- luxury goods would be an example.
Inelastic goods are those we tend to buy in fixed amounts more or less regardless of price - necessities are typically cited as examples.
If you put a tax on an inelastic good, you will raise revenue and not affect consumption much.
If you tax an elastic good, you won't raise much revenue, but consumption will decline significantly.

Consumer Behavior

Maximization of Utility

Economics assumes that consumers attempt to maximize their utility (material well being) subject to their limited incomes. The process of maximization is analyzed using differential calculus. This method simply looks at how much each successive step adds to utility - hence our focus on "marginal" utility. The method we use focuses on the next, or "marginal" act of consumption. Maximization assumes that we're trying to reach the "highest value" we can achieve. One analogy is trying to reach the highest point on a hill. The "calculus" method of doing this is precisely like putting on a blindfold and seeing if one could find the highest point. Clearly, this would be done by taking tentative, small steps and choosing those steps that took one upward. When you got to the point where no step took you upward, you could safely conclude that you've reached to top of the hill - or maximized you height. Maximization of utility is examined in just the same way: we look at the utility contribution of the next act of consumption - the "marginal" utility.
 
 

Diminishing Marginal Utility

In order to be maximizable, utility has to increase, reach a maximum and then decline. For this to happen, the additional utility provided by successive units of products consumed has to fall. If each additional unit consumed provided the same additional (marginal) utility as the last, there would be no utility maximum. If you could get an infinite supply of the product you most enjoy, you could get an infinite amount of utility simply by consuming an infinite amount it. In such a world, everyone would spend their entire income on their favorite product of service, and would purchase nothing else. Obviously, then, marginal utility does decline or diminish beyond some level of consumption. This is called diminishing marginal utility; a proposition which states that 'at some level of consumption of a given good, further units consumed will add smaller and smaller increments of utility".

Diminishing Marginal Utility and the Demand Curve

While we can't argue that a demand curve is a marginal utility curve, it does show properties that reflect diminishing marginal utility.
 

When prices are high (P1), people tend buy less (Q1) because only the first few items consumed can offer enough marginal utility to offset the high price (sacrifice) being paid to have them. When the price is lower (P2) people tend to consume more because, given the low sacrifice (price) necessary to get the product, a large number (Q2) can be consumed before diminishing marginal utility lowers the enjoyment derived from the last unit consumed to the (low) price level.
 
 

Utility Maximization Subject to an Income Constraint

In an unconstrained maximization (like the example of getting to the top of the hill) we know we're at the maximum when no "step" takes us any higher; or in other words, when the "marginal height gain" is zero. Similarly, we would reach an absolute, unconstrained utility maximization when marginal utility is zero for all products. When an additional unit of any product contributes nothing to our utility, our utility is fully maximized. We never get to do this, however.

To get to an absolute utility maximum, we'd need an incredible amount of money. Few have it. Most of us simply have to get by with the incomes we have. We can't get to the "top of the hill", rather we have to go as far up it as we can.

Since income is our constraint, we want to get as much utility per penny of income as we can. I we didn't have diminishing marginal utility, the process would be simple: we'd just buy what gave us the most utility and spend all our income on it. Since marginal utility does diminish, we find that after consuming a bit of the product that gave us the most utility per penny, we find marginal utility for that product diminishing. Eventually, some other product will look more attracting in terms of utility per penny and we'll start buying that one. Gradually marginal utility will diminish for that product so that yet another looks more attractive. This process will continue until we've exhausted our incomes. It follows that when we've reached a maximum, there can be no redistribution of spending that gives us a higher level of utility. This can only be the case where the marginal utility per penny derived from each product is the same. If the marginal utility per penny of any product differs from the others, then some readjustment of purchases will get us a higher level of utility. For example, if we have two products which give us 5 utils per penny for Product A and 3 utils per penny for Product B. Clearly we should give up a penny's worth of Product B and buy a penny more of Produce A. We lose 3 utils by giving up B, but we pick up 5 utils by buying A for a net gain of 2 utils. Having given up B will increase its marginal utility, lest say from 3 utils to 4 utils per penny. Buying more A will lower its marginal utility, say from 5 utils per penny to 4. Now, both products give us 4 utils per penny, and no reshuffling will get us more utility.

Thus, at utility maximum:

MU1   =    MU2    =   MU3   = ..................................................=MUn
  P1             P2             P3                                                             Pn

The marginal utilities per penny (MU/P) for all of the "n" products we consume shall be the same when utility has been maximized.
 
 

Indifference Curves

One way of examining the process of utility maximization is through indifference curve analysis. Indifference curves are lines that map out a constant height on the utility surface shown in the graph below.
 
 
 
 

The utility surface, above, measures the utility associated with every possible combination of Products "A" and "B". The consumer's goal is to get as high as possible on the utility surface subject to his limited income. The limited income is shown by the straight line running from the Product B axis to the Product A axis. The intersection of the line with the Product B axis is determined by dividing income by the price of Product B. Similarly the intersection with the Product A axis is determined by dividing income by the price of Product A. Connecting these two intersection points with a straight line locates the total set of possible "A" "B" combinations. The consumer is allowed any combination of A and B that lies on or to the left of the straight line (Budget Line or Income Constraint), but he is not allowed any combination to the right of the budget line.

It is difficult to clearly see how the consumer maximized his income using the 3 dimensional approach, above. To make things clearer, we will convert the graph above to two dimensions.
 
 
 
 
 

The curved lines in the graph above are "indifference curves". They trace out a locus of points of equal height on the utility surface, and since they are of equal height (equal utility) we are indifferent as to where we are along the curve. Our objective is to get to the highest indifference curve we can. The Budget Line (Y - Y) traces out the range of combinations of A and B that we can achieve. We will want to choose combinations the lie on the Budget Line since doing so get us to the highest set of indifference curves possible. The optimal point (the highest curve reachable) is at the tangency of the Budget Line and an indifference curve. A tangency is the point at which the straight Budget Line just touches and indifference curve. At the point of tangency, the slopes of the Budget Line and the indifference curve are the same. Since the slope of the Budget Line is equal to Pb/Pa (P = price), and the slope of the indifference curve is equal to Mub/Mua (MU = marginal utility), we know that:
 

since MUb = Pb Then MUa * MUb = MUa * Pb  and MUb * 1  =  MUa Pb * 1  Then
          MUa   Pa                        MUa               Pa                      Pb        Pa          Pb
 

 MUa = MUb
  Pa            Pb

 Which is to say that, at a utility maximum, the marginal utility per penny for each product consumed is the same - the same postulate as the one stated above.