# Consumer theory

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Consumer theory is a theory of economics which helps to predict and illuminate consumer behaviour. It relates preferences, indifference curves and budget constraints to consumer demand curves. The mathematical models that make up consumer theory can be used in a constrained optimization problem to estimate the optimal goods bundle for an individual buyer.

## Indifference curves and budget constraints

Using indifference curves and an assumption of constant prices and a fixed income in a two good world will give the following diagram. The consumer can choose any point on or below the budget constraint line BC. This line is diagonal since it comes from the equation $xp_X + y p_Y \leq \mathrm{income}$. In other words, the amount spent on both goods together is less than or equal to the income of the consumer. The consumer will choose the indifference curve with the highest utility that is within the budget constraint. I3 has all the points outside of their budget constraint so the best that the consumer can do is I2. This will result in them purchasing X* of good X and Y* of good Y.

Income effect and price effect deal with how the change in price of a commodity changes the consumption of the good. The theory of consumer choice examines the trade-offs and decisions people make in their role as consumers as prices and their income changes.

## Price effects

These curves can be used to predict the effect of changes to the budget constraint. The graphic below shows the effect of a price shift for good y. If the price of Y increases, the budget constraint will shift from BC2 to BC1. Notice that since the price of X does not change, the consumer can still buy the same amount of X if they choose to buy only good X. On the other hand, if they choose to buy only good Y, they will be able to buy less of good Y since its price has increased.

To maximize the utility with the reduced budget constraint, BC1, the consumer will re-allocate consumption to reach the highest available indifference curve which BC1 is tangent to. As shown on the diagram below, that curve is I1, and therefore the amount of good Y bought will shift from Y2 to Y1, and the amount of good X bought to shift from X2 to X1. The opposite effect will occur if the price of Y decreases causing the shift from BC2 to BC3, and I2 to I3.

If these curves are plotted for many different prices of good Y, a demand curve for good Y can be constructed. The diagram below shows the demand curve for good Y as its price varies. Alternatively, if the price for good Y is fixed and the price for good X is varied, a demand curve for good X can be constructed.

## Income effect

Another important item that can change is the income of the consumer. As long as the prices remain constant, changing the income will create a parallel shift of the budget constraint. Increasing the income will shift the budget constraint right since more of both can be bought, and decreasing income will shift it left.

Depending on the indifference curves the amount of a good bought can either increase, decrease or stay the same when income increases. In the diagram below, good Y is a normal good since the amount purchased increased as the budget constraint shifted from BC1 to the higher income BC2. Good X is an inferior good since the amount bought decreased as the income increases.

## Substitution effect

Every price change can be decomposed into an income effect and a substitution effect. The substitution effect is a price change that changes the slope of the budget constraint, but leaves the consumer on the same indifference curve. This effect will always cause the consumer to substitute away from the good that is becoming comparatively more expensive. If the good in question is a normal good, then the income effect will re-enforce the substitution effect. If the good is inferior, then the income effect will lessen the substitution effect. If the income effect is opposite and stronger than the substitution effect, the consumer will buy more of the good when it becomes more expensive. An example of this might be a Giffen good.