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The theory of consumer choice is the branch of microeconomics that relates preferences to consumption expenditures and to consumer demand curves. It analyzes how consumers maximize the desirability of their consumption as measured by their preferences subject to limitations on their expenditures, by maximizing utility subject to a consumer budget constraint.
Consumption is separated from production, logically, because two different economic agents are involved. In the first case consumption is by the primary individual; in the second case, a producer might make something that he would not consume himself. Therefore, different motivations and abilities are involved. The models that make up consumer theory are used to represent prospectively observable demand patterns for an individual buyer on the hypothesis of constrained optimization. Prominent variables used to explain the rate at which the good is purchased (demanded) are the price per unit of that good, prices of related goods, and wealth of the consumer.
The law of demand states that the rate of consumption falls as the price of the good rises, even when the consumer is monetarily compensated for the effect of the higher price; this is called the substitution effect. As the price of a good rises, consumers will substitute away from that good, choosing more of other alternatives. If no compensation for the price rise occurs, as is usual, then the decline in overall purchasing power due to the price rise leads, for most goods, to a further decline in the quantity demanded; this is called the income effect.
In addition, as the wealth of the individual rises, demand for most products increases, shifting the demand curve higher at all possible prices.
The basic problem of consumer theory takes the following inputs:
Consider an economy with two types of homogeneous divisible goods, traditionally called X and Y.
The consumer will choose the indifference curve with the highest utility that is attainable within his budget constraint. Every point on indifference curve I3 is outside his budget constraint so the best that he can do is the single point on I2 where the latter is tangent to his budget constraint. He will purchase X* of good X and Y* of good Y.
Indifference curve analysis begins with the utility function. The utility function is treated as an index of utility. All that is necessary is that the utility index change as more preferred bundles are consumed.
Indifference curves are typically numbered with the number increasing as more preferred bundles are consumed. The numbers have no cardinal significance; for example if three indifference curves are labeled 1, 4, and 16 respectively that means nothing more than the bundles "on" indifference curve 4 are more preferred than the bundles "on" indifference curve 1.
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.
As a second example, consider an economy which consists of a large land-estate L.
The indifference curves and budget constraint can be used to predict the effect of changes to the budget constraint. The graph below shows the effect of a price increase for good Y. If the price of Y increases, the budget constraint will pivot from BC2 to BC1. Notice that because the price of X does not change, the consumer can still buy the same amount of X if he or she chooses to buy only good X. On the other hand, if the consumer chooses to buy only good Y, he or she will be able to buy less of good Y because 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.
Another important item that can change is the money income of the consumer. The income effect is the phenomenon observed through changes in purchasing power. It reveals the change in quantity demanded brought by a change in real income. Graphically, as long as the prices remain constant, changing 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, as income increases, the amount purchased of a good can either increase, decrease or stay the same. 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.
is the change in the demand for good 1 when we change income from to , holding the price of good 1 fixed at :
Every price change can be decomposed into an income effect and a substitution effect; the price effect is the sum of substitution and income effects.
The substitution effect is the change in demands resulting from a price change that alters the slope of the budget constraint but leaves the consumer on the same indifference curve. In other words, it illustrates the consumer's new consumption basket after the price change while being compensated as to allow the consumer to be as happy as he or she was previously. By this effect, the consumer is posited to substitute toward the good that becomes comparatively less expensive. In the illustration below this corresponds to an imaginary budget constraint denoted SC being tangent to the indifference curve I1. Then the income effect from the rise in purchasing power from a price fall reinforces the substitution effect. If the good is an inferior good, then the income effect will offset in some degree the substitution effect. If the income effect for an inferior good is sufficiently strong, the consumer will buy less of the good when it becomes less expensive, a Giffen good (commonly believed to be a rarity).
The substitution effect, , is the change in the amount demanded for when the price of good falls from to (represented by the budget constraint shifting from BC1 to BC2 and thus increasing purchasing power) and, at the same time, the money income falls from to to keep the consumer at the same level of utility on :
The substitution effect increases the amount demanded of good from to in the diagram. In the example shown, the income effect of the fall in partly offsets the substitution effect as the amount demanded of in the absence of an offsetting income change ends up at thus the income effect from the rise in purchasing power due to the price drop is that the quantity demanded of goes from to . The total effect of the price drop on quantity demanded is the sum of the substitution effect and the income effect.
The behavioral assumption of the consumer theory proposed herein is that all consumers seek to maximize utility. In the mainstream economics tradition, this activity of maximizing utility has been deemed as the "rational" behavior of decision makers. More specifically, in the eyes of economists, all consumers seek to maximize a utility function subject to a budgetary constraint. In other words, economists assume that consumers will always choose the "best" bundle of goods they can afford. Consumer theory is therefore based on generating refutable hypotheses about the nature of consumer demand from this behavioral postulate.
In order to reason from the central postulate towards a useful model of consumer choice, it is necessary to make additional assumptions about the certain preferences that consumers employ when selecting their preferred "bundle" of goods. These are relatively strict, allowing for the model to generate more useful hypotheses with regard to consumer behaviour than weaker assumptions, which would allow any empirical data to be explained in terms of stupidity, ignorance, or some other factor, and hence would not be able to generate any predictions about future demand at all. For the most part, however, they represent statements which would only be contradicted if a consumer was acting in (what was widely regarded as) a strange manner. In this vein, the modern form of consumer choice theory assumes:
Note the assumptions do not guarantee that the demand curve will be negatively sloped. A positively sloped curve is not inconsistent with the assumptions.
In Marx's critique of political economy, any labor-product has a value and a use value, and if it is traded as a commodity in markets, it additionally has an exchange value, most often expressed as a money-price. Marx acknowledges that commodities being traded also have a general utility, implied by the fact that people want them, but he argues that this by itself tells us nothing about the specific character of the economy in which they are produced and sold.
One can also use consumer theory to analyze a consumer's choice between leisure and labor. Leisure is considered one good (often put on the horizontal axis) and consumption is considered the other good. Since a consumer has a finite amount of time, he must make a choice between leisure (which earns no income for consumption) and labor (which does earn income for consumption).
The previous model of consumer choice theory is applicable with only slight modifications. First, the total amount of time that an individual has to allocate is known as his "time endowment", and is often denoted as T. The amount an individual allocates to labor (denoted L) and leisure (ℓ) is constrained by T such that
A person's consumption is the amount of labor they choose multiplied by the amount they are paid per hour of labor (their wage, often denoted w). Thus, the amount that a person consumes is:
When a consumer chooses no leisure then and .
From this labor-leisure tradeoff model, the substitution effect and income effect from various changes caused by welfare benefits, labor taxation, or tax credits can be analyzed.