Economists have worked out a theory of the consumer which appears to be a general theory explaining what people buy. In actuality explaining the the behavior of any specific individual would be too complex a problem and probably require a psychological approach. But economics is not concerned with explaining the behavior of any specific consumer; instead it is concerned with explaining the behavior of markets. In order to explain the behavior of a typical consumer in a market it is not necessary to have a completely realistic and detailed model of consumers. All that is required is a model that captures the market-relevant influences of the average and allows the individual differences to aveage out.
The economic model of the consumer was originally formulated in terms of the concept of a utility function and that formulation is still valid. Unfortunately the concept of utility has some puzzles for beginning students of economics. The problems are about how utility is measured and what are its units. If there are two goods whose quantities of consumption are x and y then a utility function would have the form U(x,y). But any always increasing function of U, say f(U(x,y)) would an equally valid utility function.
For beginning students in economics it is better to replace the concept of utility with the notion of benefit. The benefit function B(x,y) is the amount of income a person would consider equivalent to the consumption bundle (x,y); i.e., x units of good X and y units of good Y. A consumption bundle (x,y) has a benefit B is when a person is given the choice of the bundle (x,y) or some amount of income less than B that person will choose the bundle but if the amount of income is more than B that person will take the income. For a choice of (x,y) or B the person is indifferent, one being consider just as good but no better than the other.
Now suppose the level of y is held fixed at y0 and B is plotted as a function of x as the diagram below.
If the price of the good X is px then the cost of consuming an amount x is pxx. This is plotted in the above diagram as the cost. The net benefit of consuming an amount x is the difference between the B(x,y0) and the cost pxx. The net benefit is shown in the diagram above in red. A consumer wants to get the greatest net benefit; i.e., the consumer would choose a level of consumption of x such that the net benefit is a maximum. Note that when the net benefit is a maximum the slope of the net benefit curve is zero. This means that at the level of x where net benefit is a maximum the increase in benefit from another unit of X is exactly equal to the increase in cost of consuming another unit of X.
The increase in cost for consuming another unit of X is just the price of a unit of X. The increase in benefit can be computed from the benefit function. It is called the marginal benefit of another unit of X. The marginal benefit usually goes down; i.e. the more X someone is already consuming the less valuable another unit of X is to the consumer.
The marginal benefit curve for an individual is important because it determines how much that individual would purchase of the good at any price. For any price a horizontal line is drawn in the graph at that level. Where the price line intersects the marginal benefit curve gives the quantity which would be demanded at that price. If the price and quantity data are plotted in a different graph to construct the demand schedule for the individual one finds that the marginal benefit curve is just being replotted. In other words,
The demand curve is exactly the same as the marginal benefit curve. The downward sloping of the demand curve is just the diminishing marginal benefit of the increasing consumption of the good.
While the above tells us that if we know the marginal benefit curve then we can construct the demand curve, the significance of the result is that if know the demand curve then we have the marginal benefit curve.
From mathematics it is known that the change in some quantity, say benefit, over some interval is equal to the area under the marginal curve, in this case the marginal benefit curve, over that same interval. (This is known as the Fundament Theorem of Calculus.) Therefore if we want to know the benefit consumers get from increasing their consumption of a good from x1 to x2 we just need to find the area under the demand curve from x1 to x2.
Furthermore if we want to know the total benefit consumers get from consuming an amount x1 of a good we just need to find the area under the demand curve for that good from 0 to x1. This is the total or gross benefit. The net benefit to consumers of being able to purchase the good at price p1 is the gross benefit they get from the amount x1, which is the amount they are willing to purchase when the price is p1 less the amount they have to pay for that amount of the good; i.e., p1x1. In terms of a graph the gross benefit consumer get is the area under the demand curve from 0 to x1 and the cost of that consumption is the area of the rectangle with height p1 and width x1. The net benefit is the area between the demand curve and the price line over the interval from 0 up to the quantity consumed. This net benefit is usually called consumer surplus. It is the surplus benefit consumers get above the cost of the consumption.
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