MANAGERIAL ECONOMICS
If the price a consumer is willing to pay for an additional unit of a good increases initially as function of amount then the maximum price pmax he is willing to pay is more than the price he would be willing to pay for the first unit. At this price pmax there is a non-zero amount A for which the consumer surplus is zero; at this price and amount the negative consumer surplus for the first units is compensated by the more attractive later units, for each of which the consumer would be willing to pay more than pmax. At this amount the price he is willing to pay for an additional unit has decreased back to pmax. If the price is lower than pmax the consumer will buy more. Thus he buys either nothing or at least A. In this case the individual demand curve has a discontinuity, where, after decreasing with price as usual, the demand jumps to zero. At this price he is indifferent between buying this minimum amount and buying nothing (spending the money on something else). Geometrically pmax is the slope of the steepest line through the origin and another point of the graph of the total price the consumer is willing to pay as function of amount. In the case of a smooth function this line is tangent to the graph. If the price a consumer is willing to pay for an additional unit of a good goes up and down more often, then the demand curve has more discontinuities, each associated with a line through two points of the graph of the total price the consumer is willing to pay as function of amount, with no part of the graph above the line.
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